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satify

ˈsatify, v. Chiefly Sc. Also 5 satefy, 6 satyfy, satifie. [a. OF. satifier, satefier, var. of satisfier: see satisfy.] trans. = satisfy. Still locally used in Scotland, in the form settifee.c 1475 Partenay 1917 Hit is gret reson ye were satefied Off your ful good will don And applied. 1513 Douglas æ... Oxford English Dictionary

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satefy

satefy variant of satify v. Obs. Oxford English Dictionary

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Shin-hanga

To satify foreign collectors, colors became brighter and more saturated. wikipedia.org

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Does a local minimum of a function always satify the Armijo rule Does a local minimum of a function always satify the Armijo rule?

Assuming that the function $f$ is continuous (and so $\nabla f$ is defined), then the Armijo rule can't be satisfied as an equality for a **_global_** minimum. That is you can rewrite the rule as: $$f(\mathbf{x}_k+\alpha_k\mathbf{p}_k)\leq f(\mathbf{x}_k)+c_1\alpha_k\mathbf{p}_k^{\mathrm T}\nabla f(...

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How many ordered pairs $(a,b)$ of positive integers satify the following equation $1/a+1/b=1/120$? So far I've only agebra bashed it, as there seems to be no other way of solving it. Am I missing some key insight into...

\begin{align} \frac 1a + \frac 1b & = \frac1{120}\qquad \implies a,b >120\\\ \frac {b+a}{ab} & = \frac1{120}\\\ \frac {ab}{b+a} & = 120\\\ ab & = 120(a+b)\\\ ab - 120 a & = 120b\\\ a(b-120) & = 120b\\\ (b-120) & = \frac{120b}{a}\\\ \text{Similarly } \quad(a-120) & = \frac{120a}{b} = \frac {120^2}{b-...

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What does the minimum x that satify $x=24n+12=15m+6=11k+2$? My attempt so far was: let $x=24n+12=15m+6=11k+2$ find $x$ as the form $x=2415a+2411b+1511c$ $$2\equiv 24\cdot 15\cdot a\quad (mod\quad 11)\quad \Rig...

$\\!x\equiv 12\pmod{\\!24}\\!\iff x/3\,\equiv\ \ \ 4\,\pmod{\\! 8}$ $\\!\\!\left.\begin{align} &x\equiv \ 6\\!\\!\pmod{\\!15}\\!\iff x/3\,\equiv\ \ \ 2\\!\\!\\!\pmod{ 5}\\\ &x\equiv \ 2\\!\\!\pmod{\\!11}\\!\iff x/3\,\equiv -3\\!\\!\\!\pmod{\\!\\!11}\\\ \end{align}\right\\}\\!\\!\\!\iff\\!\dfrac{x}3\...

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Let $p(n)$ is the biggest prime divisor of $n$. Prove that, exist infinite $n \in N$ satify : $p(n) <p(n+1)<p(n+2)$ Let $p(n)$ denote the biggest prime factor of $n$. Prove that, there are infinite $n \in N$ satisfy ...

From page 320 of "On the largest prime factors of $n$ and $n+1$" by Paul Erdos and Carl Pomerance ( _Aequationes Mathematicae_ 17, 1978, pp. 311-321): > Suppose now $p$ is an odd prime and > > $$k_0=\inf\\{k:P(p^{2^k}+1)\gt p\\}$$ > > (note that $P(p^{2^{k_0}}+1)\equiv 1$ mod$(2^{k_0+1})$, so $k_0\l...

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Upper bound for the number of positive (and negative) eigenvalues in a certain symmetric matrix Suppose we are given a finite set $S$. For $X,Y\subseteq S$, $X\cap Y=\emptyset$, define $A^{X,Y}\in M_{S\times S}(\mathb...

.$ A vector $x$ in this space would satify $x^tAx>0$ (respectively $x^tAx<0$), but the orthogonality implies $x^tAx=0.$

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Exercise On topology not separated but satisfy the Borel-Lebesgue property I have a set $E\neq \emptyset $ with the cofinite topology.< The question is if $E$ is infinite prove that is not separated but it satify the...

Any two points will do to show that $E$ is not Hausdorff (or separated). Take any $x \neq y$ in $E$. Let $U_x$ be any open neighbourhood of $x$ in $E$, and $U_y$ be any open neighbourhood of $y$. Then $E \setminus U_x$ is finite and $E \setminus U_y$ is finite, so their union is finite as well. The ...

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Measure theory problems. Prove or disprove the following: a)If $\mathscr A$ is a $σ$-Algebra on $Ω$ then {$Ω$ \ $A$ : $A$ element of $\mathscr A$} too. b)A $σ$-Algebra with 3 elements exists. c)A measure $μ$ on $P(...

a) A $\sigma$-algebra is stable under complementation, hence $\\{\Omega\setminus A,A\in\mathcal A\\}=\mathcal A$ (it cannot be equal to $\Omega\setminus \mathcal A$, because $\mathcal A$ is a _class of subsets of $\Omega$_ , while $\Omega$ is a set. b) Your $\mathcal A$ is not a $\sigma$-algebra (it...

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Subalgebra Definition If A is an algebra over a field K, and B is a subalgebra, must B be an algebra over K or can it also be an algebra over some subfield of K? For example, if you take $\mathbb{R}$ as an algebra ov...

