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Archive for Rational Mechanics and Analysis
pp 1–46 | Cite as
On the Averaged Green's Function of an Elliptic Equation with Random Coefficients
Jongchon Kim
Marius Lemm
We consider a divergence-form elliptic difference operator on the lattice \(\mathbb {Z}^d\), with a coefficient matrix that is an i.i.d. perturbation of the identity matrix. Recently, Bourgain introduced novel techniques from harmonic analysis to prove the convergence of the Feshbach-Schur perturbation series related to the averaged Green's function of this model. Our main contribution is a refinement of Bourgain's approach which improves the key decay rate from \(-2d+\epsilon \) to \(-3d+\epsilon \). (The optimal decay rate is conjectured to be \(-3d\).) As an application, we derive estimates on higher derivatives of the averaged Green's function which go beyond the second derivatives considered by Delmotte–Deuschel and related works.
Communicated by F. Otto
The authors would like to thank Wilhelm Schlag and Tom Spencer for helpful discussions. The authors are grateful to the Institute for Advanced Study for its hospitality during the 2017-2018 academic year. They also thank Alexis Drouot, Antoine Gloria, Felix Otto and Israel Michal Sigal for useful comments on a preprint version of this paper. This material is based upon work supported by the National Science Foundation under Grant No. DMS - 1638352.
A Proof of Corollary 1.5 on Derivatives of the Averaged Green's Function
The proof is based on the standard fact that existence of derivatives in Fourier space (which we get from Theorem 1.1) can be translated to decay in physical space via integration by parts. For the endpoint case \(|\alpha |=d+1\), we use a variant of the argument which only requires the Fourier transform to be Hölder continuous.
Let \(d\ge 2\) and assume that \(\alpha \) is a multi-index such that \(|\alpha |>2-d\). This condition ensures that the symbol of \(\nabla ^{\alpha } G\) (and \(\nabla ^{\alpha } G^{\mu }\)) is integrable on \(\mathbb {T}^d\). We shall prove the first statement for \(d\ge 3\) as the proof of the second statement is identical.
Fix \(0<\epsilon <1\) and let \(0<\delta <c\epsilon \), where c is the constant \(\tilde{c}_d\) from Theorem 1.1. Note that the operator \(\mathcal {L}\) is a convolution operator whose symbol is given by
$$\begin{aligned}m(\theta ) = (1+\delta \mathbb {E}\sigma ) \sum _{j=1}^d 2(1-\cos \theta _j) + \sum _{1\le j,k\le d} (e^{-i\theta _j}-1) \widehat{K_{j,k}^{\delta }}(\theta ) (e^{i\theta _k}-1)\end{aligned}$$
for \(\theta \in \mathbb {T}^d\). By Theorem 1.1, we have
$$\begin{aligned} ||{\widehat{K_{j,k}} }||_{C^{2d-1,1-\epsilon } (\mathbb {T}^d) }\le C\delta ^2. \end{aligned}$$
In particular, we may find \(0<c_d \le c\epsilon \) such that for any \(0<\delta <c_d\), we have the lower bound
$$\begin{aligned} |m(\theta )| \ge C |\theta |^2 \end{aligned}$$
(A.1)
for some constant \(C>0\) for any \(\theta \) in \(\mathbb {T}^d\) which we identify with \([-\pi ,\pi ]^d\).
Next, let \(m^{\alpha }\) be the symbol of \(\nabla ^{\alpha }\), i.e. \( m^{\alpha }(\theta ) = \prod _{j=1}^d (e^{i\theta _j}-1)^{\alpha _j }.\) Since \(|m^{\alpha }(\theta )|\le \prod _{j=1}^d |\theta _j|^{\alpha _j } \le |\theta |^{|\alpha |}\), we see that
$$\begin{aligned} \left| {\frac{m^{\alpha }(\theta )}{m(\theta )}}\right| \le C |\theta |^{|\alpha |-2}, \end{aligned}$$
which is integrable on \(\mathbb {T}^d\) provided that \(|\alpha |>2-d\).
The kernel \(\nabla ^{\alpha } G(x)\) is the Fourier inverse of \(m^{\alpha }(\theta )[m(\theta )]^{-1}\). We estimate \(\nabla ^{\alpha } G(x)\) using a dyadic decomposition of \(\mathbb {T}^d\) as follows. Let \(\varphi \) be a smooth even function compactly supported on \([-2,2]\) and \(\varphi (r) = 1\) for \(r\in [-1,1]\). Let \(\psi (r) := \varphi (r) - \varphi (2r)\) and \(\psi _l(r) := \psi (2^{l} r)\) for \(l\ge 1\) and \(\psi _0(r) := 1-\varphi (2r)\). Note that \(\sum _{l\ge 0} \psi _l(r) = 1\) for any \(r\ne 0\). We write \(\nabla ^{\alpha } G(x) = \sum _{l\ge 0} \nabla ^{\alpha } G_l(x)\), where we denote by \(\nabla ^{\alpha } G_l(x)\) the Fourier inverse of \(\psi _l(|\theta |) m^{\alpha }(\theta )[m(\theta )]^{-1}\).
