Citation: Fitriani Tupa R. Silalahi, Togar M. Simatupang, Manahan P. Siallagan. A system dynamics approach to biodiesel fund management in Indonesia[J]. AIMS Energy, 2020, 8(6): 1173-1198. doi: 10.3934/energy.2020.6.1173
[1] |
Kengo Matsumoto .
|
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On |
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In [22] and [23], D. Ruelle has introduced the notion of Smale space. A Smale space is a hyperbolic dynamical system with local product structure. He has constructed groupoids and its operator algebras from the Smale spaces. After the Ruelle's initial study, I. Putnam in [14] (cf. [9], [15], [16], [17], [26], etc.) constructed various groupoids from Smale spaces and studied their
In this paper, we will focus on the study of the latter class, the hyperbolic toral automorphisms from the view points of
d(x,y)=inf{‖z−w‖:q(z)=x,q(w)=y,z,w∈R2} for x,y∈T2 |
where
GaA={(x,z)∈T2×T2∣limn→∞d(Anx,Anz)=limn→∞d(A−nx,A−nz)=0} | (1) |
with its unit space
(GaA)(0)={(x,x)∈T2×T2}=T2. | (2) |
The multiplication and the inverse operation on
(x,z)(z,w)=(x,w),(x,z)−1=(z,x) for (x,z),(z,w)∈GaA. |
As in [14], the groupoid
Let
Theorem 1.1 (Theorem 2.10 and Proposition 3.1). The
U1U2=U2U1,V1V2=V2V1,V1U1=e2πiθ1U1V1,V1U2=e2πiθ2U2V1,V2U1=e2πiθ3U1V2,V2U2=e2πiθ4U2V2, |
where
θ1=12(1+a−d√Δ(A)),θ2=c√Δ(A),θ3=b√Δ(A),θ4=12(1−a−d√Δ(A)). |
The range
τ∗(K0(C∗(GaA)))=Z+Zθ1+Zθ2+Zθ3inR. | (3) |
We note that the slopes
Since the étale groupoid
As commuting matrices have common eigenvectors, we know that if two matrices
For a vector
rA:=⟨vu|vs⟩. |
Define two vectors
v1:=vu−rAvs,v2:=rAvu−vs. |
Lemma 2.1. For two vectors
(ⅰ)
(ⅱ)
(ⅲ)
Proof. For two vectors
z≡x+tvu≡x+svs(modZ2) for some t,s∈R. | (4) |
In this case, we see that
⟨tvu−svs|vu⟩=⟨(m,n)|vu⟩, | (5) |
⟨tvu−svs|vs⟩=⟨(m,n)|vs⟩ | (6) |
and we have
t=11−r2A⟨(m,n)|v1⟩,s=11−r2A⟨(m,n)|v2⟩. | (7) |
This shows the implications (ⅰ)
Assume that (ⅱ) holds. By putting
Let us define an action
αA(m,n)(x):=x+11−r2A⟨(m,n)|v1⟩vu,(m,n)∈Z2,x∈T2. |
For a fixed
Lemma 2.2. Keep the above notation.
(ⅰ) If
(ⅱ) For
Proof. (ⅰ) Suppose that
(ⅱ) Let
{x+11−r2A⟨(m,n)|v1⟩vu∣(m,n)∈Z2} |
is dense in
The action
If a discrete group
Proposition 2.3. The étale groupoid
T2×αAZ2={(x,αA(m,n)(x))∈T2×T2|(m,n)∈Z2} |
defined by the action
Proof. By the preceding discussions, a pair
Remark 2.4. Define a map
αA(m,n):=11−r2A⟨(m,n)|v1⟩vu,(m,n)∈Z2. | (8) |
It is easy to see that the étale groupoid
GaA=T2×αA(Z2) | (9) |
as a transformation groupoid.