No, for the same reason it is not sensible to call a subset of $\Bbb R^n$ which is a $\Bbb Q$ vector space an "subspace of $\Bbb R^n$. Lots of stuff would break down, most obviously dimension theorems. For both vector $F$ vector spaces and $F$-algebras, it's implied that the subobjects inherit the s...

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Show that exists $x \in [a,b]$ such that $\int_a^x f(t)dt = \int_x^b f(t)dt$ Suppose that $f$ is an admissible function (bounded and with the set of discontinuity with volume zero) in $[a,b]$. Show that exists a numbe...

If you want to use intermediate value theorem(IVT), define $$G(x) = \int_a^x f(u) du - \int_x^b f(u) du$$ Observe that $G(a) = -G(b)$. Thus either they are both zero in which case you are done, or if $G(b) = \alpha > 0$, then $G(a) = -\alpha < 0$ and so by IVT, there exists $x$ such that $G(x)=0$. T...

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Differentiability class: Example of maps that are $C^k$ but not $C^{k+1}$. Is there a classical example for the fact that the differentiability class satify $$ C^{k+1} \subsetneq C^{k} $$ I'm interested in the $C^{k+1...

Is the Weierstrass function classical enough? It is **_continuous but nowhere differentiable_** ; if we integrate it $k$ times we obtain a function which is $C^k$ but not $C^{k + 1}$ for any point in its domain!

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Combinatorics using Linear Transformation > Determine the number of integer solutions to $x_1+x_2+x_3+x_4 \le 72$ such that: > > * $1 \le x_1 \le 12$ > * $0 \le x_2\le 10$ > * $3 \le x_3\le 13$ > * $5 \le x_4...

Any choice of $(x_1,x_2,x_3,x_4)$ that satify the constraints \begin{eqnarray*} 1 \le x_1 \le 12 \\\ 0 \le x_2\le 10 \\\ 3 \le x_3\le 13 \\\ 5 \le x_4\ le 36 \end{eqnarray*} will satify the constraint $x_1+x_2+x_3+x_4 \le 72$ so there are $12$ choices for $x_1$,$11$ choices for $x_2$,$11$ choices for $

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Non-linear function such that $f(ax)=af(x)$ for every $a \in \mathbb R, x \in \mathbb R^n$ > Let $f : \mathbb R^n \to \mathbb R^n$ be a function such that $f(ax)=af(x)$ for every $a \in \mathbb R, x \in \mathbb R^n$. ...

Wikipedia helps here: For linearity, a function needs to satify two conditions: * **additivity** (this is missing in your excercise):$$f ( x + y ) =

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satify

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satify

satefy

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Does a local minimum of a function always satify the Armijo rule Does a local minimum of a function always satify the Armijo rule?

How many ordered pairs $(a,b)$ of positive integers satify the following equation $1/a+1/b=1/120$? So far I've only agebra bashed it, as there seems to be no other way of solving it. Am I missing some key insight into...

What does the minimum x that satify $x=24n+12=15m+6=11k+2$? My attempt so far was: let $x=24n+12=15m+6=11k+2$ find $x$ as the form $x=2415a+2411b+1511c$ $$2\equiv 24\cdot 15\cdot a\quad (mod\quad 11)\quad \Rig...

Let $p(n)$ is the biggest prime divisor of $n$. Prove that, exist infinite $n \in N$ satify : $p(n) <p(n+1)<p(n+2)$ Let $p(n)$ denote the biggest prime factor of $n$. Prove that, there are infinite $n \in N$ satisfy ...

Upper bound for the number of positive (and negative) eigenvalues in a certain symmetric matrix Suppose we are given a finite set $S$. For $X,Y\subseteq S$, $X\cap Y=\emptyset$, define $A^{X,Y}\in M_{S\times S}(\mathb...

Exercise On topology not separated but satisfy the Borel-Lebesgue property I have a set $E\neq \emptyset $ with the cofinite topology.< The question is if $E$ is infinite prove that is not separated but it satify the...

Measure theory problems. Prove or disprove the following: a)If $\mathscr A$ is a $σ$-Algebra on $Ω$ then {$Ω$ \ $A$ : $A$ element of $\mathscr A$} too. b)A $σ$-Algebra with 3 elements exists. c)A measure $μ$ on $P(...

Subalgebra Definition If A is an algebra over a field K, and B is a subalgebra, must B be an algebra over K or can it also be an algebra over some subfield of K? For example, if you take $\mathbb{R}$ as an algebra ov...

Show that exists $x \in [a,b]$ such that $\int_a^x f(t)dt = \int_x^b f(t)dt$ Suppose that $f$ is an admissible function (bounded and with the set of discontinuity with volume zero) in $[a,b]$. Show that exists a numbe...

Differentiability class: Example of maps that are $C^k$ but not $C^{k+1}$. Is there a classical example for the fact that the differentiability class satify $$ C^{k+1} \subsetneq C^{k} $$ I'm interested in the $C^{k+1...

Combinatorics using Linear Transformation > Determine the number of integer solutions to $x_1+x_2+x_3+x_4 \le 72$ such that: > > * $1 \le x_1 \le 12$ > * $0 \le x_2\le 10$ > * $3 \le x_3\le 13$ > * $5 \le x_4...

Non-linear function such that $f(ax)=af(x)$ for every $a \in \mathbb R, x \in \mathbb R^n$ > Let $f : \mathbb R^n \to \mathbb R^n$ be a function such that $f(ax)=af(x)$ for every $a \in \mathbb R, x \in \mathbb R^n$. ...