$$\begin{aligned} g^{\alpha }_l(\theta ) := \frac{\phi (\theta )m^{\alpha }(2^{-l}\theta )}{m(2^{-l}\theta )}, \end{aligned}$$
where \(\phi (\theta ) := \psi (|\theta |)\). Then for \(l\ge 1\), we may write by a change of variable
$$\begin{aligned} \nabla ^{\alpha } G_l(x) = 2^{-ld} \int _{\mathbb {R}^d} g^{\alpha }_l(\theta ) e^{i2^{-l}x \cdot \theta } \frac{d\theta }{(2\pi )^d}. \end{aligned}$$
First note that, by (A.2), \(|\nabla ^{\alpha } G_l(x)| \le C 2^{-l(d-2+|\alpha |)}\) for any \(x\in \mathbb {Z}^d\). This bound may be improved when \(2^{-l}|x|\ge 1\). We claim that when \(|x|\ge 2^l\) and \(l\ge 1\), we have
$$\begin{aligned} |\nabla ^{\alpha } G_l(x)| \le \frac{C2^{-l(d-2+|\alpha |)}}{(2^{-l}|x|)^{2d-\epsilon }}. \end{aligned}$$
Given the estimate (A.3), Corollary 1.5 follows quickly. First of all, one can check, using integration by parts, that
$$\begin{aligned} |\nabla ^{\alpha } G_0(x)| \le C(1+|x|)^{-(2d-1)}. \end{aligned}$$
Using this bound and (A.3), we get
$$\begin{aligned} |\nabla ^{\alpha } G(x)| \le C \sum _{l\ge 0} 2^{-l(d-2+|\alpha |)}\le C \end{aligned}$$
for any \(x\in \mathbb {Z}^d\), since we assume \(|\alpha |>2-d\). Next we assume that \(|x|\ge 100\) and study the sum over \(2^l > |x|\) and \(2^l \le |x|\) separately. We have
$$\begin{aligned} \sum _{l\ge 0 :\; 2^l> |x|} |\nabla ^{\alpha } G_l(x)| \le C\sum _{l\ge 0 :\; 2^l > |x|} 2^{-l(d-2+|\alpha |)} \le C |x|^{-(d-2+|\alpha |)}. \end{aligned}$$
On the other hand, if \(|\alpha |\le d+1\), we have
$$\begin{aligned} \sum _{l\ge 0 :\; 2^l \le |x|} |\nabla ^{\alpha } G_l(x)|\le & {} C|x|^{-(2d-1)} + C\sum _{l\ge 1 :\; 2^l \le |x|} 2^{l(d + 2 - |\alpha | -\epsilon )} |x|^{-2d+\epsilon }\nonumber \\\le & {} C |x|^{-(d-2+|\alpha |)}. \end{aligned}$$
Observe that (A.4), (A.5) and (A.6) implies Corollary 1.5.
It remains to verify (A.3). We need the following lemma:
Lemma A.1
For \(0<\delta < c_d\) and \(l\ge 1\), we have
$$\begin{aligned} ||{g_l^{\alpha }}||_{C^{2d-1,1-\epsilon } (\mathbb {R}^d) }\le C 2^{-l(|\alpha |-2)}. \end{aligned}$$
When \(\theta \in \,\mathrm {supp}\,\phi \), \(|m(2^{-l}\theta )|\) is comparable to \(2^{-2l}\) as \(|\theta |\sim 1\). In addition, we have the estimates
$$\begin{aligned} |[(2^{-l}\partial )^{\beta } m](2^{-l}\theta )|&\le C_\beta 2^{-2l} \\ |[(2^{-l}\partial )^{\beta } m^{\alpha } ](2^{-l}\theta )|&\le C_{\beta ,\alpha } 2^{-l|\alpha |} \end{aligned}$$
for all multi-index \(\beta \) with \(|\beta |\le 2d-1\). From these estimates, if follows that
$$\begin{aligned} ||{g_l^{\alpha }}||_{C^{2d-1} (\mathbb {R}^d) }\le C 2^{-l(|\alpha |-2)}. \end{aligned}$$
For the Hölder estimate, we note that when \(|\beta | = 2d-1\), we may write
$$\begin{aligned} \partial ^{\beta } g_l^{\alpha }(\theta ) =\frac{\chi (\theta ) 2^{-l(2d-1)} \partial ^{\beta } m (2^{-l}\theta ) m^{\alpha } (2^{-l}\theta )}{m(2^{-l}\theta )^2} + R(\theta ), \end{aligned}$$
where \(||{R}||_{C^1} \le C 2^{-l(|\alpha |-2)}\). Thus, it remains to show that the \(C^{0,1-\epsilon }\) norm of the first term is \(O(2^{-l(|\alpha |-2)})\). This again reduces to quantify the \(C^{0,1-\epsilon }\) norm of the functions resulting from replacing \(\partial ^{\beta } m(2^{-l}\theta )\) in the first term by
$$\begin{aligned} (e^{-i2^{-l}\theta _j} -1)(e^{i2^{-l}\theta _k} -1) \partial ^{\beta } \widehat{K^{\delta }_{j,k}}(2^{-l}\theta ) \end{aligned}$$
for each \(1\le j,k\le d\). One can verify that \(C^{0,1-\epsilon }\) norm of the resulting functions are \(O(2^{-l(|\alpha |-2)})\). \(\quad \square \)
Finally, we may deduce (A.3) from Lemma A.1 by a standard argument. Let \(|x| \ge 2^l\). Without loss of generality, we may assume that \(|x_1| = \max _j |x_j|\), hence \(|x_1| \sim |x|\). Using integration by parts, we see that
$$\begin{aligned} \nabla ^{\alpha } G_l(x) = \frac{C2^{-ld}}{(2^{-l}x_1)^{2d-1}} \int (\partial _1)^{2d-1} g^{\alpha }_l(\theta ) e^{i2^{-l}x\cdot \theta } d\theta . \end{aligned}$$
After the change of variable \(\theta _1 \rightarrow \theta _1 + \frac{\pi }{2^{-l}x_1}\) in the integral, we also see that
$$\begin{aligned} \nabla ^{\alpha } G_l(x) = - \frac{C2^{-ld}}{(2^{-l}x_1)^{2d-1}} \int (\partial _1)^{2d-1} g^{\alpha }_l\left( \theta _1+\frac{\pi }{2^{-l}x_1}, \theta ' \right) e^{i2^{-l}x\cdot \theta } d\theta , \end{aligned}$$
where we write \(\theta ' = (\theta _2,\cdots ,\theta _d)\). Estimating the average of these expressions for \(\nabla ^{\alpha } G_l(x)\) using Lemma A.1, we obtain (A.3) which finishes the proof.
B Proof of Corollary 1.6 on Averaged Solutions
We have \(f\in H^{-1}(\mathbb {Z}^d)\) by (2.1) and \(u_\omega =L_\omega ^{-1} f\) is the unique solution in \(H^1(\mathbb {Z}^d)\) to the equation \(L_\omega u_\omega = f\).