We set
θ1:=u1s2u1s2−u2s1,θ2:=u2s2u1s2−u2s1, | (10) |
θ3:=−u1s1u1s2−u2s1,θ4:=−u2s1u1s2−u2s1. | (11) |
Lemma 2.5. The real numbers
θ2θ1=θ4θ3=u2u1,θ1θ3=θ2θ4=−s2s1, | (12) |
θ1+θ4=1. | (13) |
Conversely, if real numbers
ζ2ζ1=ζ4ζ3=u2u1,ζ1ζ3=ζ2ζ4=−s2s1, | (14) |
ζ1+ζ4=1, | (15) |
then we have
Proof. The identities (12) and (13) are immediate. Conversely, suppose that real numbers
{u2u1(−s2s1)+1}ζ4=1, |
so that
ζ4=−u2s1u1s2−u2s1 |
and hence
ζ1=u1s2u1s2−u2s1,ζ2=u2s2u1s2−u2s1,ζ3=−u1s1u1s2−u2s1. |
Proposition 2.6. For
αA(1,0)(x1,x2)=(x1+θ1,x2+θ2),αA(0,1)(x1,x2)=(x1+θ3,x2+θ4), |
and hence
αA(m,n)(x1,x2)=(x1+mθ1+nθ3,x2+mθ2+nθ4)for(m,n)∈Z2. |
Proof. We have
αA(m,n)(x1,x2)=(x1,x2)+11−r2A⟨(m,n)|vu−rAvs⟩vu=(x1,x2)+11−r2A⟨(m,n)|(u1−rAs1,u2−rAs2)⟩(u1,u2). |
In particular, for
αA(1,0)(x1,x2)=(x1+11−r2A(u1−rAs1)u1,x2+11−r2A(u1−rAs1)u2),αA(0,1)(x1,x2)=(x1+11−r2A(u2−rAs2)u1,x2+11−r2A(u2−rAs2)u2). |
We put
αA(1,0)(x1,x2)=(x1+ξ1u1,x2+ξ1u2), | (16) |
αA(0,1)(x1,x2)=(x1+ξ2u1,x2+ξ2u2). | (17) |
We then have
ξ1=11−r2A{u1−(u1s1+u2s2)s1}=11−r2A{u1(1−s21)−u2s2s1}=11−r2A(u1s2−u2s1)s2 |
and similarly
ξ2=11−r2A{u2−(u1s1+u2s2)s2}=11−r2A{u2(1−s22)−u1s1s2}=11−r2A(u2s1−u1s2)s1. |
Hence we have
ξ1u1+ξ2u2=11−r2A{(u1−rAs1)u1+(u2−rAs2)u2}=11−r2A{u21+u22−rA(u1s1+u2s2)}=11−r2A(1−r2A)=1. |
By Lemma 2.5, we have
We will next express
Lemma 2.7. The following identities hold.
(ⅰ)
\begin{gather*} a\theta_1 + b \theta_2 = \lambda_u \theta_1, \qquad a\theta_3 + b \theta_4 = \lambda_u \theta_3, \\ c\theta_1 + d \theta_2 = \lambda_u \theta_2, \qquad c\theta_3 + d \theta_4 = \lambda_u \theta_4, \end{gather*} |
and hence
\begin{equation} a\theta_1 + b \theta_2 + c\theta_3 + d \theta_4 = \lambda_u. \end{equation} | (18) |
(ⅱ)
\begin{gather*} a\theta_3 - b \theta_1 = \lambda_s \theta_3, \qquad a\theta_4 - b \theta_2 = \lambda_s \theta_4, \\ c\theta_3 - d \theta_1 = -\lambda_s \theta_1, \qquad c\theta_4 - d \theta_2 = -\lambda_s \theta_2, \end{gather*} |
and hence
\begin{equation*} a\theta_4 - b \theta_2 - c\theta_3 + d \theta_1 = \lambda_s. \label{eq:abcds} \end{equation*} |
Proof. By the identities
\begin{gather*} {\begin{bmatrix} \theta_1\\ \theta_2 \end{bmatrix}} = \frac{ s_2}{u_1 s_2 - u_2 s_1} {\begin{bmatrix} u_1\\ u_2 \end{bmatrix}}, \qquad {\begin{bmatrix} \theta_3\\ \theta_4 \end{bmatrix}} = \frac{ -s_1}{u_1 s_2 - u_2 s_1} {\begin{bmatrix} u_1\\ u_2 \end{bmatrix}}, \\ {\begin{bmatrix} \theta_3\\ -\theta_1 \end{bmatrix}} = \frac{ -u_1}{u_1 s_2 - u_2 s_1} {\begin{bmatrix} s_1\\ s_2 \end{bmatrix}}, \qquad {\begin{bmatrix} \theta_4\\ -\theta_2 \end{bmatrix}} = \frac{ -u_2}{u_1 s_2 - u_2 s_1} {\begin{bmatrix} s_1\\ s_2 \end{bmatrix}}, \end{gather*} |
with
Lemma 2.8.
