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Recent topics on Multiplier Ideals(Arc Spaces and Multiplier Ideals)

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(1)

Recent

topics

on

Multiplier

Ideals

Shunsuke

Takagi

(Kyushu

University)1

This article is written by Daisuke

Hirose.2

Contents

1

Introduction

to multiplier

ideals

1

2

Multiplier

ideas

and

inversion

of adjunction

8

3

Applications of asymptotic multiplier

ideals

18

4 References

26

1Department

of

Afathematics,

Kyushu University,

6-10-1

Hakozaki,

Higashi-ku,

Fukuoka,

812-8581

Japan

(e-mail: [email protected])

2Department

of

Mathematics,

Hokkaido

University,

Kita

10,

Nishi

8, Kita-Ku,

Sapporo,

(2)

$1_{\aleph\uparrow 1^{\cap}0}d$

$utC^{\cdot}\Gamma_{1}^{r}0|’1$

$+0$

$M_{t_{\lambda}}\{\cdot\dagger\sim|\gamma|_{1}^{\wedge}$

er

$\iota$

de

$u1$

\S .

$R^{\backslash })\backslash |\cdot[k_{\neq}^{\mu_{1}}K\neq$ $ag_{\ulcorner\backslash \Re_{\backslash }^{r_{C}^{\iota_{T}}}ffi}^{\backslash \backslash \prime}+$

$\mathfrak{s}_{a\neg}^{-}\nearrow t\backslash$ $\uparrow affi^{\backslash }$

$(DeP^{\propto k^{-\dagger\cdot me\mathfrak{n}i}}$

$oP$

$\mathfrak{m}_{\infty}*ew\iota\dot{\infty}\dagger^{\backslash }tQ$

\S

$/k\gamma \mathfrak{u}sA_{\mathfrak{U}}$ $0\mathfrak{n}_{1}$

Veb

$\epsilon|\dagger y\backslash$

.

$Sh\mathfrak{u}nsu6e$

$T_{t}\theta\nwarrow\backslash 3^{i})$

$(X_{3}D)$

$\cross$

:

$t\uparrow 0\vdash\eta\zeta\iota|$

$\vee AY^{\backslash }|\backslash \in\dagger J\backslash$

)

$D\geq c$

:

$arightarrow d_{t}v\iota S^{Q\}^{\wedge}}O$

va

$\cross$ $(Darrow\sim Ld_{\backslash D\overline{\prime\backslash }}^{\backslash })d_{\overline{t}\in\otimes}\geq oj$

$D_{\grave{\iota}^{C}}\cross\backslash P^{\dagger^{-}||\eta\in}\backslash$

$d_{_{1}So1^{\wedge}}^{\backslash \neg}|)$

$k_{X}+D$

$\overline{|}S$ $\otimes\sim c\infty\triangleright T_{t}^{t}e\mathfrak{t}^{\tau}\backslash$

$\overline{\wedge}$

.

$e$

.

$\sim 9re|\aleph$

$S_{\backslash }t$

.

$rCk_{X}+\circ\rangle$

$\overline{|}S$ $C_{kY^{\backslash }}\uparrow\dagger e\}^{\cap}$

.

(X,

$\Re*$

)

$X$

,

$\underline{\mathfrak{Q}-}GQ$

rew.

$nor\mathfrak{m}\iota|_{f}\cap,$

$t\succ 0$

i.e.

$\underline{a}_{\ulcorner\epsilon N}5_{t}t$

.

$rK_{X}\dagger R$

ccxp

$t_{i}^{\backslash }$

eh

.

$(X_{j}\backslash \llcorner$

)

$\Re^{T})$

.

.

.

$ou\vdash \mathfrak{n}\alpha\iota\eta$

te

Sevehce

es

$L\alpha g\alpha\vdash s\{\triangleleft i’sA_{00}k\mathfrak{c}L\alpha 2$

) $*t$

the

$ek_{0}\vdash t$

of

$\frac{p_{\infty\vdash es_{0}A}}{\sigma}$

$\mathfrak{m}uIt\dot{c}p\}_{\grave{t}}e\vdash\grave{\iota}\sqrt ds$

.

$f^{\sim}:\cross\ovalbox{\tt\small REJECT}arrow\cross$

$R\Leftrightarrow@$

resc2

$.\vee\circ\S D\mathfrak{c}_{\mathfrak{i}^{\wedge}es_{?}}$

.

$e1$

)

$ffl-\rangle(\cdot f\backslash \sim p\}^{\wedge}\circ$

pe

$rb^{*\backslash }|V\propto\dagger^{Q}$

$|_{\backslash \#\beta*}^{\acute{\check{\cross}}.Stnc_{C}\#\backslash }S_{\lambda^{\backslash }}^{\backslash }(f^{-1}D)\sim\wedge\cup E_{X}c.(\dagger\backslash :$

SNC

$c|_{\{}\sim- V|s\circ r$

$st_{\Gamma 1C}’\backslash +\uparrow\dagger^{\sim}\sigma_{\backslash }\}\backslash sf_{\circ v\sim \mathfrak{m}}6f\cdot b$

$(r\mathfrak{e}sP$

.

$a\otimes_{\wedge}rightarrow-\zeta g_{\wedge}(\sim F)$ $\backslash i|\backslash v^{/}$

.

1

$]S\mu.PPF.$

.

Exc.

$\llcorner^{\backslash }\{$

)

$i_{S}$

(3)

$\frac{Dl^{\backslash .rightarrow\cdot J_{e_{C\backslash }ks}}\uparrow\zeta\searrow\downarrow}{1}$

.

$8^{(D)\approx}\#(\cross,\circ)\backslash \backslash --f_{\eta^{r}_{X}^{\cap\sim}(}k_{\tilde{\wedge}_{\llcorner}^{-l}}+*ckx*D\searrow Jcc’\iota_{\wedge}$

—-$\sim\backslash \backslash \backslash \perp\triangleright+*(r(\grave{K}_{X}\dotplus D))$

$\oint(61^{\backslash \underline{-}8^{t}})’\backslash X_{l}\emptyset_{-}^{t})\backslash \backslash --+(\sim$

(

$k_{\lambda^{-L}}\sim$

(

$t^{*}$

.

Kx

$+tF$ )

)

$cC_{\wedge}^{r}$ $t\sqrt qco_{\iota i1}de+\backslash ||\epsilon\oint\iota\prime X,$ $\Theta 1_{i}^{L\iota}$

.-af

$\nearrow\int^{(X}$

,

$\backslash \mathfrak{x}_{\iota^{\sim}Mtt}\cdot|_{k\cap}|f$

.

(X,

D):

$\S_{k\dagger}^{q}$

(kcxtv

$c\backslash \mathfrak{l}\not\in\backslash t\dot{\nwarrow}\dagger\dot{c}_{\backslash }k^{\eta}c@$

te

$\backslash n1^{\backslash }\iota\}\backslash A$

)

$rightarrow\partial^{C\cross,D)=}$

O,x

(X,

D)

$\backslash \backslash Rk+\alpha b$ $x\subset\overline{\sim}\rangle$

$\theta^{cX_{l}D)_{X}}\subset\approx G_{\cross,x}^{-}$

X

}

$n_{Q_{\mathfrak{l}}}sQ\}^{e}\backslash \backslash J^{\backslash }\backslash \cdot\dagger S_{\int}^{\backslash }|$

}

$\backslash \cdot 0_{\backslash }\uparrow X\in\crossrightarrow(X_{\mathfrak{s}^{\vee}}’\backslash )|\kappa RQ\dagger\cdot\alpha_{\vee}\dagger\lambda\in\cross$

$(f_{0}ae4W^{\iota}bl)$

.

$A_{S\tilde{s}\{A\}\eta e}$

X

$\}_{t^{\backslash }\backslash S}c\mathfrak{n}^{i_{1\backslash }}f$

At

$k^{\backslash }h\backslash _{i}\int$

$o^{\vee}t$

Xe

$\cross$

$2_{C}\cdot\backslash \{te\mathbb{Q}|_{\sqrt{}}CX,t\cdot Dx=0_{x_{i}x}$

\S

$\phi$

ct

$( \mathfrak{R}_{l}^{\backslash }\lambda)\backslash \backslash =s_{\alpha}p\uparrow\star\in\otimes|\oint\cdot x-O_{\wedge X}$

}

$\frac{s_{\infty S’cD\rho 0_{I}3e\dot{r}\uparrow\dot{|}es}1}{l1}$

(})

$lCD1,t^{j}4\backslash \backslash \Theta^{p}t^{t}1$

,

etc.

oxve

$:|\dagger\uparrow\hat{c}\dagger eP,$

$0+\dagger t\iota ec\ovalbox{\tt\small REJECT}\backslash \circ$

ece of

\dagger {tt

$t_{\circ}3$

resoi.

$+$

.

Iva

$p\vee\backslash t\backslash \uparrow_{tC\ltimes}\}_{\alpha r},$

.

X;

$\Sigma|\mathfrak{n}0\circ t\downarrow\iota$

$–;\phi^{(D)arrow(,)}\wedge$

$S_{4\iota}pp^{\iota D_{1_{\backslash }^{\backslash }SNC}}$

(4)

$t^{\Gamma}-\}\backslash _{j}\mathfrak{J}_{\mathfrak{j}}|\geq D_{\wedge}$

$\Rightarrow\partial 1\backslash 4\wedge d$

$\theta)_{1}\underline{c}\sigma\iota_{-}\underline{\urcorner}=)\partial:\backslash J\iota_{1_{J}^{\wedge}}$

.

$|\vee^{\wedge}\backslash ore\wedge.oe\triangleright$ $|\dagger\cdot\Omega x^{c}\sim\overline{\mathfrak{S}1}_{\mathfrak{j}}$

$- \tau\oint\acute{(}fft_{1}^{\zeta}t=\oint^{(\mathfrak{R}_{1}^{t})}$

$(\backslash \sim_{\iota}1’.arrow\cross\cdot\{\dot{\partial}_{\backslash }\dagger^{\backslash f1.Vtr\backslash 0\backslash }\cap^{\wedge}Ybt_{0\vee\vee-\mathfrak{u}_{P}}.C\backslash .\backslash \circ||@C_{L}^{\Psi}S\backslash t\Re\zeta 3_{t^{\approx\bigotimes_{Y}(-E1})}$

(3)

$hss\omega_{ttq}$

X

[

$t^{Q}\backslash So1\iota_{\vee}\mathfrak{g}_{1}\backslash$

$\acute{A}_{-}^{\grave{1}}+\prime S$

}}

$int\backslash$

.