By the definition of \(\mathcal {L}\), we have \(\mathbb {E} [u_\omega ] = \mathcal {L}^{-1} f\). In addition, we have
$$\begin{aligned} \mathcal {L} (G*f) = (\mathcal {L} G)*f = \delta _0 * f = f \end{aligned}$$
(B.1)
which yields \( \mathcal {L} ^{-1} f = G*f\). We need to verify the first equality of (B.1), which is trivial when f is compactly supported. For general \(f\in \ell ^{p_d}(\mathbb {Z}^d)\), it suffices to show that
$$\begin{aligned} \nabla _i^* K^{\delta }_{i,j} \nabla _{j} (G*f) =( \nabla _i^* K^{\delta }_{i,j} \nabla _{j} G)*f. \end{aligned}$$
To see this, first note that the sum defining the convolution \(G*f\) converges absolutely since \(G\in \ell ^{q_d}(\mathbb {Z}^d)\) and \(f\in \ell ^{p_d}(\mathbb {Z}^d)\) and \(\frac{1}{p_d}+\frac{1}{q_d} = 1\). This shows that \(\nabla _j (G*f) = (\nabla _j G)*f\) with \(\nabla _j G \in \ell ^{q_d}(\mathbb {Z}^d)\). In fact, \(\nabla _j G\in \ell ^2(\mathbb {Z}^d)\) since \(G\in H^1(\mathbb {Z}^d)\), but we do not use this fact here. Moreover, the kernel of \(K_{i,j}\) belongs to \(\ell ^1(\mathbb {Z}^d)\) and we have \(K_{i,j} [( \nabla _j G) * f] = (K_{i,j} \nabla _j G) * f \) by Fubini's theorem and \(K_{i,j} \nabla _j G \in \ell ^{q_d}(\mathbb {Z}^d)\). The argument for \(\nabla _i^*\) is the same and this establishes (B.2).
The pointwise estimate is a direct consequence of Corollary 1.5. \(\quad \square \)
C Proof of the Deterministic Bound in Lemma 2.2
We closely follow [8] and provide some details. Recall that
$$\begin{aligned} T^n(x_0,x_n) = \sum _{\underline{x}} K^1(x_0,x_1)K^2(x_1,x_2)\ldots K^n(x_{n-1},x_n), \end{aligned}$$
where \(\underline{x}= (x_1,x_2,\ldots ,x_{n-1})\in (\mathbb {Z}^d)^{n-1}\). When \(x_0\ne x_n\), we may write
$$\begin{aligned} \sum _{\underline{x}} = \sum _{m\ge 0} \sum _{\underline{x}:\; 2^m \le \max _j{|x_j-x_{j+1}|} < 2^{m+1}} = \sum _{j_0=0}^{n-1} \sum _{m\ge 0} \sum _{\underline{x}\in S_{j_0}^{m}}, \end{aligned}$$
where \(S_{j_0}^{m}\) is defined in (3.6). When \(x_0 =x_n\), this yields a decomposition for the sum \(\sum _{\underline{x}}\) except for \(\underline{x}= (x_0,\cdots ,x_0)\) for which we may invoke the bound \(|K^1(x_0,x_0)\cdots K^n(x_0,x_0)|\le A^n\).
Let \(\mathbf {I}_m = [0,2^m)\). Observe that
$$\begin{aligned}&\sum _{\underline{x}\in S^m_{j_0} } K^1(x_0,x_1)\ldots K^n(x_{n-1},x_n) \nonumber \\&\quad = \sum _{\underline{x}\in (\mathbb {Z}^d)^{n-1}} \prod _{j=1}^{j_0} K^j_{\mathbf {I}_m} (x_{j-1},x_j) K^{j_0+1}_{\mathbf {I}_{m+1}\setminus \mathbf {I}_{m}}(x_{j_0}, x_{j_0+1}) \prod _{j=j_0+2}^{n} K^j_{\mathbf {I}_{m+1}}(x_{j-1},x_j) \nonumber \\&\quad = \sum _{x_{j_0}, x_{j_0+1} } T^{j_0}_{\mathbf {I}_m}(x_0,x_{j_0}) K^{j_0+1}_{\mathbf {I}_{m+1}\setminus \mathbf {I}_{m} }(x_{j_0}, x_{j_0+1}) \widetilde{T}^{j_0}_{\mathbf {I}_{m+1}} (x_{j_0+1},x_n), \end{aligned}$$
(C.1)
where \(T^{j_0}_{\mathbf {I}_m} := \prod _{j=1}^{j_0} K^j_{\mathbf {I}_m}\) and \(\widetilde{T}^{j_0}_{\mathbf {I}_{m+1}} :=\prod _{j=j_0+2}^{n} K^j_{\mathbf {I}_{m+1}}\). Here, the sum over \(x_{j_0}\) is in fact a finite sum; \(|x_0 - x_{j_0}| \le |x_0- x_1| + \ldots +|x_{j_0-1}-x_{j_0}| \le n 2^{m+1}.\) Similarly, the sum over \(x_{j_0+1}\) is a finite sum over \(|x_{j_0+1}-x_n|\le n2^{m+1}\). From this, Hölder's inequality, and Assumption (i),
$$\begin{aligned}&|(C.1)|\\&\quad \le A2^{-md} \sum _{x_{j_0}} |T^{j_0}_{\mathbf {I}_m} (x_0,x_{j_0})| \sum _{x_{j_0+1}} |\widetilde{T}^{j_0}_{\mathbf {I}_{m+1}} (x_{j_0+1},x_n)| \\&\quad \le C A2^{-md} (n2^m)^{2d(p-1)/p} \Big (\sum _{x_{j_0}}| T^{j_0}_{\mathbf {I}_m} (x_0,x_{j_0})|^p\Big )^{1/p} \Big (\sum _{x_{j_0+1}}|\widetilde{T}^{j_0}_{\mathbf {I}_{m+1}} (x_{j_0+1},x_n)|^p \Big )^{1/p} \end{aligned}$$
for \(p>1\) selected by \(2d(p-1)=\epsilon \).