(ⅰ)
(ⅱ)
Hence we have
\begin{equation*} b \theta_2 = c \theta_3. \end{equation*} |
Proof. (ⅰ) By the first and the fourth identities in Lemma 2.7 (ⅰ), we know the identity (ⅰ). The identities of (ⅱ) is similarly shown to those of (ⅰ). By (ⅰ) and (ⅱ) with the identity
Recall that
Lemma 2.9. The identities
\begin{gather*} \theta_1\cdot \theta_4 = \theta_2\cdot \theta_3, \qquad \theta_1 +\theta_4 = 1,\\ (a\theta_1 + b \theta_2) \theta_4 = (c\theta_3 + d \theta_4) \theta_1, \qquad (a\theta_3 - b \theta_1) \theta_2 = (-c\theta_4 + d \theta_2) \theta_3 \end{gather*} |
imply
\begin{align} &(\theta_1, \theta_2,\theta_3,\theta_4) \end{align} | (19) |
\begin{align} = & \begin{cases} \left( \frac{1}{2}( 1 + \frac{|a-d|}{\sqrt{\Delta(A)}}), \frac{|a-d|}{a-d}\frac{c}{\sqrt{\Delta(A)}}, \frac{|a-d|}{a-d}\frac{b}{\sqrt{\Delta(A)}}, \frac{1}{2}( 1 - \frac{|a-d|}{\sqrt{\Delta(A)}}) \right) & \mathit{\text{or}}\\ \left( \frac{1}{2}( 1 - \frac{|a-d|}{\sqrt{\Delta(A)}}), -\frac{|a-d|}{a-d}\frac{c}{\sqrt{\Delta(A)}}, -\frac{|a-d|}{a-d}\frac{b}{\sqrt{\Delta(A)}}, \frac{1}{2}( 1 + \frac{|a-d|}{\sqrt{\Delta(A)}} ) \right) & \mathit{\text{if}}\; a \ne d,\\ (\frac{1}{2}, \frac{1}{2}\sqrt{\frac{c}{b}},\frac{1}{2}\sqrt{\frac{b}{c}}, \frac{1}{2}) & \mathit{\text{or}}\\ (\frac{1}{2}, -\frac{1}{2}\sqrt{\frac{c}{b}},-\frac{1}{2}\sqrt{\frac{b}{c}}, \frac{1}{2}) & \mathit{\text{if}} \;a = d. \end{cases} \end{align} | (20) |
We thus have the following theorem.