$-? \oint^{(.e\tau)\geq cX}$

$\mathfrak{m}_{oreo\vee et^{\neg}}|+D_{t}s\propto c\infty\triangleright t_{\mathfrak{l}R^{\dot{\gamma}\neg}}^{\backslash }\wedge|\mathfrak{n}\uparrow$

.

$d_{f\vee}^{\wedge}$

.

%

$\oint(D)\simeq C^{\prime\backslash }(\sim D)$ $\backslash \{f\cdot\Re_{|\epsilon os_{P^{u}}\kappa}^{-}|\tau tf|$

$arrow\theta^{(a)\approx}\mathfrak{S}\iota$

$(\cdot\cap\uparrow+\infty\overline{|}S$

of

$\psi$

}

$eb\iota 196t\sim|S$

$|^{\backslash }q*|_{\epsilon\cross 1\vee^{1}e_{\backslash }}^{\backslash }$

$(+)\cross:\mathbb{Q}-\acute{q}_{ot\epsilon t^{r}\iota}$

.

$\ltimes f^{\backslash }\cdot\}_{1}^{-}$

}

$\backslash e\backslash ,\propto|^{A}$

.

,

$\mathfrak{S}\iota^{\underline{c}}O_{x}^{r}$

,

$t>0$

$F\backslash X$ $t<P\backslash e\mathbb{N}$

$T\propto ke$

\S e

$\ovalbox{\tt\small REJECT}$

\iota e

$iu^{\gamma}\mathfrak{e}$

}

$\mathfrak{n}e\iota\backslash 7\S X\iota,\{\backslash \backslash ,\lambda R^{S}\vee$

A

$\grave{4}^{\backslash =}\backslash d_{t\vee}^{-}X_{-\backslash }$

,

$D\backslash \backslash =\cdot g\Sigma A’\backslash \backslash$

$\Rightarrow$

$\theta^{c\infty_{\backslash }^{t})}\underline{-}\partial^{C’ t\cdot D)}$

(5)

$A_{C}\{CD^{l}x$

),

$1ct(\alpha’,x)\epsilon\emptyset\gamma_{O}$

$\frac{E_{X^{R_{\grave{V}}}1\backslash D}1_{Q}}{1}$

$\zeta\downarrow)$ $\cross:S^{1l}\tau\circ\circ t^{:}\}_{1}v’\propto|^{\cap}$

.

$0\xi d_{\overline{i}11\backslash }$

tl

,

3

(5)

$\mathfrak{l}y_{r}^{t}$

$(.\uparrow\iota^{t_{t,-rightarrow}}\vee^{\cap}f\eta\uparrow^{L}\backslash \sim^{i|-\varphi_{l_{\backslash }}}+ f\overline{k}^{t}t^{r\rho})\underline{-}\varphi_{\backslash }$

$C\dagger^{\backslash }\backslash \cross\neg\cross\sim$

:

$b^{I}Ao\vee A_{V}I-\iota xp\infty+$

$|\ulcorner x$

$|($

$\mathfrak{W}\supset x^{=}\prime k_{\grave{\aleph}/}\cross\simrightarrow(\eta- i_{1})E$

$($

$\theta*\cdot’\bigcup_{\check{\hat{\wedge}}}^{-}’\langle(\eta-\backslash -Lt\perp)\simeq\uparrow n\llcorner\{\Delta+$

]

$-\ell\backslash$

$t^{t}\not\geq)\cross=\mathbb{C}_{J}^{1}D\sim x_{t}3arrow)$

$|\epsilon X_{1/x^{\sim}}rightarrow E_{t}$

/

$kx_{\sqrt{}}\neg\simeq E_{\iota^{+2}}E_{\iota}\cross$ $/\dot{K}\cross\nu_{x^{\sim}}^{-E_{1.\uparrow 2}E_{1}+\vdash E_{S}}$

$+_{1}^{\uparrow}D-\sim 2E_{1}$

\dagger

$D_{l_{f}},+_{\backslash }^{*}\sim D\approx 2^{g}\vdash\iota^{\vdash 3}\Xi_{2}.\succ D_{2}$

,

Sl

$D\approx 2E_{i}\dagger 3E_{2}+6\S+D_{3}$

$(+_{\backslash }\backslash \backslash =\nearrow_{\sqrt{}}t_{\grave{\Lambda}^{Q}}^{f} .\backslash \cdot o{}_{/}C\{|^{\backslash }\backslash x_{\langle}arrow\cross)$

$\partial*\cross 3\ulcorner\ulcorner\neg\ulcorner_{1\dagger;}$

,

.

$k_{C}+_{\vee}(D-\Xi$

$\oint$

(

$\Xi q$

.

V)

\sim

-$(x_{f}g)$

(3)

$X\approx S\uparrow^{ecR_{Lq\cdot\cdot t\prime}\cap k\backslash ]\backslash }C\backslash \backslash +\gamma_{1}\rho_{\backslash }-||\uparrow e\dagger Q\backslash _{1}\ovalbox{\tt\small REJECT}^{r.\backslash }|\cap$

.

$\propto)\underline{\Leftrightarrow}\dot{\hslash}t\cdot:\mathfrak{m}_{A}\backslash |A\dot{k}AA$

$\sigma(\sim P\backslash e\iota\vee.oV\backslash Py^{\star_{(B}}P_{+\mathfrak{e}se_{I}\circ t_{\dagger^{\circ\ltimes \mathfrak{e}n1X}}}^{e_{0}+\emptyset\iota}l.e_{Co\nu\backslash \vee Qxh_{1A}||_{\Phi}++}t_{t\backslash }QX$

(6)

$Thr\tau$

.

$tR|_{tC}k\backslash e\zeta B11,$

$H\alpha\vdash\alpha- Yo*i\sqrt{}\alpha \mathfrak{k}HY3$

)

Ass

$\mathfrak{U}$

wte

$\backslash \langle=Spec|$

ft

$CT^{\triangleright}0\uparrow A^{\cdot}1$

is

$\sim\Im_{oV^{4}C\iota}r$

$a_{(AeM}s.t$

$d|- vx^{4rightarrow\sim}- rK_{X}$

$|.e.a\vdash e\mathbb{N}$

$s_{\backslash }trk_{x}$

:

$c_{Rt\uparrow 1*}$

$\omega:=\Delta|-$

.

$\Rightarrow\oint\cdot(oi^{t})\approx<x^{\nu_{|1\int\cdot\dagger\cdot \mathfrak{U}\wedge e1_{\aleph}tCt\cdot Pc\sigma\iota_{t})_{\sim}^{Q}M_{R}>}}$

$\underline{C_{0}r.}(E\circ w\nwarrow 1A\mathfrak{c}Hol1)$

$X=\mathbb{C}^{\mathfrak{n}}$

,

er..

$\underline{c}\mathbb{C}Lx_{-\downarrow 1J}x_{\mathfrak{n}1}$

:

$bbV\backslash om|\backslash A$

\‘A

$deA$

9

$\oint\cdot C\propto\iota^{t)\overline{\sim}}<x_{-|\nu_{\dagger ielr+(t\cdot Pco\iota\backslash )\underline{\backslash }R^{\eta}\rangle}}^{\triangleright}$

.

$\mu:Y-\cross:t\circ Y^{\sim}|C|_{Q}\S\triangleright \mathfrak{e}s_{\circ}^{1.\circ}f\sigma\iota S\backslash [$

.

$\infty\zeta\}^{\sim}rightarrow O_{V\sim}\mathfrak{c}- F$

)

$\sim\triangleleft\#(\sigma\iota^{\{});Mo\eta 0\mathfrak{m}_{t}^{\backslash }A$

$\tau_{br\{AS\iota^{\backslash }\mathfrak{n}\nu}$

.

$k+\alpha\lambda\epsilon I,\backslash \dagger(.t\cdot Pc\sigma\iota))$

$\Leftrightarrow\iota r+vrightarrow alf’\sigma t\cdot Pco\iota)(0c^{\forall}\epsilon<<1, \forall\nu’e1_{k}\uparrow\cdot(\tau)\cap M)$

(7)

$+\sigma \mathbb{C}LXI\sim)\infty c\iota\cross l;|4.d_{3^{eh}}$

.

$b_{\gamma}$

the

tWoho.

$\propto pP^{e\nwarrow r_{\overline{|}\mathfrak{n}}}\S\sim|\mathfrak{n}\cdot 9$

8

$(t\cdot d_{1\vee\theta))_{\sim\oint C\Theta i^{t_{f}}.)}^{q}}-$

$I\cdot\dagger+\neg\overline{|}s’\prime 3^{e\mathfrak{n}er\propto\lambda’\sim>}’-$

a

$( t\cdot dt^{-}\vee(f))\sim\sim\oint(\theta\iota+t)(oe^{\forall}\uparrow\nwarrow()$

$\underline{Q.}H_{0}w\prime_{t}3^{e\wedge erA’’?}$

$\ovalbox{\tt\small REJECT} Tow\propto$

$+<cc\gamma 1:hoh\sim 4_{e}r^{\mathfrak{n}er\propto\dagger e}$

.