Let \(\delta _y\) be the delta function on \(\mathbb {Z}^d\); \(\delta _y(x)\) is equal to 1 if \(x=y\) and 0 otherwise. Note that the product of two \(\ell ^p\) sums in the last inequality is bounded by
$$\begin{aligned} ||{(T^{j_0}_{\mathbf {I}_m} )^* \delta _{x_0}}||_{\ell ^p(\mathbb {Z}^d)} ||{\widetilde{T}^{j_0}_{\mathbf {I}_{m+1}} \delta _{x_n}}||_{\ell ^p(\mathbb {Z}^d)}, \end{aligned}$$
which is bounded by \([A/(p-1)]^{j_0} [A/(p-1)]^{n-j_0-1} =\left( \frac{2dA}{\epsilon }\right) ^{n-1}\) by Assumption (2). Therefore, we get
$$\begin{aligned} |(C.1)| \le C n^{\epsilon } \left( \frac{2dA}{\epsilon }\right) ^{n} \epsilon 2^{-m(d-\epsilon )} . \end{aligned}$$
It only remains to sum (C.2) over \(m\ge 0\) and \(j_0\). For this, we distinguish the cases \(|x_0-x_n|\ge 2n\) and \(|x_0-x_n|< 2n\). For the first case, the sum over m is restricted to
$$\begin{aligned} 2^m \ge \frac{|x_0-x_n|}{ 2n}, \end{aligned}$$
which follows from (given that \(\max _j|x_j-x_{j+1}| < 2^{m+1}\))
$$\begin{aligned} |x_0-x_n| \le \sum _{j=0}^{n-1} |x_j-x_{j+1}| \le n 2^{m+1}. \end{aligned}$$
In the first case, therefore, summing (C.2) over m and \(j_0\) yields
$$\begin{aligned} |T^n(x_0,x_n)|&\le C n^{1+\epsilon }\left( \frac{2dA}{\epsilon }\right) ^{n} \epsilon \sum _{m: \; 2^m \ge |x_0-x_n|/ (2n)} 2^{-m(d-\epsilon )} \\&\le (C_d A/\epsilon )^n \epsilon \langle {x_0-x_n}\rangle ^{-(d-\epsilon )}. \end{aligned}$$
When \(|x_0-x_n|< 2n\), we sum (C.2) over \(m\ge 0\) and \(j_0\). Then we get
$$\begin{aligned} |T^n(x_0,x_n)| \le C n^{1+\epsilon } \left( \frac{2dA}{\epsilon }\right) ^{n} \epsilon , \end{aligned}$$
which completes the proof since \(1 \le Cn \langle {x_0-x_n}\rangle ^{-1}\).
D Proof of Lemma 2.7 on Disjointification
Since \(S'=\emptyset \) when \(E_l \cap F_l \ne \emptyset \) for some l, we may assume that \(E_l \cap F_l = \emptyset \) for all \(1\le l\le m\).
We closely follow the argument given in Section 4 of [8]. We introduce an additional set of variables ("Steinhaus system") on the torus \(\mathbb {T}=\mathbb {R}/2\pi \mathbb {Z}\)
$$\begin{aligned} \overline{\theta }:=(\overline{\theta }^1, \overline{\theta }^2, \ldots , \overline{\theta }^m ), \text { where } \overline{\theta }^l := \left\{ {\theta ^l_x \in \mathbb {T}}\; : \;{x\in \mathbb {Z}^d}\right\} . \end{aligned}$$
We use these variables to define the complex-valued functions \(e_j:\mathbb {Z}^d\rightarrow \mathbb {C}\),
$$\begin{aligned} e_j(x,\overline{\theta })&:=\prod _{l=1}^m \exp \left( i \nu ^l_j \theta ^l_{x}\right) ,\\ \text {where }\quad \nu ^l_j&:={\left\{ \begin{array}{ll} 1,\qquad \;\text { if }j\in E_l,\\ -1,\qquad \text {if }j\in F_l,\\ 0,\qquad \;\text { otherwise}. \end{array}\right. } \end{aligned}$$
Note that \(\Vert e_j(\cdot ,\overline{\theta })\Vert _{\infty } \le 1\) for all \(\overline{\theta }\).
Assume first that the set S is finite. Define
$$\begin{aligned}&\tilde{T}^n_S(x_0,x_n,\overline{\theta }):= \sum _{\underline{x}\in S} \tilde{K}^1(x_0,x_1)\tilde{K}^2(x_1,x_2)\ldots \tilde{K}^n(x_{n-1},x_n) \\&\quad = \sum _{\underline{x}\in S} K^1(x_0,x_1) \ldots K^n(x_{n-1},x_n) \prod _{l=1}^{m} \exp \left( i \left( \sum _{j\in E_l} \theta ^l_{x_j} -\sum _{k\in F_l} \theta ^l_{x_k} \right) \right) , \end{aligned}$$
where we introduced the operators \(\tilde{K}^j(x,y) :=K^j(x,y)e_j(y,\overline{\theta })\) for \(2\le j\le n\) and \(\tilde{K}^1 (x,y):=e_0(x,\overline{\theta })K^1(x,y)e_1(y,\overline{\theta })\). It is important to observe that, by the assumption, we have
$$\begin{aligned} |\tilde{T}^n_S(x_0,x_n,\overline{\theta })|\le M(x_0,x_n) \end{aligned}$$
(D.1)
for all \(\overline{\theta }\).