Theorem 2.10. The
\begin{gather*} U_1 U_2 = U_2 U_1,\qquad V_1 V_2 = V_2 V_1, \\ V_1 U_1 = e^{2\pi i \theta_1}U_1 V_1, \qquad V_1 U_2 = e^{2\pi i \theta_2}U_2 V_1, \\ V_2 U_1 = e^{2\pi i \theta_3}U_1 V_2, \qquad V_2 U_2 = e^{2\pi i \theta_4}U_2 V_2, \end{gather*} |
where
\begin{equation} \theta_1 = \frac{1}{2}( 1 + \frac{a-d}{\sqrt{\Delta(A)}}), \quad \theta_2 = \frac{c}{\sqrt{\Delta(A)}}, \quad \theta_3 = \frac{b}{\sqrt{\Delta(A)}}, \quad \theta_4 = \frac{1}{2}( 1 - \frac{a-d}{\sqrt{\Delta(A)}}). \end{equation} | (21) |
Hence the
Proof. As in Lemma 2.2, the action
Since the
Proposition 2.11 (Slawny [24], Putnam [14]). The
Remark 2.12. (ⅰ) We note that the simplicity of the algebra
(ⅱ) Suppose that two hyperbolic matrices
In this section, we will describe the trace values
In [20], M. A. Rieffel studied K-theory for irrational rotation
\begin{equation*} K_0(C( \mathbb{T}^2)\times_{\alpha^A} \mathbb{Z}^2) \cong K_1(C( \mathbb{T}^2)\times_{\alpha^A} \mathbb{Z}^2) \cong \mathbb{Z}^8 \end{equation*} |
([6], cf. [24]). For
\begin{equation*} (a_1, b_1, a_2, b_2) \wedge (c_1, d_1, c_2, d_2) = \left( \begin{vmatrix} a_1 & c_1 \\ b_1 & d_1 \end{vmatrix}, \begin{vmatrix} a_1 & c_1 \\ b_2 & d_2 \end{vmatrix}, \begin{vmatrix} a_2 & c_2 \\ b_1 & d_1 \end{vmatrix}, \begin{vmatrix} a_2 & c_2 \\ b_2 & d_2 \end{vmatrix} \right) \end{equation*} |
where
(\Theta\wedge\Theta) (x_1\wedge x_2)\wedge(x_3\wedge x_4) = \frac{1}{2!2!} \sum\limits_{\sigma\in \frak{S}_4} \operatorname{sgn}(\sigma) \Theta(x_{\sigma(1)}\wedge x_{\sigma(2)})\Theta(x_{\sigma(3)}\wedge x_{\sigma(4)}) |
for
{{{\operatorname{exp}}}}_\wedge(\Theta) = 1 \oplus \Theta \oplus \frac{1}{2}(\Theta\wedge\Theta) \oplus \frac{1}{6}(\Theta\wedge\Theta\wedge\Theta) \oplus \cdots: \wedge^{\operatorname{even}} \mathbb{Z}^4 \longrightarrow \mathbb{R} |
becomes
{{{\operatorname{exp}}}}_\wedge(\Theta) = 1 \oplus \Theta \oplus \frac{1}{2}(\Theta\wedge\Theta). |
Let
\begin{equation} {{{\operatorname{exp}}}}_\wedge(\Theta)(\wedge^{\operatorname{even}} \mathbb{Z}^4) = \tau_*(K_0(A_\Theta)). \end{equation} | (22) |
Proposition 3.1. Let
\begin{equation} \tau_*(K_0(C^*(G_A^a))) = \mathbb{Z} + \mathbb{Z}\theta_1 + \mathbb{Z}\theta_2 + \mathbb{Z}\theta_3 \quad\mathit{\text{in}} \mathbb{R}. \end{equation} | (23) |
Proof. Take the unitaries
u_j u_k = e^{2\pi i \theta_{jk}} u_k u_j, \qquad j,k = 1,2,3,4. |
As
\begin{equation*} \theta_{12} \theta_{34} -\theta_{13}\theta_{24} + \theta_{14}\theta_{23} = 0. \end{equation*} |
By (22) or [6] (cf. [3,2.21], [13,Theorem 3.9]), we have
\begin{align*} \tau_*(K_0(C^*(G_A^a))) = & \mathbb{Z} + \mathbb{Z}(\theta_{12} \theta_{34} -\theta_{13}\theta_{24} + \theta_{14}\theta_{23} ) + \sum\limits_{1\le j < k\le 4} \mathbb{Z}\theta_{jk} \\ = & \mathbb{Z} + \mathbb{Z}\theta_1+ \mathbb{Z}\theta_2+ \mathbb{Z}\theta_3. \end{align*} |
Remark 3.2. (ⅰ) It is straightforward to see that the skew symmetric matrix
(ⅱ) Suppose that two hyperbolic toral automorphisms
\tau_{A*}(K_0(C^*(G_A^a))) = \tau_{B*}(K_0(C^*(G_B^a))). |
We may also find a matrix
In this section, we will present some examples.