$(^{e}+_{0\triangleright\forall+\alpha ce\tau\circ+p_{(\S\backslash }}dF_{l\cdot 1Showkeoe\vee ah\iota s,.k_{8^{o_{h}}}(.C^{*})^{\eta}}^{\wedge}+.\delta+\phi^{Q;++Pt\cdot\}\rangle}\propto oe.0.:\approx Pc\theta\iota+)1A$

$arrow_{\oint i\vee(f)=}(\cdot t\cdot d)\oint^{(}\%^{t})$

$0<\forall t<1$

ts

$+=X_{1}^{d_{I}}+\cdots+x_{\mathfrak{n}}^{d\mathfrak{n}}1Sh\circ \mathfrak{n}- 4_{3^{e\mathfrak{n}er\propto\dagger e\cdot Ass\alpha me}}qn\#_{\backslash }\nwarrow\{$

$Si$

Ace

$P(+)’–((\cdot\prime 1\lambda e\mathbb{R}^{\eta}\backslash ’$

$A_{ct-(}A_{\iota vcf)},$

$0$

)

$=A_{c\dagger(\theta 1_{f\prime}0)}\simeq\Sigma i^{1}\nearrow dt$

$\frac{\ovalbox{\tt\small REJECT}_{\alpha\iota\backslash |sk_{thq.\dagger\dagger\iota m}^{-}}^{f}}{C}$

$(()(A_{oC\propto}A\nu\propto \mathfrak{n}_{t}sk_{3}\iota n$

$+:\sim\cross-?\aleph$

:

$A\circ s$

re

$S^{\circ\#_{\mathfrak{l}}}\cdot\cdot\circ+D$

$(be\S p\cdot\propto t$

$s\cdot t$

.

$\circ\iota \mathcal{O}_{X}^{\sim}\overline{\sim}0_{x(-F))}^{\sim}$

(8)

$\Rightarrow^{-}|R^{\grave{6}}\cdot f\cdot*O_{X}^{\backslash }(k\grave{\cross}-LF^{*}(|<x+\mathfrak{d})\lrcorner)-\sim Q,$

$(^{\forall_{\grave{3}^{>0)}}}$

$(resp\cdot R^{\overline{k}}f*O_{\cross x^{-}}^{\sim(k\backslash }\llcorner f^{*}K_{X}+3^{\backslash }$

$(\backslash \backslash )(N\propto Aql. v\propto\ell_{1\overline{1}}sh_{\dot{|}h}3)$

$L:c\infty\triangleright t|er1\iota\iota+$

.

dtv.

$0\nu\iota\cross$ $R_{c}C$

.

$L\sim Di_{R}\mathfrak{n}ef\cdot hhdk_{1J}$

$\Rightarrow H^{\backslash }(X,$

$\mathcal{O}x_{C^{l}’}^{(.\kappa_{x}+L)\otimes\#\mathfrak{c}b))\overline{\sim}O},$

$t^{v_{\backslash >0)}}\backslash$

$C_{0\triangleright}$

.

$\cross:_{P^{ro}\overline{d}}$

.

ho

$\gamma\cdot w\omega\vee\alpha r$

.

$R:ve_{7}\propto w\iota pled-$

$L:c\infty\vdash\uparrow|er$

$i\mathfrak{n}t\cdot A-$

.

$\circ^{yt}\cross s_{\backslash }t$

.

$L-b_{1}^{\backslash }s\mathfrak{n}ef\propto \mathfrak{n}db_{1\S}\backslash$

$\simeq\rangle$

$(D_{X} (.

k_{x}+L+W\backslash B)\otimes\oint CD)\backslash tSa^{\mathfrak{g}}\cdot J^{e_{4}}$

$-|f\cdot \mathfrak{m}\geq di\psi$

$O$

$[ \frac{Lem}{F:c}c\mathfrak{m}_{t\wedge \mathfrak{n}fd\zeta L,.\propto 1,.Tk_{okbI}a.sJ)}\circ\gamma\cdot\backslash oken\mathfrak{n}\dagger s_{c}\cdot[H^{\backslash }(\aleph,F\otimes \mathcal{O}_{X}t\sim ib))\approx b_{i}^{y}\backslash >6$

$N\propto l_{e}\backslash \nirightarrow-\rangle H^{\grave{t}}(\cross.\mathcal{O}_{X}Ck_{X}\star L+(\mathfrak{m}-\backslash c)B)\copyright\oint(D))\underline{-}0^{y_{\grave{1}\rangle 0}}\ulcorner-\overline{|}S3^{A}\cdot 3^{e\ltimes}$

,

9

$O\backslash k$ $\mathfrak{U}$

$( \downarrow b\backslash \backslash ,\vdash g\not\in K\not\in\not\in^{\backslash }\backslash \Re\wedge\ovalbox{\tt\small REJECT}^{c}\frac{\backslash }{\overline{0}}\mathfrak{z})$

$WF\grave{\iota}t\zeta e\eta 4_{b}$

.

Da

$\grave{t}S\mathfrak{u}keH\grave{c}\vdash 0\Re$

(9)

$\uparrow Au.\backslash \dagger\iota pl_{1}- e\vdash-\downarrow\ \infty 1sahA\overline{\mathfrak{l}}hver\S ioY\backslash 0+\infty d\tilde{J}^{\mathfrak{U}k_{C}}\tau_{\overline{\iota}^{Q}h}$

$\iota_{l1^{\backslash }|k\not\in K^{\backslash }+}\backslash H\oplus\ovalbox{\tt\small REJECT} E^{\backslash }rightarrow\neq a\overline{r}_{\iota}^{ln\phi}$

\S *

$\iota_{\sim R^{\backslash }}^{t\iota}$

(De

$p\propto rt$

ment

$\circ f^{\neg}M\propto tk_{CM\alpha}\uparrow$

ics

,

$k\cross\ltimes sk_{\mathfrak{U}}0niVers\dot{|}\nu$

.

$Sk\ltimes ns\ltimes$

ke

$T\nwarrow k_{t}J^{\iota}$

)

${\rm Re}_{ic}c.\propto A_{\grave{l}}^{\Gamma}$

$\propto Q(\overline{J}^{\iota_{A}\mathfrak{n}c\uparrow\iota 0\mathfrak{n}}$

$r

$mu^{1}\iota\nwarrow$

$\cross\backslash \backslash S^{\eta_{1}}cc\uparrow\dagger\gamma$ $\gamma_{cX\backslash }\backslash s_{|^{\rho}\cap OO}\dot{r}_{c}\downarrow t^{-}$

viiso

$\gamma\backslash$

$|<\cross+Y|_{Y}-\sim k)’$

$a^{e1\eta erc_{\backslash }}\backslash \wedge 1\not\in\Leftrightarrow\sim\rangle$

$(X ., S_{\backslash }i^{-}B)$

X

$\backslash \backslash$

ho

$\triangleright n\backslash \ ^{A}_{A}^{\prime r}\}_{*}^{A}$

$Sc\cross\backslash \backslash Y^{\sim}\mathfrak{e}d\alpha cedd_{tV}$

-$s_{0\dagger^{A}}$

$s\underline{\backslash }O^{\backslash }\sim \mathbb{Q}- c\propto r\backslash \uparrow\overline{\iota}e\}\wedge ov\backslash \cross$

$S_{t}t(\int_{k}\prime x\dagger_{f}S+B|J_{a^{p\cdot*s_{\eta}\mu S.\iota}}^{\eta Co\dagger \mathfrak{n}}-CQ_{\backslash }1_{l}\wedge t_{t}^{\wedge}e\triangleright$

$\nu:S^{\iota/}arrow S\backslash \backslash |t0|^{\wedge}Wo_{4}|_{t}\sim\backslash ’$

$\exists_{B^{\vee}\geq C}\bigcap_{\backslash }s-d_{i}^{1}V\dot{t}|Kc^{\backslash }r$

on

$S^{t/}(\theta|i^{\neg}fe\mathbb{R}^{\rho}\backslash t\circ+8\circ\dot{\eta}S^{d})$

$K_{s}k$

.

$|<s^{\nu+}8^{\nu}\sim\sim\nu^{*}(kx\dagger S+\S|_{S})$

$\}\vee|\sim\backslash \cross\supset Sl\nearrow\cross\supset S\S\iota_{\swarrow}^{\backslash }\Delta S’$

$f:e\mathfrak{m}led4\triangleleft\}_{G}s_{0}\lambda$

.

$k_{X}^{\sim}\backslash +S\equiv+^{-x}(kx^{+}S+\S 1^{+\underline{\rangle}_{1}\backslash }-\backslash$

$|<s\backslash \sim--y_{(}ks^{V+}8^{\triangleright})+\overline{L}^{Q_{A}}E_{A}^{\backslash }|_{S}^{\sim}$

(10)

$\underline{ex}$

.

$S\backslash \uparrow_{0\}}\mathfrak{g}co_{\backslash }\iota\cap\urcorner\cdot\dagger e\}^{\wedge}\underline{-})b^{\vee}\simeq 81_{\lambda}^{\backslash }$

(X

$S$

\dagger

$B1\underline{\underline{o_{\backslash }d_{1_{\backslash }^{\iota\backslash \langle}\llcorner}^{\backslash }I\backslash \iota 0}\prime}(S^{\nu}B^{t/}1$

$|Y1\backslash /\circ\iota\cap d_{\grave{\rfloor}}\backslash \cdot$

$d^{\varphi}\backslash =\cdot m|\mathfrak{n}$

{

$\alpha_{\dot{t}}|i$

.

(EK5

$cS$

}

$a_{\overline{\mathfrak{J}}}\cdot-\wedge$

.

F-k

$|_{S+\uparrow\}}^{\sim}$

$\ovalbox{\tt\small REJECT}_{b}$

$\tilde{L}_{tt}3^{e\}\uparrow e\}^{\wedge l^{l}}}\backslash .$

.

$d\leq d_{S}$

$\underline{Tk\mathfrak{n}}$

$(\Lambda^{\backslash })tko11^{\nearrow}o_{\backslash }r[k\dagger],$

$Shok_{l1}\}_{Q}\psi \mathfrak{c}SA1$

)

Cl

$>arrow 1<-\neg\supset$

ds

$>-t$

$(\dot{\backslash }\backslash \backslash )(K\alpha w\mathfrak{a}k\grave{\iota}t\iota CK\alpha J)$

$C|\geq^{l}-|\Leftarrow\rangle C(s\geq- 1$

$Def$

$(l_{\backslash It\cross,D_{1}}^{\backslash }6^{\urcorner}t)X\circ|^{\wedge}\mathfrak{n}_{1C\iota}^{\zeta/}.\nearrow D^{\backslash }’\backslash j$

$k_{X}*D\iota sarrow \mathbb{Q}rightarrow cat\uparrow_{\mathfrak{l}}^{\backslash }et^{\wedge}$

,

$\}^{\backslash }\backslash \crossarrow\cross\backslash p_{0}\S\gamma\approx S^{Q}Q.$

of

$tD_{i}e\iota)_{i}\sigma\iota C_{X}^{\backslash -\sim}\sim C_{X}^{r_{1}\sim}(\sim\vdash)$

$\theta^{(\aleph;D}$

,

ed

$)_{\backslash }^{\backslash }=+*C/x$

(11)

$(t\grave{t})(X’\Sigma_{i}B_{;^{\Theta}}\grave{\iota}^{t}Iarrow.\backslash \backslash$

(

$X,$

$S,$

R.)