The next step is to average the bound (D.1) over the variables \(\overline{\theta }\) with respect to specific probability measures to be chosen. Define the set
$$\begin{aligned}&\mathbb {Z}^d_S := \{ x_0,x_n\}\\&\qquad \cup \{ x\in \mathbb {Z}^d: x=x_j \text { for some } (x_1,\ldots ,x_{n-1})\in S \text { and } 1\le j\le n-1\}, \end{aligned}$$
which is finite since S is finite by assumption. For each \(-1<t<1\), let \(P_t(\theta )\) be the Poisson kernel of the unit disk
$$\begin{aligned} P_t(\theta )=\sum _{n=-{\infty }}^{\infty } t^{|n|}e^{in\theta }. \end{aligned}$$
Note that \(P_t(\theta ) \frac{d\theta }{2\pi }\) is a probability measure on \(\mathbb {T}\). For each \(1\le l\le m\) and \(|t|<1\), consider the product measure \(\mathrm {d}\mu _t^l\) on \(\mathbb {T}^{\mathbb {Z}^d_S}= \prod _{x\in \mathbb {Z}^d_S} \mathbb {T}\) given by
$$\begin{aligned} \mathrm {d}\mu _t^l (\overline{\theta }^l) := \prod _{x\in \mathbb {Z}^d_S} P_t(\theta ^l_x) \frac{d\theta ^l_x}{2\pi }. \end{aligned}$$
We first average (D.2) over the probability space \(\mathbb {T}^{\mathbb {Z}^d_S}\) equipped with the measure \(\mathrm {d}\mu _{t}^1\). On the one hand, since (D.1) holds pointwise in \(\overline{\theta }\), we have
$$\begin{aligned} \left| \int _{\mathbb {T}^{\mathbb {Z}^d_S}} \tilde{T}^n_S(x_0,x_n,\overline{\theta }) \mathrm {d}\mu _{t}^1\left( \overline{\theta }^1 \right) \right| \le M(x_0,x_n) \end{aligned}$$
for any \((\overline{\theta }^2, \ldots , \overline{\theta }^m)\) and \(|t|<1\). On the other hand, we may write the integral above as
$$\begin{aligned}&\sum _{\underline{x}\in S} K^1(x_0,x_1)K^2(x_1,x_2)\ldots K^n(x_{n-1},x_n) \prod _{l=2}^{m} \exp \left( i \left( \sum _{j\in E_l} \theta ^l_{x_j} -\sum _{k\in F_l} \theta ^l_{x_k} \right) \right) \\&\quad \times \int _{\mathbb {T}^{\mathbb {Z}^d_S}} \exp \left( i \left( \sum _{j\in E_1} \theta ^1_{x_j} - \sum _{k\in F_1} \theta ^1_{x_k} \right) \right) \prod _{x\in \mathbb {Z}^d_S} P_{t}(\theta ^1_x) \frac{\mathrm {d}\theta _{x}^1}{2\pi }. \end{aligned}$$
As was observed in [8], the integral in the above line is equal to \( t^{w_{(x_0,x_1,\ldots ,x_n)}}\), where
$$\begin{aligned} w_{(x_0,\ldots ,x_n)} = \sum _{x \in \mathbb {Z}^d_S} \bigl | { | \{ j\in E_1: x_j=x \}| - | \{ k\in F_1: x_k=x \}| }\bigr | \le |E_1| + |F_1|. \end{aligned}$$
Moreover, \(w_{(x_0,\ldots ,x_n)}= |E_1|+|F_1|\) if and only if \(\underline{x} \in S_1 \), where
$$\begin{aligned} S_1 := S\cap \{\underline{x}: \{x_j: j\in E_1 \} \cap \{x_k:k\in F_1 \} =\emptyset \}. \end{aligned}$$
Therefore, we may write \(\int _{\mathbb {T}^{\mathbb {Z}^d_S}} \tilde{T}^n_S(x_0,x_n,\overline{\theta }) \mathrm {d}\mu _{t}^1(\overline{\theta }^1 )\) as a polynomial
$$\begin{aligned} f(t)= a_D t^D +a_{D-1}t^{D-1} + \ldots + a_0, \end{aligned}$$
where \(D= |E_1| + |F_1|\) and
$$\begin{aligned} a_D= & {} \sum _{\underline{x}\in S_1} K^1(x_0,x_1) K^2 (x_1,x_2) \ldots K^n(x_{n-1},x_n) \\&\prod _{l=2}^{m}\exp \left( i \left( \sum _{j\in E_l} \theta ^l_{x_j} - \sum _{k\in F_l} \theta ^l_{x_k} \right) \right) . \end{aligned}$$
At this point, we recall a special case of the Markov brothers' inequality.
Lemma D.1
Let f(t) be a polynomial as in (D.3). Then we have
$$\begin{aligned} |a_D| \le 2^{D-1} \max _{ -1\le t \le 1} |f(t)|. \end{aligned}$$
Combined with (D.2), we get, with \(D= |E_1| + |F_1|\),
$$\begin{aligned} |a_D| \le 2^{D-1} M(x_0,x_n) \end{aligned}$$
for any \((\overline{\theta }^2, \ldots , \overline{\theta }^m)\). What comes next is a similar averaging argument for the top coefficient \(a_D\) over the measure \(\mathrm {d}\mu _t^2\), which yields
$$\begin{aligned}&\left| \sum _{\underline{x}\in S_2} K^1(x_0,x_1)K^2(x_1,x_2) \ldots K^n(x_{n-1},x_n) \prod _{l=3}^{m} \exp \left( i \left( \sum _{j\in E_l} \theta ^l_{x_j} - \sum _{k\in F_l} \theta ^l_{x_k} \right) \right) \right| \\&\quad \le \left( \prod _{1\le l \le 2} 2^{|E_l|+|F_l|-1} \right) M(x_0,x_n) \end{aligned}$$
for any \((\overline{\theta }^3, \ldots , \overline{\theta }^m)\), where
$$\begin{aligned} S_2 := S_1 \cap \{\underline{x}: \{x_j: j\in E_2 \} \cap \{x_k:k\in F_2 \} = \emptyset \}. \end{aligned}$$
A successive averaging over \(\mathrm {d}\mu _{t}^3, \ldots , \mathrm {d}\mu _{t}^m\) finishes the proof.