1.
\begin{equation} (\theta_1, \theta_2,\theta_3,\theta_4) = (\frac{1}{2}(1+\frac{1}{\sqrt{5}}), \frac{1}{\sqrt{5}}, \frac{1}{\sqrt{5}}, \frac{1}{2}(5-\frac{1}{\sqrt{5}}). \end{equation} | (24) |
By the formula (23), we have
\begin{equation*} \tau_*(K_0(C^*(G_A^a))) = \mathbb{Z} + \frac{5 + \sqrt{5}}{10} \mathbb{Z}. \end{equation*} |
Proposition 4.1. Let
Proof. Let
(\theta_1, \theta_2,\theta_3,\theta_4) = (\theta, 2\theta -1,2\theta -1,1-\theta) |
by (24), we have
\begin{gather*} U_1 U_2 = U_2 U_1,\qquad V_1 V_2 = V_2 V_1, \\ V_1 U_1 = e^{2\pi i \theta}U_1 V_1, \qquad V_1 U_2 = e^{2\pi i 2 \theta}U_2 V_1, \\ V_2 U_1 = e^{2\pi i 2\theta}U_1 V_2, \qquad V_2 U_2 = e^{-2\pi i \theta}U_2 V_2, \end{gather*} |
We set
u_1 = U_1 U_2^2, \qquad u_2 = U_2, \qquad v_1 = V_1 V_2^2, \qquad v_2 = V_2. |
It is straightforward to see that the following equalities hold
\begin{gather*} u_1 u_2 = u_2 u_1,\qquad v_1 v_2 = v_2 v_1, \\ v_1 u_1 = e^{2\pi i 5\theta}u_1 v_1, \qquad v_1 u_2 = u_2 v_1, \\ v_2 u_1 = u_1 v_2, \qquad v_2 u_2 = e^{-2\pi i \theta}u_2 v_2. \end{gather*} |
Since the
\begin{equation*} C^*(G_A^a)\cong C^*(u_1, v_1) \otimes C^*(u_2, v_2) \cong A_{5\theta} \otimes A_\theta. \end{equation*} |
2.
(\theta_1, \theta_2,\theta_3,\theta_4) = (\frac{3+\sqrt{3}}{6}, \frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{6}, \frac{3-\sqrt{3}}{6}) |
and
\lambda_u = a \theta_1 + b \theta_2 + c\theta_3 + d \theta_4 = 2 + \sqrt{3}, \qquad \lambda_s = a \theta_4 - b \theta_2 - c\theta_3 + d \theta_1 = 2 - \sqrt{3}. |
Since
\begin{equation*} \tau_*(K_0(C^*(G_A^a))) = \mathbb{Z} + \mathbb{Z}\theta_1 + \mathbb{Z} \theta_2 + \mathbb{Z} \theta_3 = \frac{1}{2} \mathbb{Z} + \frac{\sqrt{3}}{6} \mathbb{Z}. \end{equation*} |
Proposition 4.2. Let
Proof. Since the
\tau_*(K_0(C^*(G_{A_1}^a))) = \mathbb{Z} + \frac{5+\sqrt{5}}{10} \mathbb{Z}, \qquad \tau_*(K_0(C^*(G_{A_1}^a))) = \frac{1}{2} \mathbb{Z} + \frac{\sqrt{3}}{6} \mathbb{Z}, |
we see that
The author would like to deeply thank the referee for careful reading and lots of helpful advices in the presentation of the paper. This work was supported by JSPS KAKENHI Grant Numbers 15K04896, 19K03537.
