The name is absent

After collecting terms

{ι+ɪ rφ
⁺ {^-2⅛J '

f ∖ ^c∖ — 1φ /∖ ^c∖ [Bkr + 2X_cr + r² + ∆σ2]1 l
σv       2σv       σv

( —^c---) [Bkr + 2cr + r² + ∆σ² ] +

[X_c —

σ_υ

dc

φ' (—c) [Bkr + 2X_cr + r² + ∆σ2] I

dσ_v

dc

+ I-Λ φfXc-^ )

I ^2σV ∖ ^σv J L

Bkr + 2cr + r² + ∆σ2 —

^[Xc ^—
σ²
σ_v

— [Bkr + 2X_cr + r² + ∆σ,2] j>

dσ_v

The second line uses φ'(x) = -xφ(x). If X_c is as defined above, we know that φ (⅜-ⁱ) = Φ(1)-

Using this in the derivative we get

dc

—2 [Bkr + 2cr + r² + ∆σ² — Bkr — 2X_cr — r² — ∆σ² ]

^2σv ^{l u u}t

dσ_v

₁ I φ(1) I

1 + _ r +
σv

ɪ [Bkr + 2X_cr + r² + ∆σ2 ]
2σv l                                            ^u-∣

1 + ^φ(¹) r + ɪ [Bkr + 2X_cr + r² + ∆σ²]
σ_v           2,σ_v ^{l                c                   uj}

—rφ(1)

σ_v + φ(1) r + ɪ [Bkr +

kσv [ J -B]+2σV-2rσv[1-Φ(1)]-φ(1)[Bkr+r²+∆σ² ]

[rφ(1)+σv ]

r + r² + ∆σ² ]

The last term of the denominator becomes

1

r + ---[Bkr +

1

kσv [¹ - Bl + 2σ2 - 2rσ_υ [1 - Φ(1)] - φ(1)[Bkr + r² + ∆σ² ]     _{2      2}

------------------------------------------------------------r + r² + ∆σ* ]

[rφ(1) + σ_υ ]

2σ_v [rφ(1) + σ_v ]

1

2σv [rφ(1) + σ_v ]

^2σ_υ r[rφ(1) + σ_υ ] + Bkr [rφ(1) + σ_υ ] + krσ_υ - - B j + 2rσ2 - 2r² σ_υ [1 - Φ(1)] - rφ(1)[Bkr + r² + ∆σj ] + [r² + ∆σj ] [rφ(1) + σ_υ ]j
Bkrσv + krσv - b] + 4rσV + 2r²σ^[Φ(1) + φ(1) - 1] + σ_v [r² + ∆σ^ ]] > 0

k rɪ

z∞

-∞

• (⅛^c )l

+ —— φ (— ^cʌ) [Bkr + 2Xcr + r² + ∆σ²] h(X,.)dX,. = 0

2σ_v ∖ σ_υ J^l-

32