Next, assume that S is not a finite set. By dominated convergence and the a priori bound (2.6), we have \(T^n_{S'} (x_0,x_n)=\lim _{k\rightarrow \infty } T^n_{ S' \cap X_k}(x_0,x_n)\). Therefore, it is sufficient to show that
$$\begin{aligned} |T^n_{S' \cap X_k}(x_0,x_n)| \le 2^{\sum _{1\le l\le m} |E_l|+|F_l|} M(x_0,x_n) \end{aligned}$$
for all large \(k\ge 1\), which follows from applying the result for the finite set to \(S\cap X_k\). \(\quad \square \)
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© Springer-Verlag GmbH Germany, part of Springer Nature 2019
1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
2.Department of MathematicsHarvard UniversityCambridgeUSA
Kim, J. & Lemm, M. Arch Rational Mech Anal (2019). https://doi.org/10.1007/s00205-019-01409-1
Received 31 May 2018
DOI https://doi.org/10.1007/s00205-019-01409-1
Publisher Name Springer Berlin Heidelberg


A northwest suburban Elgin man accused of swallowing heroin in an attempt to hide it from police was ordered held on a $50,000 bond Thursday for multiple felony charges.
During the course of a four month investigation, 32-year-old Angelo Hopson delivered and sold heroin to an undercover officer on three separate occasions, according to a statement from Elgin police.
On Monday, police executed a search warrant at his home in the 800 block of Seminole Drive. Just before police went inside, Hopson swallowed an unknown amount of heroin in an attempt to destroy the evidence, police said.
Police said he was taken to Presence Saint Joseph Hospital in Elgin, where he was treated and released to police Wednesday.
Hopson was charged with unlawful delivery of a controlled substance within 1,000 feet of a church, five counts of unlawful delivery of a controlled substance, unlawful possession of a controlled substance and obstructing justice, all felonies, police said.
Cook County Judge Joseph Cataldo ordered a $50,000 bond for Hopson on Thursday morning at the Rolling Meadows courthouse, court records show. He is next scheduled to appear in court on April 20.


The City of Flint will hold a memorial tree lighting ceremony in front of City Hall on Friday.
According to a news release from the city, there will be a tree for firefighters and a tree for police officers to honor those that have fallen in the line of duty. Families and friends of police and firefighters, as well as the general public, are welcome to attend.
Flint Emergency Manager Darnell Earley, Mayor Dayne Walling, Fire Chief David Cox, Jr. and Police James Tolbert will be in attendance. The ceremony begins at 4:30 p.m.


text: require('nvim-tree').setup {}

redpajama_set_name: RedPajamaGithub


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Mount Sterling – wieś w Stanach Zjednoczonych, w stanie Ohio, w hrabstwie Madison.

Wsie w stanie Ohio

redpajama_set_name: RedPajamaWikipedia


SHANGHAI, Nov. 9 (SMM) –Trump won majority of US general election, allowing risk aversion to grow. SHFE 1701 zinc fell from RMB 20,185/mt to RMB 19,630/mt after opening, and closed at RMB 19,840/mt, up RMB 115/mt or 0.58%. Trading volumes decreased 269,000 to 672,000 lots, and positions decreased 9,848 to 258,000. SHFE 1701 zinc is expected to return to RMB 20,000/mt this evening.


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Home » Context of 'September 1999: FBI Investigates Flight School Attendee Connected to Bin Laden'
Context of 'September 1999: FBI Investigates Flight School Attendee Connected to Bin Laden'
This is a scalable context timeline. It contains events related to the event September 1999: FBI Investigates Flight School Attendee Connected to Bin Laden. You can narrow or broaden the context of this timeline by adjusting the zoom level. The lower the scale, the more relevant the items on average will be, while the higher the scale, the less relevant the items, on average, will be.
Early 1993: Bin Laden Buys Airplane in US to Help Kill US Soldiers
Essam al Ridi. [Source: CNN]Osama bin Laden buys a US military aircraft in Arizona, paying about $210,000 for a converted Saber-40. The transaction is arranged through Wadih El-Hage, a bin Laden employee in Sudan, and Essam al Ridi, a US-based helper for radical Islamists. Before the purchase is made, the two men discuss the transaction on the phone (see August 1992-1993) and El-Hage sends money to al Ridi, who had learned to fly in the US (see Between August 1992 and 1993). Bin Laden apparently wants to use the plane to transport stinger missiles from Pakistan to Sudan, but it is unclear whether it is ever actually used to do this. After modifying the plane, al Ridi flies it from the US to Khartoum, Sudan, where he meets El-Hage, bin Laden, al-Qaeda leader Mohammed Atef, and others. They have dinner, where al Ridi also sees "quite a few" AK 47s, and men in Sudanese military uniforms. Al Ridi also visits bin Laden at the offices of one of his companies, Wadi al Aqiq, and bin Laden offers him a job as a pilot, spraying crops and then shipping them to other countries. However, al Ridi, who argued with bin Laden during the Soviet-Afghan war, rejects the offer, saying bin Laden is not offering him enough money. [United States District Court for the Southern District of New York, 1/14/2001; Sunday Herald (Glasgow), 9/16/2001; Washington Post, 5/19/2002] The plane will later be used to transport bin Laden operatives on a trip to Somalia before the "Black Hawk Down" incident (see Before October 1993), but al Ridi will later crash it (see (1994-1995)).