[1] | Abokyi E, Appiah-Konadu P, Abokyi F (2019) Industrial growth and emissions of CO2 in Ghana: The role of financial development and fossil fuel consumption. Energy Reports 5: 1339-1353. |
[2] | EPA (2009) Opportunities to reduce greenhouse gas emissions through materials and land management practices. U.S. environmental protection agency. |
[3] | EPA (2020) Global greenhouse gas emissions data. United states environmental protection agency. |
[4] | Bimanatya TE (2018) Fossil fuels consumption, carbon emissions, and economic growth in Indonesia. Int J Energy Econ Policy 8: 90-97. |
[5] | MEMR (2019) Handbook of energy and economic statistics of Indonesia 2018. Jakarta: Ministry of energy and mineral resources republic of Indonesia. |
[6] | Živković SB, Veljković MV, Banković-Ilić IB, et al. (2017) Technological, technical, economic, environmental, social, human health risk, toxicological and policy considerations of biodiesel production and use. Renewable Sustainable Energy Rev 79: 222-247. |
[7] | GoI (2014) Government regulation no 79 of 2014 about national energy policy. President of republic Indonesia. |
[8] | Silalahi FTR, Simatupang TM, Siallagan MP (2019) Biodiesel produced from palm oil in Indonesia: Current status and opportunities. AIMS Energy 8: 81-101. |
[9] | Fauzia M (2018) Oil and gas imports contribute to the biggest deficit of trade balance deficit kompas.com. Available from: https://ekonomi.kompas.com/read/2018/09/17/150041626/impor-migas-sumbang-penyebab-terbesar-defisit-neraca-perdagangan. |
[10] | MEMR (2015) MEMR regulation number 12 of 2015. In: MEMR, editor. Jakarta: MEMR. |
[11] | OEC (2020) Palm oil. Available from: https://oec.world/en/profile/hs92/1511/. |
[12] | Basri Wahid M, Abdullah SNA, Henson IJPPS (2005) Oil palm-achievements and potential. Plant Prod Sci 8: 288-297. |
[13] | Espinoza A, Bautista S, Narváez P, et al. (2017) Sustainability assessment to support governmental biodiesel policy in Colombia: A system dynamics model. J Cleaner Prod 141: 1145-1163. |
[14] | Moncada JA, Junginger M, Lukszo Z, et al. (2017) Exploring path dependence, policy interactions, and actor behavior in the German biodiesel supply chain. Appl Energy 195: 370-381. |
[15] | Barisa A, Romagnoli F, Blumberga A, et al. (2015) Future biodiesel policy designs and consumption patterns in Latvia: a system dynamics model. J Cleaner Prod 88: 71-82. |
[16] | Musango JK, Brent AC, Amigun B, et al. (2012) A system dynamics approach to technology sustainability assessment: The case of biodiesel developments in South Africa. Technovation 32: 639-651. |
[17] | Indrawan N, Thapa S, Rahman SF, et al. (2017) Palm biodiesel prospect in the Indonesian power sector. Environ Technol Innovation 7: 110-127. |
[18] | Arrumaisho US, Sunitiyoso Y (2019) A system dynamics model for biodiesel industry in indonesia. Asian J Technol Manage 12: 149-162. |
[19] | Wijaya H, Arkeman Y, Hambali E (2017) Formulation of Indonesian palm oil biodiesel policy for energy security by using system dynamics model. Agric Eng Int: CIGR J 2017: 268-282. |
[20] | Kuo TC, Lin S-H, Tseng M-L, et al. (2019) Biofuels for vehicles in Taiwan: Using system dynamics modeling to evaluate government subsidy policies. Resour, Conserv Recycl 145: 31-39. |