$a_{S}c\backslash 00\grave{v}q1je\tau_{-\simeq C_{\aleph}^{r}}^{-}/t>b$

$+_{\backslash \cross}\simarrow\cross:R_{\mathfrak{B}}re\backslash \vee\wedge\wedge.q_{0}\sim+^{\wedge}(\neg \mathfrak{d}\star B\omega.\backslash _{j}S_{\backslash }^{\backslash }tiS\backslash \overline{arrow}+-|\wedge sarrow S_{\mathcal{W}to\dot{o}}\}\ltimes\wedge^{\prime IS}\sim$

$\alpha d_{\grave{J}^{(X_{1}B_{1}\alpha_{-}^{t)\cdot\cdot\sim}}i’*}’-u^{t\{*-}$

$\theta^{iX_{r}^{\vee}S+S,\otimes t^{X})}$

$Ren\uparrow t\iota rk$

(o)

B-c,

$\Re=^{r}\circ x\Leftrightarrow\prime Ad_{\grave{J}^{(X_{j}\S)^{\backslash }} ’(\tilde{J}}\backslash \approx\alpha d(X S_{1}^{\backslash }\S_{\mathfrak{N}}\dagger)$

$(\backslash )\backslash \alpha\dot{d}_{1}^{\sim}(\cross,S, @.,\Phi^{} )$

ls

$\backslash !\dagger 1d_{\mathfrak{e}}p\sim\circ+t\dot{k}eC_{Y}^{}\lambda 0\{CQ_{-}|_{\backslash }Q++.$

$t\overline{t}\_{\iota}^{\wedge})x_{\backslash }\backslash \mathfrak{g}\cap$

.

$\circ\backslash +f_{\iota^{\backslash }v1e}\nearrow\lfloor’\iota\dagger\cdot C^{\eta.\underline{>}}2,$

$+e\theta_{c^{1}}^{\backslash }SJ^{\zeta\dot{|}\tau e\psi_{c’}\hat{A^{1}}}$

$= \rangle\oint\backslash ’\cdot\cross,\theta\iota)=$

’A

$d$

(

$j^{(\cross}$

,

cl;

$\psi(+)$

)

$d_{S}>arrow\uparrowrightarrow\#tS^{\vee},$

$B^{\dot{\vee}-\sim\zeta g_{S^{\psi}}}$

)

$rightarrow(s_{1}^{\nu\prime}B^{\triangleright}’)_{\backslash }\backslash$

\S R\dagger

.

$d>\sim 1\Leftarrow-\rangle$

$\mathfrak{a}_{\iota}d_{\grave{J}}$ \sim

Ox

$\# 1eo_{\iota}\}^{\wedge}rS$

$\langle\Rightarrow(\cross, S\neg\dagger B)_{\backslash }^{\backslash }(pu\}e\zeta_{8^{\rho_{Q}}a\not\in a\}1r_{1L^{\backslash }}\uparrow|t^{\wedge}\lambda}^{1.+1eo_{4}\triangleright S_{\mathfrak{g})}}|’$

$\underline{E\wedge}$

$(\backslash ^{\backslash })$

X

$\underline{-}\mathbb{C}^{1},$

$s\simeq(x_{3^{\underline{-}01_{1}}}.$

B\sim

$\vee’\eta=C_{\lambda}^{\wedge}$

$– \dashv---r_{--\}-rightarrow}^{f_{-}---}s\backslash .\frac{T^{1}}{c}\backslash ]/^{Y}|||$

$K_{X!\wedge}^{\backslash }=E$

$+^{\dagger} \int\approx\sim\S$

\dagger

$2\in$

$tc\dot{l}\grave{\lrcorner}tX_{r}S)\approx+*O_{x^{\backslash }}(K_{\tilde{X}}- t\uparrow kx^{rightarrow}f^{Y}S^{\sim}\dagger S)$

$=\cdot\sigma)(-\overline{b})=(X_{1}$

$10$

(12)

(

$\backslash /\backslash r\backslash \backslash _{f}X_{\backslash ^{t}}’\backslash \mathfrak{Q}rightarrow\S_{01’Q_{1\}v}^{r_{\cap}}}nc\}-\}\gamma 1$

A

$s_{\mathfrak{U}}r\neg^{\zeta}\mathfrak{c}_{k’}ce,$ $s\wedge\backslash t^{A}\backslash \mathfrak{e}0_{\backslash }\triangleright 7_{1}^{\backslash }er\sqrt tV^{1}\grave{t}So\vdash$

.

$=_{\nearrow}\searrow C(d\overline{J}(X_{j}S\backslash _{t}C_{S}^{\cap=}C(_{p}S);\simeq A\mathfrak{n}\mathfrak{n}(*’\vee^{\bigwedge,}\hat{5}^{\vee}\nearrow c-s’)$

$(\cap\tilde{\cross}-)S^{1_{\backslash \geq\alpha_{4}\neg\cdot 0_{A}}}\cap^{\backslash .Y\backslash cr\mu c}\aleph^{\backslash }\backslash e\uparrow\eta Q_{*e}\{4Q\dot{4}ks_{0}\lambda\wedge\backslash |)$

Th

$n\iota C{\rm Res}\uparrow_{l^{\backslash }\mathfrak{i}}^{\backslash }ct\backslash \backslash \circ V\backslash \star b_{\iota}w,$ $C+.r\llcorner\alpha 2,1\dagger t^{\underline{\circ}}okt\iota\uparrow\uparrow.$

S.

$\mathfrak{l}$

])

(X

$\iota S_{j}\cdot B,\varpi^{t}1RSo_{\backslash }b\circ\vee e_{/}Assa\mathfrak{m}e\infty kI_{S}\approx C_{X}^{\cap}arrow S$

)

$e_{\backslash d_{\backslash ^{i}},(X,S,8_{;}\Re^{t)\mathcal{O}s}}’.-=\mu_{*}b^{\eta_{(S^{V},8^{\dot{\nu}},C^{\bigcap_{i}}}}’$

IA

$p\propto\dagger^{\wedge}t\cdot {}_{\backslash }Cb\backslash$

$d>- 1rightarrow d_{S}>- t$

$t_{t}^{t}\gamma\sqrt{}$

)

$|S\backslash c_{\vee}\backslash \prime sey_{\approx}\sim|_{\backslash }S_{\backslash }\mathfrak{n}_{C^{1\wedge}}\mathfrak{m}\alpha\#$

)

$\ulcorner oo$

$F_{0}rs|\}\uparrow\backslash p^{1_{\overline{\iota}\zeta\dot{|}\uparrow\backslash }^{\sim}}\vee)\sim ass_{\mathfrak{U}\}it}e\theta t=C^{\backslash }x$

$f_{\vee}^{\cross\supset S_{3}}\sim\backslash |1^{\searrow}s^{\nu}\sim$

$+:e\uparrow\tau l\Leftrightarrow d_{\iota}4e\sqrt{}*5^{\cdot}0$

?

$\cross\supset s^{\swarrow\triangleright}$

$Carrow(0_{X}^{\sim}(k_{\grave{X}^{-\llcorner}}’+*\mathfrak{c}kx^{\{}S+\S)_{\Delta})arrow 0_{\tilde{\cross}}(\kappa_{\tilde{X}^{-L^{\cdot}}}\not\in*(\sim k_{X}+S+81^{\sim}\theta S)$

$.arrow^{S}\zeta\supset\grave{s}(k_{S^{\sim}}^{\sim}\llcorner 3^{*}(k_{S^{t’f}}8^{\nu})\lrcorner)0\simrightarrow\div 0$

$\zeta_{f_{t}}$

$O^{\vee}a_{\grave{i}^{(\aleph_{l}S\dagger\S)}}^{\eta}-9\alpha d_{\grave{J}}(X,rS$

;

$Bt^{0_{S}}\sim\downarrow 1^{*}\theta^{(S^{\nu_{J}}B^{\iota/})}$

$arrow R^{I}t_{*\cross}o\sim(\dagger_{1<\grave{x}}’-L+^{*}(k_{X}+\int+B)_{\lrcorner})\uparrow-\sim O$

$p_{oc\phi}\downarrow\cdot C\backslash Y\backslash |s_{\ovalbox{\tt\small REJECT}}\backslash \}_{1^{1|(\S}}\ell$

.

(13)

3

$c\uparrow r^{i}$ $T(/lt_{\backslash }\backslash -, (k_{C!_{\backslash }VvC\nwarrow}k\grave{\iota}t\alpha)$ $Tr,1_{\backslash }Q\vee’\backslash Ae_{\overline{\aleph}}t^{-}|i^{\tau}0lA\backslash |SA_{cc}A^{r}|\sim>$

$\iota\backslash |\backslash \backslash \dagger scxS\cap>c_{v’}$

er

$Ct3^{er_{\grave{\nu}V1}}c_{\iota^{-}}$

}

ex

$c|_{Q^{\neg}}x$

ecl

pt-

$x\in S=\cross$

$(\grave{x}\underline{-}s_{P^{ec}}R \ltimes\backslash \backslash \mathfrak{g}_{\circ cc}Q)$

ASStxn$e

$d_{\iota\backslash }\succ\sim\sim\sqrt{}$

$(<--\rangle(tS^{\psi}|B^{\psi})\iota S\backslash fi_{C})$

$C^{\urcorner_{-0^{\backslash rightarrow}}^{\backslash \sim}}\mathfrak{c}\backslash d_{1}^{\sim}(X_{i}B|\backslash B)cC_{x}^{\urcorner}$

$o^{\propto\gamma_{\llcorner}}\mathfrak{n}\dagger\uparrow\backslash \sim\backslash \sim\circ d_{\backslash }\vee(B ’ \Re_{h}^{1\sim S_{1}})$

/

$C<S_{1\gamma}<<4$

$\mathcal{O}1_{1}C_{S}^{\wedge}=ad_{j^{(}}XjS_{J}\backslash B_{j}\Re_{0}^{1-E})C_{S}^{\cap=}l^{1}*\theta^{(}’\sim^{t}\rangle\acute{u}^{G1c}$

$(Od_{5}\underline{\backslash }-1, \Re O-\triangleright_{*\theta^{(S_{1}^{\triangleright}}}^{1}B^{\nu}))$

$\alpha_{0}o_{S}$

$S\neg\sim$

.