Entity Tags: Wadi al Aqiq, Wadih El-Hage, Essam al Ridi, Osama bin Laden, Mohammed Atef
Timeline Tags: Complete 911 Timeline
1998: FBI Agent Starts First Investigation into Arizona Flight Students
Ken Williams. [Source: FBI]The FBI field office in Phoenix, Arizona, investigates a possible Middle Eastern extremist taking flight lessons at a Phoenix airport. FBI agent Ken Williams initiates an investigation into the possibility of Islamic militants learning to fly aircraft, but he has no easy way to query a central FBI database about similar cases. Because of this and other FBI communication problems, he remains unaware of most US intelligence reports about the potential use of airplanes as weapons, as well as other, specific FBI warnings issued in 1998 and 1999 concerning Islamic militants training at US flight schools (see May 15, 1998; September 1999). Williams will write the "Phoenix memo" in July 2001 (see July 10, 2001). He had been alerted about some suspicious flight school students in 1996, but it is not clear if this person was mentioned in that previous alert or not (see October 1996). [US Congress, 7/24/2003 ]
Entity Tags: Ken Williams, Federal Bureau of Investigation
May 18, 1999: Potential Al-Qaeda Sleeper Pilot Arrested in Florida; Later Disappears into US Custody
Ihab Ali Nawawi. [Source: FBI]Ihab Ali Nawawi is arrested in Orlando, Florida. He is considered an unindicted co-conspirator in the 1998 US embassy bombings in Africa. Nawawi's family moved from Egypt to the US in the late 1970's and he graduated from an Orlando high school. He fought in Afghanistan in the 1980's and helped bin Laden move to Sudan in 1991. Nawawi received a commercial pilot's license from Airman Flight School in Norman, Oklahoma, in 1993. He crashed an airplane owned by bin Laden in 1995 on a runway in Khartoum, Sudan (see Early 1993). He lived in Sudan until 1996 when he moved back to Orlando. Nawawi's role in al-Qaeda is revealed days after the 1998 US embassy bombings in Africa when Ali Mohamed's residence in California is raided. A letter from Nawawi is discovered asking Mohamed to give his "best regards to your friend Osama"(see August 24, 1998). Nawawi's connection to the embassy bombings were possibly discovered months earlier, because there were a series of phone calls in 1997 between an Orlando telephone owned by Nawawi's sister and an al-Qaeda safe house in Nairobi, Kenya. Many telephone numbers connected to that house were being monitored by US intelligence at the time. Given his obvious al-Qaeda ties, it is not clear why agents waited until May 1999 before arresting Nawawi. He is questioned in front of a grand jury, but prosecutors say he is lying and he refuses to talk anymore. FBI agents will visit the Airman Flight School in September 1999 to enquire about his attendance there (see September 1999). He will remain jailed and in September 2000 is finally charged for contempt and perjury. In October 2001, the St. Petersburg Times will report, "There are signs that Ali's resolve might now be weakening. Court records indicate that Ali's lawyers seemed to reach an understanding with the government in March [2001]. Since that time, all documents in the case have been filed under seal." [St. Petersburg Times, 10/28/2001] In May 2002, three full years after his arrest, the New York Times will report that "Nawawi remains in federal custody even now, although he has not been charged with conspiring in the embassy bombing." [New York Times, 5/18/2002] As of the end of 2005, there appears to be no further news on what has happened to Nawawi, and no sign of any trial. When Nawawi is arrested, he is working as a taxi driver. At this time Al-Qaeda operative Nabil al-Marabh is working as a taxi driver about 80 miles away in Tampa, Florida, and while the similarity is intriguing, there is no known reported connection between the two men (see February 1999-February 2000). [St. Petersburg Times, 10/28/2001]
Entity Tags: Ihab Ali Nawawi
September 1999: FBI Investigates Flight School Attendee Connected to Bin Laden
Agents from Oklahoma City FBI office visit the Airman Flight School in Norman, Oklahoma to investigate Ihab Ali Nawawi, who has been identified as bin Laden's former personal pilot in a recent trial. The agents learned that Nawawi received his commercial pilot's license at the school 1993, then traveled to another school in Oklahoma City to qualify for a rating to fly small business aircraft. He is later named as an unindicted coconspirator in the 1998 US Embassy bombing in Kenya. The trial witness who gave this information, Essam al Ridi, also attended flight school in the US, then bought a plane and flew it to Afghanistan for bin Laden to use (see Early 1993). [Boston Globe, 9/18/2001; CNN, 10/16/2001; Washington Post, 5/19/2002; US Congress, 10/17/2002] When Nawawi was arrested in May 1999, he was working as a taxi driver in Orlando, Florida (see May 18, 1999). Investigators discover recent ties between him and high-ranking al-Qaeda leaders, and suspect he was a "sleeper" agent. [St. Petersburg Times, 10/28/2001] However, the FBI agent visiting the school is not given most background details about him. [US Congress, 7/24/2003] It is not known if these investigators are aware of a terrorist flight school warning given by the Oklahoma City FBI office in 1998. Hijackers Mohamed Atta and Marwan Alshehhi later visit the Airman school in July 2000 but ultimately will decide to train in Florida instead. [Boston Globe, 9/18/2001] Al-Qaeda agent Zacarias Moussaoui will take flight lessons at Airman in February 2001 (see February 23-June 2001). One of the FBI agents sent to visit the school at this time visits it again in August 2001 asking about Moussaoui, but he will fail to make a connection between the two visits (see August 23, 2001).