[21] | Chanthawong A, Dhakal S, Kuwornu JK, et al. (2020) Impact of subsidy and taxation related to biofuels policies on the economy of Thailand: A dynamic CGE modelling approach. Waste Biomass Valorization 11: 909-929. |
[22] | GoI (2015) Presidential regulation no 61 about establishment of Indonesian palm oil fund management agency. President of republic Indonesia. |
[23] | MoF (2016) Regulation of the minister of finance of the republic Indonesia no. 80/PMK.05/2016. |
[24] | Dharmawan A, Sudaryanti D, Prameswari A, et al. (2018) Pengembangan bioenergi di Indonesia: Peluang dan tantangan kebijakan industri biodiesel: CIFOR. |
[25] | MEMR (2020) Market index price of biodiesel. Available from: http://ebtke.esdm.go.id/category/22/hip.bbn. |
[26] | MIGAS B (2020) Market index price for subsidized and non subsidized gas oil to calculate the difference between market index price of gas oil with market index price of biodiesel. Available from: https://migas.esdm.go.id/uploads/harga-indek-pasar-/sept-2020---hip-minyak-solar--website-migas.pdf. |
[27] | MoF (2015) Regulation of the minister of finance of the republic Indonesia no. 133/PMK.05/2015 In: Finance Mo, editor. Jakarta. |
[28] | MoF (2018) Regulation of the minister of finance of the republic Indonesia no. 81/PMK.05/2018 Jakarta: Ministry of finance. |
[29] | MoF (2019) Regulation of the minister of finance of the republic Indonesia no. 136/PMK.05/2019. |
[30] | MoA (2020) Tree crop estate statistics of Indonesia 2018-2020: Palm oil. Jakarta: Directorate general of estates ministry of agriculture. |
[31] | Nurfatriani F, Sari GK, Komarudin H (2019) Optimization of crude palm oil fund to support smallholder oil palm replanting in reducing deforestation in Indonesia. Sustainability 11: 4914. |
[32] | Sterman J (2010) Business dynamics: Irwin/McGraw-Hill c2000. |
[33] | Bautista S, Espinoza A, Narvaez P, et al. (2019) A system dynamics approach for sustainability assessment of biodiesel production in Colombia. Baseline simulation. J Cleaner Prod 213: 1-20. |
[34] | MEMR (2019) FAQ: Program mandatori biodiesel 30% (B30). Directorate of new renewable energy and energy conservation, ministry of energy and mineral resources republic of Indonesia. |
[35] | MoA (2018) Tree crop estate statistics of Indonesia 2017-2019 palm oil. Jakarta: Directorate general of estate crops, ministry of agriculture. |
[36] | DGoP (2017) Guidelines for private oil plantations of planters, development of human resources and facilities and infrastructure assistance in the funding of the palm oil plantation fund management agency. |
[37] | Asianagri (2019) Land rejuvenation success, oil palm farmers duplicate harvest production. Available from: https://www.asianagri.com/id/media-id/artikel/sukses-peremajaan-lahan-petani-kelapa-sawit-gandakan-hasil-panen. |
[38] | MEMR (2015) Regulation of the minister of energy and mineral resources Indonesia about certain sector industry mandatory to use biodiesel and bioethanol as a fuel mixture with certain mixtures from 2015 to 2025. Minister of energy and mineral resources. |
[39] | Indonesia PotRo (2014) Regulation of the president of the republic of Indonesia number 191 of 2014 concerning provision, distribution and retail price of oil fuel. Jakarta: President of Indonesia. |