$\mathfrak{N}_{0}\supset(\vee\circ q_{T_{/}}$

$\sigma 1_{i}\acute{C}_{S}^{\cap}=a\circ \mathfrak{c}_{S}^{-}$

1

$|_{c}arrow e$

.

$\cup^{\circ\gamma*I- s}"\cdot i=’\eta_{b}+I_{S}$

$\eta_{\backslash xS}$

$(^{ct_{c-}^{\tau}} e\bigcap_{c1}>Ttz\overline{\sim}\supset\sim\backslash$

$\sigma\iota_{0^{+}}I_{S}$

$\Re_{t}+I_{S}\approx\cup\eta_{\iota}+I_{R}\approx\cdot\sim\backslash$

$s_{\alpha p?^{0se}}$

$\partial<\sim 1_{f}$

$(\sim\underline{=}$

$–\rangle\exists_{E_{A}:}+-\mathfrak{e}\cross c-$

$\oint_{1v|Sc\}\sim}\backslash \wedge’.v\tau\cross\sim$

$S_{\}^{-\zeta}$

$\mathfrak{a}_{\grave{t}<}\sim\uparrow$

$\theta\iota_{0}=ac^{(}\backslash \grave{j}(X \prime S, B)Ct_{*\grave{\cross}\alpha\backslash }^{\prime^{\wedge}\wedge.(\backslash }\ulcorner\urcorner E_{\grave{\iota}})=+_{*C_{X}^{\wedge\sim}(\sim E)}A^{\backslash }$

$\overline{\vee}L|\overline{\sim}\alpha d_{\overline{J}}(X_{/}S_{i}B, \Re_{c}^{1rightarrow\in})cc(c^{1}j^{(}\cross, s_{iB,}f*\wedge E_{\backslash })^{|-8})$

$c\cdot f_{*^{t}}^{\prime,.\sim}\vee\tau(\backslash$

$=\cdot\dagger*(\vee-$

ft

$(\sim IE_{\backslash }\backslash )$

$(\ulcorner C^{\backslash } 8<<1)$

$\backslash \backslash \backslash 01\}\eta c\mp xC_{X}^{\sim}t\sim(M+\mathfrak{i})E_{A}^{-)}$

$\nu_{I1\geq 0}$

(14)

$o_{\mathfrak{n}}\mathfrak{t}Ae\circ\dagger\ltimes e|^{\wedge}k\mathfrak{m}d$

,

$b_{J}\backslash Na_{@^{\alpha C}}$

Os’s

$\dagger^{\downarrow}\wedge \mathfrak{m}_{Z}$ $\forall p_{e\ltimes\dagger}’/a\hslash cA\tau e\mathbb{N}S_{t}^{\dagger_{1}^{\backslash }}.$

.

$\tau\cap*(Dx\sim(\sim\S(A)E)c\eta\ltimes^{R_{x}}$

.

$\sigma\iota_{0}c\bigcap_{VeN}(\mathfrak{S}’t_{k}\dagger I_{S})c\bigcap_{{\rm Re} N}(\mathfrak{m}_{x,x}^{A}\dagger I_{S})=I_{S}$

$\h_{1\S}$

$|n\rho^{1_{t}}es$

$\nu_{*l^{(S^{\psi},B^{\psi})=0}}$

.

$c_{0}nh\nwarrow d_{1C}\vee\}_{|\circ}\gamma_{1}$

$..d\underline{\supset}-1$

$E$

$\frac{c_{\circ 41}(k_{\circ}1_{1\propto r.Sk_{0}k_{ur_{\Phi\vee}})}^{1\prime}}{\backslash J}$

(See

$[k\star]\alpha\eta\triangleleft[_{\backslash >\{-}^{\neg}|]$

)

$\forall g_{c}S:_{C}\}_{\circ}$

se

$ds\mathfrak{u}bse\dagger$

.

$d(\not\in)_{\backslash }=m|\int\backslash \{\alpha_{\backslash }|_{J}C$

.

$(\underline{R}_{A}\backslash )c$

a

$t$

$ds^{(\gtrless)^{\backslash }}\backslash =\mathfrak{m}|\mathfrak{n}\{a\backslash |E_{\dot{t}}|_{S}^{\backslash }*\oint, \not\in(F-\backslash |_{S}^{\backslash })c8\}$

$d- d_{s^{(\not\in)}}$

?

$(\leq 0.||<.

)$

$cf\cdot[EMY1)$

X: A.

C.

$\dot{A}/S\backslash ho\vdash v\mathfrak{n}\propto AC\infty\triangleright\uparrow i_{C\triangleright}$

$\frac{Hiqkey\backslash }{t\lrcorner}-C\underline{\circ}\underline{d_{t}\cdot me\mathfrak{n}StoV1}$

X:

$\mathbb{Q}-\S_{b}re^{\gamma\backslash }\cdot ho\vdash m\propto A\vee\lambda r./c$

$\gamma_{:==\dagger_{\wedge}Y_{\backslash }}^{t}.$

,

$t_{\backslash }>0,$

$Y_{\backslash \backslash }^{c}\cross:c|_{0}seAs_{lA}b_{S^{C}}kew\backslash e$

$\theta 1_{\backslash \sim}^{c}\mathcal{O}_{X}$

:

da\S .

$\dot{A}AAo\cdot\dagger Y_{\backslash }$

$+:X\neg\sim\cross:\lambda\circ s.$

re\S ol.

$\circ+\theta t1,$

$\backslash ,$

$\Re g$

$e\iota_{i^{(}J_{\tilde{X}^{=}}}\circ\neg_{\grave{X}}(-p_{\backslash }\backslash )$

(15)

$k_{X/x}^{\sim}\sim Lt_{\wedge}.F_{\nwarrow}\equiv L0_{\backslash }E_{\dot{A}}\dot{A}$

(X

Y)

:

$\theta_{R}A\daggerrightarrow a_{\dot{A}}>rightarrow\{,$

$v_{f^{\backslash }}$

$(X, Y)$

:

.Rc

$arrow\rangle$

$\alpha_{\dot{A}}\geqrightarrow 1$ $\nu_{\dot{A}}$

Tkm

(T-C

Tcx

1])

$(X, Y)\mathbb{R}A_{0}ve$

.

A

$SS|\lambda Wte\cross|SsM^{Q}\circ t^{1}\kappa$

$\gtrless c\backslash -\cross:B-bote\mathfrak{n}$

.

$c1_{0\lambda Q}da_{Ab}^{t}v\alpha r$

.

$S\backslash \ddagger$

.

a

$k^{r}|JY\backslash \backslash$

(

$\not\in,$ $Y^{1}\downarrow\approx 1$

:

Ac

–\rangle

$(X ’ Y\vdash\not\geq)$

:

A

c

$\mathfrak{n}e\alpha r*$

$F_{or}s|\backslash w\iota p^{1_{\dot{\iota}}}c1\dagger y$ $\alpha.SSuv\mathfrak{n}e$

$Y=0$

$\llcorner c_{\backslash }^{q}$

;

$A_{oClA\S}o*A_{C}s^{-}|\mathfrak{n}g$

.

$|e$

.

$L$

is

cle

$t_{1\eta e}4$ $b_{y}$

$(s_{\overline{\mathfrak{l}}}\mathfrak{n}ce*tSA_{C}/\llcorner|S$

$’\theta^{(*)=}\theta^{(8,\mathcal{O}_{S})cCo\gtrless}$

$r_{R}4_{\mathfrak{U}C^{q}}A)$

$(I_{i^{C}})$

I

$L^{C(0_{X}:}de^{f_{J}}$

.

$|\partial e\alpha\#\circ+L\overline{|}\eta\cross$

$|.e$

$tke|_{1}f\dagger\cdot\circ*$

$\oint- \mathfrak{c}*$

)

$w_{e}k\propto ve\dagger^{1}neL_{Q}j||_{ow|\mathfrak{n}}\backslash 8+w_{\circ}re\epsilon\uparrow\ovalbox{\tt\small REJECT} p_{I}^{\backslash }c\uparrow\overline{t}04+1_{\cap n\backslash }$

$o_{\mathfrak{l}}\oint(*, (01(0_{S})^{t})cI_{L\#}t,$

$w_{\theta 1^{C}}^{l}$

Ox,

$v_{t>0}$

$\otimes\oint^{(\gtrless,(\sigma\iota\leq)^{t})c\oint(X,6\iota^{t}I_{*})O_{i,}}\mathcal{O}I-\sigma v_{\mathcal{O}’t\subset O_{X}}/\forall t>0_{/}$

$0<\forall \mathfrak{e}<<\iota$

$(|N\approx pr_{0}\vee e \uparrow^{1}\wedge ese by c^{1}\cap ut.

p>0 m\mathfrak{e}\dagger_{\iota}k_{0}d, |_{\infty}+_{l}e|\vdash)$

(16)

$\gtrless:$

$A_{C}\Rightarrow 0^{\tau}\leq(1_{(\approx,(I_{L}tD)^{1-E})}$

$\supset T:$

.

$\llcorner\{|C’\urcorner\leq$

/

$0<\xi_{-}<<7\forall$

$\theta^{(*)}$

$\theta^{(\approx\rangle}$

b7

$(D,$

$\overline{1}_{L},(0gck/4\approx\overline{\Phi}\llcorner\oint^{(\cross,I_{L}^{1-\zeta}1O_{8}}$

$\Rightarrow d\cdot|\sim t’-$

$b_{\sqrt{}}O^{\underline{T}_{\llcorner}},\cdot\llcorner \mathfrak{l}-\epsilon^{\mathfrak{G}}’$

$S\overline{1}hCQ\theta^{(\cross,r_{\llcorner}^{\iota-\epsilon_{I_{t}^{1-t})}}}\supset$

I

$*\theta^{C\aleph,I_{L})}|-\epsilon\approx I_{R,}$

$I_{\llcorner}c\sigma^{0_{(\cross,\iota_{L}^{\iota-\epsilon_{I_{8}^{\mathfrak{l}-t})}}}}$

/

$0<\vee a<<1$

$\sim\rangle(X, \geq)\backslash \backslash$

A

$c\dagger\tau e\propto r\gtrless$

ez

$Ske+_{1}c\ltimes o_{I}^{L_{1}}pr_{QQ}f\cdot$

\copyright

$( tx\int ecat_{1}’p\mathfrak{l}^{\wedge}ove\Phi Sc\backslash t\eta t\lambda\alpha\vdash l_{k})$

$Ass_{\mathfrak{U}}n_{1}e\cross\approx S_{l}\theta ecR$

$((R,\eta\backslash );con\backslash p_{I}^{1}e\dagger eR_{-}^{\dagger}R\circ+c_{-}k\infty\triangleright.0)$

$R=S_{l}oecS(S=k/I\approx\ulcorner_{L^{C}}R:\iota_{1kb^{\backslash }}A)@_{l}ck\propto r.p>0$

$ETS(t(S^{r},’\backslash \sigma_{L}s_{\forall\forall:})^{C})\subset\tau_{-tR\Re^{t}1^{1-\epsilon}\rangle S}\epsilon\iota^{\underline{c}}R,to,0<^{}\epsilon<<I$

$i_{AQ}1l\mathfrak{c}_{J}\theta_{E_{S}}^{\circ\iota S)^{\zeta}}\supset 0_{E_{R}}^{*0\urcorner_{-{}^{t}I^{\downarrow-\epsilon_{\cap E_{S}}}}}$

$\leq\Psi$

$E_{S^{\backslash }}\backslash \approx\subseteq s^{(S\nearrow \mathfrak{m}S)}/E_{R^{\backslash }}\backslash \simeq\underline{F}_{k}(R\nearrow\eta\iota I_{J}$

$E_{S}l\backslash =(o:I)_{E_{R}}cE_{R}$

$\sigma\iota^{t_{t}^{-}}t_{\wedge}^{\urcorner}(|-t)^{\urcorner}F_{R}^{\zeta}(*)\simeq 0\in p_{R}^{e}(E_{R}1=E_{R}\forall@=P^{e_{7)C}}$

$F_{R}^{e}$

:

$E_{k}arrow+_{R}^{e}(E_{R})\cong$

ER

$p_{s}^{e}$

:

Ei

$s^{-i}F_{S}^{e}(E_{S})$

(17)

$(\beta=p^{e}\backslash$

$Vx_{e_{-s}^{\underline{\ulcorner}}}\backslash |$

,

$F_{S}^{e_{(\xi)=}}0\epsilon F_{S}^{\epsilon_{(E_{S})\not\in)}}(I\backslash \backslash I)F_{R}^{e}$

$\supset R$

(Zl\sim

$s_{1}^{\sim}nce$

$t^{4}\ulcorner bl_{\backslash ,\backslash }$

I

$cI^{b^{\sim I}}cI^{R(1-8)^{\urcorner}}$

,

$g_{\overline{\sim}}p^{e}>>0_{\nearrow}0<Z<<1\forall$

$o\iota^{\ulcorner}*t^{t}$

(I.

$Lb^{1}$

:

I)

$r_{R}\approx 0$

$\Leftrightarrow(\theta\iota B)^{\ulcorner\urcorner}\backslash \triangleright\}1^{-}\sim_{S}^{C}(a)-- O$

,

$\Rightarrow\geq\epsilon o_{E_{S}^{*(\triangleright\iota S)}}t$

/

$t\overline{\sim}be_{>\succ O}$

,

$8-\underline{-}D^{\xi}>>0\downarrow$

za

$(1b^{\backslash }\backslash \mathfrak{H}\not\in RF\hslash’\backslash$

$WF\grave{\iota}tte\mathfrak{n}A_{b}\cdot D\alpha\grave{\llcorner}S\mathfrak{u}keH\grave{c}\vdash 0$

se

(18)

$\ovalbox{\tt\small REJECT}_{\vee^{\backslash \backslash }}Ac\}p\alpha n\propto l_{0}x+\alpha\partial_{10\llcorner\uparrow TC^{\backslash }}\sqrt d_{\delta}(A_{PP}e\mathfrak{n}\partial ix1$

$(R, \mathfrak{m})$

:

F-Si

$\nu\backslash |1^{-}e$

ho

$vmA$

$Q_{bC}A\#$

$ofck\propto V^{4}$

.

$P^{>0}$

$+\tau\cdot 0$

,

Gn

$cR$

,

$t>0$

$t^{d_{t}\vee(R,f^{I}}/\mathfrak{R}^{t})\backslash =A_{hh}Ro_{e}’$

$E:\approx E_{R}(R/\eta_{(})\sim\overline{\sim}H_{\mathfrak{n}}^{\{}(\omega_{k})$

$\approx\epsilon o^{*(f\iota^{k})}s_{R^{O^{C}}}’\prime 6(g_{a}\not\in\forall_{m_{1h}}\cdot$

.

$P^{t\iota^{\backslash }}me$

$\circ\{\nu_{+}$

$s_{\backslash }t$

.

$c\cdot\}^{\S\sim \mathfrak{l}_{\Psi_{L}}^{\ulcorner}}{}^{t}t_{S}^{\urcorner}t\approx o,$

$t\cdot\gamma^{e_{>\rangle 0}}$

$(^{F_{c}^{Q}}-$

If

$R$

is

$\mathfrak{g}_{\sim}G\circ rc4$

$\nu_{\dagger}$

IS

$\mathbb{Q}-\S_{0}\nu e\mathfrak{n}$

,

ho

$\vdash mA$

$\Rightarrow t(\varphi_{+}/(n\Psi_{f\prime}))\approx c^{4_{t}^{\backslash }v}(R\cdot\dagger_{l}^{f}\sigma\iota^{t\rangle R\prime_{f}}$

See

$CT\alpha 3$

]

$+0\vdash\partial ett$

$\underline{E_{X}.}$

$R\approx R\mathfrak{c}\mathfrak{c}X$

,

Ylts

.

$+\simeq\cross Y$

,

$\Re\overline{\sim}R$

$\neg-r^{4_{1\vee(R}}$

,

$\simeq(X, Y)$

$\dot{\backslash }\backslash rightarrow d_{iV}R_{l}f’R)$

$(T-\zeta Tox3J)$

$(R,\Uparrow);\eta ohn_{0}\}1\circ\Phi\lambda\}\cdot ir_{k}ess$

.

$0+f^{\grave{c}}\eta_{L}\backslash tet_{b\Re}\nearrow \mathbb{C}$

$f\star 0\epsilon R,$

$\mathfrak{N}cR,$

$t>0$

$(RS, 0\iota\sim, \sim\sim)$

:

$|-\cdot ed\omega ct_{\mathfrak{l}^{\backslash }}o\eta$

to

$c\Uparrow a$

}

$.p$

))

$o0+(8_{/}f,$

$\infty I$

(19)

$A_{P\}}|_{ic\propto\dagger toh\S}$

of

$\alpha_{\Psi_{I}^{n_{1}}\}_{b}7\overline{\iota}C}\iota_{D}w^{1}$

}

$\iota\backslash \uparrow_{1}^{\backslash }\gamma^{1_{t}er}\backslash |d\mathfrak{e}d_{\backslash }$

)

$s$

$k \cdot I^{1^{\backslash }}|k\prec\#\underline{\iota}k.\frac{\backslash \backslash J}{\star}p_{\grave{K}}^{4}$ $\g_{\tilde{t}^{\iota}\Re_{t}^{t\backslash }}t^{\backslash }’/\llcorner$

Sli

$R*\perp\iota a\mathbb{S}^{\backslash }$ $(b_{e}p_{k\triangleright}\}mth\dagger\triangleright fM\propto tkcm\alpha\uparrow ic\theta_{/}k\gamma usk_{\mathfrak{U}}(y_{\mathfrak{n}\grave{t}Ve\vdash S\iota\uparrow y}\sim$

.

SkzahS

$t\lambda k\epsilon T\propto k\propto a^{\backslash }\iota$

)

$A_{oCk}kP^{\gamma_{O}}P^{er\uparrow_{1}^{\backslash }e_{S}}\dot{o}F$ $m_{A}|t_{1}p^{\mathfrak{l}_{1ek}^{-}}$

$|4e\propto Rs$

(1)

$({\rm Re} s\dagger r\grave{\iota}c_{-\uparrow 10\wedge}-\{\cdot k_{b\iota})$

$\cross:bo|rm\iota 1\mathfrak{Q}^{-}$

Go

re

$k$

.

$\vee\alpha\triangleright.\nearrow \mathbb{C}$

$Sc\cross\cdot$

.

$\mathfrak{n}_{C}rw\iota\ \mathfrak{Q}- G_{0}$

re

$\mathfrak{n}$

.

$c\alpha\vdash\uparrow_{1}^{\backslash }et\partial_{1}v|Sor$

$\theta t_{\sim}^{c}(\mathcal{D}\cross,$

$t>0.$

$A\iota’,,\vee s\not\in\overline{\nearrow}_{\vee}\vee^{\wedge}h3e\overline{s}(\circ Li$

.