[40] | USDA (2019) Indonesia biofuels report 2019. Jakarta. |
[41] | Migas B (2020) Konsumsi BBM nasional 2006-2018. Available from: https://www.bphmigas.go.id/kuota-dan-realisasi-jenis-bbm-tertentu/. |
[42] | Population growth (annual %)-Indonesia, 2020. The World Bank Data. |
[43] | BPDPKS (2019) PDPKS signs biodiesel incentive financing agreement for 2019. Palm oil fund management agency. |
[44] | Barlas Y (1996) Formal aspects of model validity and validation in system dynamics. Syst Dyn Rev: J Syst Dyn Soc 12: 183-210. |
[45] | Lawrence KD, Klimberg RK, Lawrence SM (2009) Fundamentals of forecasting using excel, Industrial Press Inc. |
[46] | Arifin R (2019) RI wants to reach B50, car manufacturers say. Available from: https://oto.detik.com/mobil/d-4667356/ri-mau-loncat-ke-b50-ini-kata-produsen-mobil. |
[47] | Sharon H, Karuppasamy K, Soban Kumar DR, et al. (2012) A test on DI diesel engine fueled with methyl esters of used palm oil. Renewable Energy 47: 160-166. |
[48] | MEMR (2019) B30 road test results: All aspects of the vehicle have passed. Ministry of energy and mineral resources of the republic of Indonesia. |
[49] | Sindo (2018) CPO export levy deleted, here are the facts (pungutan ekspor CPO dihapus, ini fakta-faktanya). Available from: https://economy.okezone.com/read/2018/11/27/320/1983508/pungutan-ekspor-cpo-dihapus-ini-fakta-faktanya. |
[50] | Ogunkunle O, Ahmed NA (2019) A review of global current scenario of biodiesel adoption and combustion in vehicular diesel engines. Energy Reports 5: 1560-1579. |
[51] | Gumilar P (2019) Gapki targets CPO productivity to be 6.9 tons per hectare per year. Available from: https://ekonomi.bisnis.com/read/20190412/99/910998/gapki-targetkan-produktivitas-cpo-jadi-69-ton-per-hektare-per-tahun. |
[52] | Harahap F, Silveira S, Khatiwada D (2019) Cost competitiveness of palm oil biodiesel production in Indonesia. Energy 170: 62-72. |
[53] | Amelia AR (2018) The government agrees to increase solar subsidies to rp 2,000 per liter, Available from: https://katadata.co.id/arnold/berita/5e9a55f50e96b/pemerintah-sepakat-naikkan-subsidi-solar-menjadi-rp-2000-per-liter. |
[54] | Arvirianty A (2019) Biodiesel B30 is implemented in 2020, how much foreign exchange will be saved?: CNBC Indonesia. Available from: https://www.cnbcindonesia.com/news/20190619092850-4-79226/biodiesel-30-berlaku-2020-berapa-devisa-yang-dihemat. |
[55] | Replanting is the key to improve livelihood of oil palm smallholders. 2018. Available from: https://www.bpdp.or.id/en/replanting-is-the-key-to-improve-oil-palm-smallholders-welfare. |
[56] | Khatiwada D, Palmén C, Silveira SJB (2018) Evaluating the palm oil demand in Indonesia: production trends, yields, and emerging issues. Biofuels 1-13. |
[57] | Population total-Indonesia, 2020. The World Bank Data. |
[58] | Nurfatriani F, Sari GK, Komarudin H (2018) Optimalisasi dana sawit dan pengaturan instrumen fiskal penggunaan lahan hutan untuk perkebunan dalam upaya mengurangi deforestasi: CIFOR. |
[59] | MIGAS B (2020) Laporan kinerja BPH migas tahun, 2019. BPH MIGAS. |
1. | Xiangqi Qiang, Chengjun Hou, Continuous Orbit Equivalence for Automorphism Systems of Equivalence Relations, 2023, -1, 1027-5487, 10.11650/tjm/231105 |