$\neq\theta^{(s,\alpha))}C61t-\sim\infty d_{j^{(\chi},S,\alpha\iota^{t}IC_{S^{C}}^{\gamma}}9^{(X,\Theta\iota^{t})\mathcal{O}s}$

$(l)CS_{lA}b_{C\kappa}dd|v^{1}\dagger)$

(De

$w\iota\propto i||- E\overline{t}\mathfrak{n}^{-}L\propto a\propto\}\sim sfe|\Lambda[DE\llcorner 1$

)

$X\backslash .$

\S moo\uparrow \ltimes

$\Rightarrow\theta^{(\sigma t^{S}\%^{t})\subset}\partial^{\mathfrak{c}r^{S})}\theta^{(}\%^{t})$

,

$\forall_{n,i^{c}\cdot 0_{X,}^{v_{S,t>0}}}$

$(M0\kappa_{\lambda e}\_{x_{\theta^{(\sigma\iota^{S}b^{t})\mathfrak{r}}}}^{c\#M_{f}} c.\sum_{\prime x*,,e\epsilon}\theta_{4_{|w\iota}\cross}^{(\mathcal{O}1^{S}}\bigwedge_{J}u>\sim O m_{X^{/\backslash }X})_{\lambda} \theta^{(b^{t}} n_{X_{\prime}X}^{\prime a}))$

$\underline{c}\theta^{(\mathfrak{N}^{S})x\oint(b^{t})_{L}}$

(20)

(3)

$(S\ltimes$

VVN

$n_{1\propto\dagger t}o\ltimes$ $)$

$(\#A$

$(\wedge\S\uparrow\infty\cdot 5\alpha_{4}\vee [M\mathfrak{u}))$

$\cross:s\mathfrak{m}oc+_{I}k$

$=)9^{(\aleph,(\sigma\iota\dagger b))c2=}t\theta^{(X,\alpha\iota^{X}t}\#^{C\cross,t^{4<})}$

$\lambda\star,k=tX^{\backslash }\mu\geq 0$

In

$P^{\alpha t\cdot\gamma_{tCtA}1_{k\triangleright}}$

$\theta^{C\cross,(.\circ 1+^{J}b)^{S+t})C}\theta(\cross, \otimes\iota^{S+})\theta^{(\cross},$

$\frac{sketck_{\circ}f\triangleright r_{99}f^{(1\backslash }}{I}$

$d_{\grave{\iota}\alpha}g$

erlo$

$\sqrt{}$

$\cross\underline{\simeq}\trianglearrow>\cross x\cross$

$k\iota^{-}r\iota ce_{-}X\backslash sn\iota\circ c+k_{/}\triangle\approx x*Xc$

.

:.

$x^{P_{\swarrow}^{t}}$ $\searrow^{p_{c_{X}}}$

$\sim\sim\sim\backslash \cross_{\iota}\Leftarrow X_{11}\cross_{1}arrow\cross\iota_{\psi_{X\cross-\cross}}\cross\aleph_{Z}^{arrow\cross z_{1}}\downarrow S$

,

$\theta\prime r\alpha t4\alpha\gamma p\downarrow$

$(P_{11}^{(yL)^{S}(p_{\overline{\iota}^{\mathfrak{l}}}b)^{t})\mathcal{O}_{\triangle}}arrow l|$

$kese\}\grave{\iota}ct|0\eta tk\mathfrak{n}$

$\uparrow_{1}^{-I}9^{(\cross,\alpha\iota^{S})\cdot p_{\overline{\iota}^{1}\oint\cdot(\cross}},$

$\Rightarrow\theta^{cx,\circ\iota^{S}b^{t})}ck^{(X,0t^{S})\oint(\cross,b^{t})}$

$\varpi\nearrow$

$\underline{E_{X}}$

(

$cf$

[

TW))

$\cross\underline{\sim}Sp_{(\lambda\S}^{Qc\mathbb{C}c_{\lambda},\dot{a}’\prime}\gtrless 3/\sim\not\in S)$

A

$*^{-}S|\mathfrak{n}\backslash \backslash$

?

$\Psi t\simeq cx,$

$A^{\backslash }\cdot b^{3}2,3^{\backslash }\gtrless.1$

es

$S^{3}$

,

$S^{4}I$

$\theta^{(\alpha\iota t=}\infty/$

$\theta^{(}\Re_{a)=(x,t^{\lambda}\prime ba\ll)}^{\sim}$

$,1l$

$\sim\div\oint_{1\dagger}^{(m,)}$

A

$\theta^{(\sigma t^{\frac{1}{a}})^{Z}}$

$\alpha\iota^{\frac{1}{\sim}}\sigma t^{\frac{l}{a}}$

$\chi\epsilon\theta^{(\Re)}$

$xs\theta^{(0’t^{\frac{1}{a}})^{2_{-}}}$

$19$

(21)

$\frac{s_{1\eta q.c\propto se}}{d}$

(

$T-$

[Ta

2))

$(z.)’(S\mathfrak{u}b\alpha.AdIt_{1}^{-}V\mathfrak{l}\dagger yI$

$\cross:$

Q-\S o

$re\nu\iota horm$

di

$\vee ur./C$

9

$J^{\cdot}8^{(\Psi t^{S}b^{t})C}b^{(\theta t^{S})}8^{(\^{\{})_{/}}v_{n,b\underline{c}\mathfrak{c}_{9x,}\forall_{S,L>G}}$

$(_{\mathcal{N}^{-}e}X)$

(3)

$(s_{t\lambda m\mathfrak{m}\propto tiok})$

$\cross:\copyright\sim\S_{ore_{h}}$

.

$borm\propto\#$

VOsb.

$- \Rightarrow\theta^{(\cross}(\sigma\iota\vdash h)t)=\Sigma\oint(\cross.

\alpha\iota^{\lambda’}b^{A})$

$\aleph+/\langle=t$

$>_{\backslash },/x\geq 0$

$L_{h}P^{\propto Vt^{icu}}\cdot|_{K\vdash}$

$Y$

a

$(\searrow, (\sigma\iota+^{t})c_{-\Sigma}\#$

(.X,

$\theta 1^{\wedge}$

)

$\int$

(

$\cross$

,

th

$A\langle$

)

$(J\sim :J^{\cdot}\propto c\Leftrightarrow 1_{1\triangleright\ltimes}\backslash )$

$X,\mu\geq 0$

$\cross+\mu=\backslash$

$Ass*we$

$\cross\simeq s_{pe\circ R}J$

$R\cdot\cdot c\circ w\backslash \triangleright le\dagger eA_{oc\propto}A\circ+ck\alpha^{\psi}\cdot 0$

$arrow ck\nwarrow\triangleright.p>0$

$arrow^{ET}T\cdot T(\sigma\iota S\%)_{C^{-}}\zeta(\psi\iota)T($

$d\ltimes \mathcal{A}(\neg!$

$T(b^{t})\backslash \simeq$

A

$v\iota v\iota 0_{E}^{*b^{t}}$

,

$E_{-R}^{:--p(\%)}$

(

$0_{E^{\theta t^{S}}}*:JI_{\mathbb{E}}\supset(0_{\Xi}:T(\Theta 1^{S}))_{E}\dot{2}O\backslash \iota$

(22)

$*t^{t}$

$\sim\rangle t(\Psi L^{S})$

a

$\in$

O\S

$i.e$

.

$\exists c\epsilon R^{o}s_{\backslash }\backslash$

.

$cb8^{\urcorner}\tau(\circ\iota^{S} )$

$r_{t}$

t.\S 1\S

*\approx O\in

$P^{e_{(\in)}}$

,

$(R^{O_{\backslash =}}\backslash R\backslash UR)I\backslash li\uparrow\dot{k}Wrfif4$

V

$8^{\simeq}P^{\xi}>>0$

$\underline{c|_{\propto\dot{t}M}}$

$\exists deR^{o}s_{\backslash }t$

.

$d\otimes\iota^{r_{\dot{S}}}t^{1}j_{Ct(\sigma)}^{\iota\^{1}\iota^{sLE\forall}8^{\overline{\sim}}P^{\mathfrak{e}}>\rangle 0}$

.

$\prime lf$

we

a

$cce\gamma ttAiSC\uparrow\dot{u}\Re$

$\Rightarrow$

cd

$0\iota^{r_{S}\triangleright\tau}b^{r_{lf^{B}}}-0\epsilon p_{(E)}v_{*\Leftrightarrow P^{a}\rangle>O}$

$–\rangle J\not\in c0_{g^{QS}}^{*b^{t}}$

$\emptyset$

$\underline{E_{X}.}$

$\chi_{f}OlkR\propto k_{0\vee e}$

Ex.

$T\overline{\sim}(X, h\cdot\prime 8^{*})/V_{I^{\underline{\backslash }}}$

(

$\chi_{f}$

us

$\tau 8$

)

$(x|g_{1}*\eta_{\theta^{C\otimes 1)c}}9^{(\otimes t^{\frac{1}{\lambda})_{\lambda}^{\perp}}}$

(X

$t8^{R1}’\theta_{*1}^{(\sigma tIk\mathfrak{g}.(\theta 1^{\frac{1}{L}})^{\frac{1}{L}}}$

$x*$

$\frac{A_{\backslash 1A}ymt\circ p_{I}c\mathfrak{m}1t1\triangleright \mathfrak{l}_{1}er}{II}$

AA

(See

$\Gamma ELS]0\mathfrak{t}CL\sigma_{\backslash }\neg\angle Jjo\vdash\sqrt eb^{\backslash }|ls$

)

$X:@\sim e_{\circ re\mathfrak{n}}\cdot horm\alpha \mathfrak{g}v\propto r$

.

$\mathfrak{R}\cdot$

:

$3^{r\propto M}f\cdot 1\backslash$

of

$|4e\propto A_{l}o\nu\backslash \aleph$

$i.e$

.

$\infty.=fn_{n\backslash }\}_{b\in \mathbb{N}}$

$m_{0}=0_{\gamma,}\infty_{1}*O,$

$\mathfrak{R}mc(0x$

$\Re R\cdot\Re_{kC}$

(SYI.

$a*t,$

$\forall R,2\in \mathfrak{l}/\backslash$

(23)

$t>0\{\backslash$

$\int-(.\alpha_{t\S c^{p_{\overline{1}}^{S})>}}\partial^{(((0lg))\iota}Q\not\in)\sim\sim 8^{\mathfrak{c}\Re_{R}^{\backslash }})$

$\approx\{\theta(\sigma\iota_{m^{\frac{t}{m}}})\}_{\mathfrak{m}eW}k\alpha.\S$

$\propto$

$\mathfrak{U}h|q\mathfrak{u}em\propto x\cdot e^{1em_{Ch\uparrow}}$

$w$

.

$r\cdot t$

.

$i$

hc

$|_{\mathfrak{U}\S to}$

va.

$De\eta 0\uparrow e\overline{\iota}$

\dagger

$b_{7}8^{C\Theta u^{t})}$

$\underline{F_{\sim X}.}$

$(\{)\Re_{m}:=\otimes\tau^{w\iota}$

,

$\theta\iota\underline{c}O_{X}$

$\Leftrightarrow 8^{(\mathfrak{R}^{\dagger})\overline{\sim}}9^{(\sigma\iota^{t})}$

(x)

$\llcorner:[;\nu\iota e\propto rs\gamma\approx tew\iota$

,

$m_{m^{\backslash }}\backslash \simeq h(|mL|):b\nwarrow seik\alpha \mathfrak{g}$

of

$|$

tu

L

I

$=)\theta^{(61^{T})--=}\theta^{Ct1\mathfrak{l}L|1)}\backslash$

(3)

$\cross=s_{P^{ecR}},$

$p_{cR:p\triangleright t\gamma\gamma\backslash e}\backslash A\mathbb{A}A$

$\otimes_{m}:=R^{(m)}:\sim\sim E^{\eta}R_{h}\cap R$

$\Leftrightarrow\theta^{C61^{T})==}\theta^{(t}$

.

$E^{(\cdot)}$

)

$\frac{B\backslash r_{0}}{I1}$

$(\{)$

.

$t_{1}>t_{t}\overline{\sim}\rangle$

$\theta^{(n^{t\prime})c}\theta^{(\otimes\iota^{t_{a)}}}$

.

$(l)$

.

$\theta_{L}\cdot/\prime b\cdot$

,

$r+0*^{S}C^{Q}C2x\S_{\backslash }t$

.

$C\Theta$

)

$wch$

vn

,

$\forall \mathfrak{m}>>0$

$\Rightarrow 9^{(\varpi^{t})c}9^{\zeta Q_{3}^{t})}$

(24)

(S).

$\infty$

a

$\theta^{(\alpha\iota^{Q})}c9^{(\Re^{R\^{Q}})}\backslash$

.

/

$R$

,

Q.

$\in\ltimes\backslash$

$Ir$

ptbt

$\iota c^{1_{\mathfrak{g}_{\backslash }\triangleright}}\iota\iota,$

$\overline{|}^{r}f\cross k\omega\circ_{h}|_{f}q_{A}$

$S^{i}h3$

(

$e\theta$

(Ox

$t\simeq(0x)$

$\Rightarrow\alpha\iota fi^{C}\theta^{(\otimes\tau^{t})}/\forall_{Re}M$

$(+).$

(

$Restri$

cf

$to\mathfrak{y}$

)

$S:\eta oW\alpha\lambda\alpha-\S ok\mathfrak{n}C\alpha$

}

$t\mathfrak{i}e\vdash d;viso\vdash orX$

$\#(s, (\alpha.0_{S})^{\iota})ck^{(X,O^{t})0_{S}}$

$(v_{l701}$

(H)

$.$

(

$S_{1A}k_{\iota}4i_{\dot{t}}$

ti

$V\mathfrak{l}i\dot{y}$

)

$Tc\otimes_{X}$

:

$T_{kCo}k_{t\propto 4}\grave{\lambda}AA$

$T^{Aarrow 1\oint(\emptyset t^{l9}\rangle}c\theta^{(\otimes).)^{q}}nearrow R_{J}\lambda e\mathbb{N}$

$(\zeta).(Summ\propto ti^{Q}\ltimes I$

$( \theta\downarrow.+\%.)_{m}:\approx\S\sum_{cdot t\mathfrak{m}^{\Re R}}.\cdot\alpha\not\subset$

$\ell.))c\sum_{\lambda+\mu\cdot t}\theta^{(\emptyset\iota^{\cross}b^{\mu})}$

$(\nabla)$

.

$0*3QcCo_{X}$

$S,t$

.

$\mathbb{C}\mathfrak{N}w^{c}\oint(\%.m)$

$\forall \mathfrak{m}>>0$

$\Rightarrow T\cdot\Phi m^{C}\theta^{(!}b^{b})$

$\forall \mathfrak{m}\Leftarrow R|$ $( Jc0_{l} :J\alpha^{\backslash }\llcorner 0^{\phi_{\backslash }}\triangleright t\alpha t\cdot|\grave{\iota}\oint\Phi’)$

$sA_{or\uparrow}pr_{oQ}+$

$(l)$

.

$9^{(o\iota^{+})=}\theta^{(\otimes 1\nu\nu^{\frac{t}{\iota^{\wedge}}}}$

)

$\overline{rightarrow}\theta^{(e^{\frac{\star}{n\backslash }}m_{n\iota^{\frac{t}{w\backslash }}})}$

$C\theta^{(b_{w^{\frac{t}{\backslash ^{r}}}})c}’\theta^{(b^{\{})}\eta\backslash \rangle)_{Q}$

$(\nabla)$

.

$CT^{A}\otimes\tau_{m^{C}}^{R}ey_{\mathfrak{G}\backslash \mathfrak{n}^{Q}}$

.

$\Gamma$

usa

$sA\alpha idif\dot{t}V\grave{t}t*$

$cJ^{R}\theta(/b^{rA}1c\theta^{(\Phi^{W})^{R},}$

$\lambda>>0$

$\Rightarrow T^{y}\iota\Uparrow c\theta^{(b^{w}T=}\theta^{Cb^{r})}$

%

(25)

$(Sw\propto\nu\backslash S\circ\ltimes rs\omega])f*$

.

$\mathfrak{n}0\vdash \mathfrak{m}\theta 40\eta\alpha i\eta$

$R\supset R$

:

$P$

1

$W\backslash e$

a

$R=R_{CE)\sigma}\mathbb{N}S\cdot t$

.

$R^{(Rm)}cR^{m}$

$\forall$

}

$\mathfrak{n}\in \mathbb{N}$

Q.

$Nk\propto t$

is

$R$

?

$\underline{Tkm}CE.- e$

$R:r_{\zeta}J^{\iota_{A}\mathfrak{l}\alpha\triangleright}uH_{\overline{1}he}do\nu_{A1th}\backslash \nearrow \mathbb{C}$

$(\cdot f_{\lambda}\cdot\alpha A_{8}\cdot over\mathbb{C}I$

$RcR:P^{\triangleright 1}$

me

$0\{k\uparrow$

.

A

$\sim\rangle-R^{c\S m)}cA^{w\iota}$

,

$V_{m\in N}$

$(\dot{\iota}.e. ficE)=$

ht

R)

Tkm

$(H_{oC}k\kappa ter^{-}H\iota_{A}.\mathfrak{n}eke\dot{[}HH1])$

$R$

:

$t\cdot eJ^{\mathfrak{U}}|_{1\triangleright}V^{4}i\nu|J$

of

$\cdot$ $\epsilon_{?^{\ltimes\theta}}ck\infty\triangleright$

.

$/fcR$

:

$P$

}

$ireo\dagger be*$

.

$R^{(\w\iota)}c$

$R^{m},$

$\forall \mathfrak{m}e\#t$

$s_{i\eta pukabc\propto se^{-}}$

Thm

$(T-[T\alpha 2])$

$R:\theta_{\iota \mathfrak{n}e}4_{om\propto i\mathfrak{n}/R}/R:p_{8\triangleright\{}ec\rceil\cdot+_{ie}\{J$

$\circ+\backslash ku\triangleright.\mathfrak{p}>0$

$\epsilon_{c}$

.

$R$

:

pri

$mcot$

At

$,

$T^{c}R:]_{RCo}^{-}b_{1\propto h}\dot{\mathcal{A}}\mathbb{A}_{\alpha}Q$

$=7J^{\eta\vdash 1}t(R)E^{(h\mathfrak{n})_{C}}B^{\mathfrak{m}}$

$\forall\psi\backslash e\mathbb{N}$

(26)

$\frac{pr_{oo}f\circ fELS}{l}$

$R^{(\cdot)}$

$:\approx\uparrow E^{(b)}\}_{Wt\Leftarrow\aleph}$

$R^{(lm1}c$

fl

wt

$R^{t\cdot 1}$

)

$c\theta^{(\lambda\cdot R^{(\cdot)})^{\eta}}$

$\theta^{(\#\iota\cdot R^{(\cdot)})}c$

.E2

$\theta^{(\%\cdot.R^{(\cdot I})g}\underline{rightarrow}\theta^{(cdot R^{t}Rp1}$

$=\theta^{((ER_{R}))}RcRRg$

$\wedge\div\theta^{(\#\iota\cdot E^{t\cdot)}I}c$

R.

8/

$\frac{P^{t_{Q}\circ\dagger\dagger\S i^{\gamma}\iota q.c\infty e}Q}{\lrcorner}$

$R^{(\cdot)}$

$:\approx\{.R^{(b)}\}_{b\sigma N}$

$I^{-m-l_{\oint(}}R)R^{tim)}C\theta^{(fim\cdot\underline{P}^{(\cdot)})J^{m-|}}$

$c\frac{\theta^{(h.E^{t\cdot 1})}}{\cap}$

wt

$R$

$\ovalbox{\tt\small REJECT}$

$\iota+R|SsP^{cc\iota\propto}-$

S2,

$C\alpha r$

we

$J^{e\uparrow}\propto b_{e}\eta_{e\triangleright}b_{01A}.\nu\backslash A$

?

$\ovalbox{\tt\small REJECT}$

(HocAstef-Hun&e

$\zeta HHz3,$

$T-Yo4ii\alpha[TY3$

)

$R:\}c_{\hslash^{\alpha\lambda\alpha r\vdash i\mathfrak{n}_{k^{0}fe*\mathcal{M}c\wedge a\triangleright}}}$

.

2

$cp;pVime$

of

At

$\hslash 22$

$I\neq R4\grave{\iota}SF-P^{4\}e}o\vdash 0\neq dms_{C}F- p\alpha ktg\gamma e(Sce\cdot\cdot CH\mathfrak{u}3)$

$3R^{tR^{\etarightarrow 1)}}c$

A

$\mathfrak{n}$

V

$\mathfrak{m}\epsilon$

IN

(Jt

$\backslash ,\backslash f\not\in K\not\in\#,*\backslash \Phi\wedge\ovalbox{\tt\small REJECT}_{0}^{\backslash ;}d$

)

(27)

References

[B1]

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on

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A subadditivity property

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