Entity Tags: Mohamed Atta, Marwan Alshehhi, Essam al Ridi, Federal Bureau of Investigation, Zacarias Moussaoui, Ihab Ali Nawawi
February 23-June 2001: Moussaoui Takes Lessons at Flight School Previously Used by Al-Qaeda
Airman Flight School. [Source: FBI]Al-Qaeda operative Zacarias Moussaoui flies to the US. Three days later, he starts flight training at the Airman Flight School in Norman, Oklahoma. (Other Islamic extremists had previously trained at the same flight school or other schools in the area (see September 1999)). He trains there until May, but does not do well and drops out before getting a pilot's license. His visa expires on May 22, but he does not attempt to renew it or get another one. He stays in Norman, arranging to change flight schools, and frequently exercising in a gym. [MSNBC, 12/11/2001; US Congress, 10/17/2002] According to US investigators, would-be hijacker Ramzi Bin al-Shibh later says he meets Moussaoui in Karachi, Pakistan, in June 2001 (see June 2001). [Washington Post, 11/20/2002]
Entity Tags: Airman Flight School, Zacarias Moussaoui, Ramzi bin al-Shibh
August 23, 2001: FBI Agents Visit Moussaoui's Former Flight School; Fail to Make Connections
Two agents from the Oklahoma City FBI office visit Airman Flight School in Norman, Oklahoma, to learn about Zacarias Moussaoui's training there earlier in the year. One of these agents had visited the same school in September 1999 to learn more about Ihab Ali Nawawi, an al-Qaeda agent who trained there in 1993. Apparently, this agent forgets the connection when he visits the school to look into Moussaoui. He later admits he should have connected the two cases. [Boston Globe, 9/18/2001; US Congress, 7/24/2003, pp. 322] The staff director of the 9/11 Congressional Inquiry later states, "No one will ever know whether a greater focus on the connection between these events would have led to the unraveling of the September 11 plot." [New York Daily News, 9/25/2002] The Oklahoma City office also does not connect Moussaoui to a memo that had come from its office in May 1998 warning that "large numbers of Middle Eastern males" were receiving flight training in Oklahoma and could be planning terrorist attacks (see May 15, 1998). Furthermore, Moussaoui's Oklahoma roommate Hussein al-Attas is also under suspicion at this time (see August 16, 2001). One of the people who attempted to post bond for al-Attas, William Webb, had previously been the subject of an extensive investigation by the same Oklahoma City FBI office. Webb is a member of the extremist group the Muslim Brotherhood and is also Vice President of Overseas Operations and Recruiting for the Palestinian group Fatah. Further, Webb is connected to Anwar al-Awlaki, an imam who has frequent ties with some of the 9/11 hijackers and is suspected of involvement in the 9/11 plot (see March 2001 and After). Al-Awlaki was the subject of an FBI counterterrorism inquiry the year before (see June 1999-March 2000). These connections are also not noticed. [US Congress, 7/24/2003, pp. 322; US Department of Justice, 11/2004, pp. 134-5 ; US District Court for the Eastern District of Virginia, Alexandria Division, 7/31/2006 ]
Entity Tags: William Webb, Hussein al-Attas, Anwar al-Awlaki, FBI Minnesota field office, FBI Oklahoma City field office, Airman Flight School, Zacarias Moussaoui, Ihab Ali Nawawi

redpajama_set_name: RedPajamaCommonCrawl


text:
Non RU Publications
Title: A process-model based approach to prospective memory impairment in Parkinson's disease
Author(s): Kliegel, M.; Altgassen, A.M. ; Hering, A.; Rose, N.S.
Source: Neuropsychologia, vol. 49, iss. 8, (2011), pp. 2166-2177
DOI: https://doi.org/10.1016/j.neuropsychologia.2011.01.024
Publication type: Article / Letter to editor
Subject: DI-BCB_DCC_Theme 3: Plasticity and Memory
Neuropsychology and rehabilitation psychology
Neuro- en revalidatiepsychologie
Organization: SW OZ DCC NRP
Neuropsychologia
Issue: iss. 8
Page start: p. 2166
Page end: p. 2177
The present review discusses the current state of research on the clinical neuropsychology of prospective memory in Parkinson's disease. To do so the paper is divided in two sections. In the first section, we briefly outline key features of the (partly implicit) rationale underlying the available literature on the clinical neuropsychology of prospective memory. Here, we present a conceptual model that guides our approach to the clinical neuropsychology of prospective memory in general and to the effects of Parkinson's disease on prospective memory in particular. In the second section, we use this model to guide our review of the available literature and suggest some open issues and future directions motivated by previous findings and the proposed conceptual model. The review suggests that certain phases of the prospective memory process (intention formation und initiation) are particularly impaired by Parkinson's disease. In addition, it is argued that prospective memory may be preserved when tasks involve specific features (e.g., focal cues) that reduce the need for strategic monitoring processes. In terms of suggestions for future directions, it is noted that intervention studies are needed which target the specific phases of the prospective memory process that are impaired in Parkinson's disease, such as planning interventions. Moreover, it is proposed that prospective memory deficits in Parkinson's disease should be explored in the context of a general impairment in the ability to form an intention and plan or coordinate an appropriate series of actions.
Non RU Publications [9448]


Discussion in 'Konoha TV' started by MacabreAngel, Oct 8, 2006.
I was scanning through the raw of 203/202/*whatever the hell it's being called now* while waiting for the sub and found THIS at the end of the new opening.
Being a food munching stereotypical American, I would recognize those arches anywhere: MCDONALDS! Do they have some sort of sponsoring deal going on? Are we going to be seeing Naruto toys in those Happy Meal boxes soon? One can only speculate... The greatest fast food chain in the world, combing forces with the greatest anime in the world (unless the fillers don't end soon, in which case that title will be handed over to Bleach). Sounds pretty interesting to me.
I need to see that opening!It's a possibility that Naruto toys will be given in that happy meal boxes in Japan.
ep 222: "oh! I want my Mc Konoha Burger... Rasengan"
Sounds a lot better than some of the garbage they've been giving us.
More like most popular animes, not greatest animes.
Yay! And I will start flippin' burgers there in a week!
It gets a whole exciting new dimension for me now.
Perhaps.. because, japanese spelling : Makudonarudo, and it's almost like MakudoNARUTO..
I sense a McDonald's arc coming up!
Naruto's not the only one with that deal, theres also Pocket Monsters and probably more =3.
Aye, i'd like to see a showdown between Naruto and Ronald.
They're sponsering One Piece as well.
ronald jumps in front of naruto and throws a hamburger shuriken at him.
and naruto eats them all, then he says in crappy english "i'm loving it"
Seriously though, if they made Naruto toys for McDonald's I'd be sure to get all of them.
Wierd, while I'm typing this, I look over at the t.v. and notice a McDonald's commercial is on. Coincidence? I think not.
Dear god, they haven't gotten to us yet.
No! Ronald is the AL!
They sponsor the anime so since the time skip hasn't happened it the anime there won't be any post time skip toys from them, yet.
...and whats wrong with that?
and orochimaru sends sasuke out to get some fast food, while recruiting grimace, ronald mc.d, and that bird girl as sound five replacements.
McDonalds sponsoring Naruto? Chouji will have a heart attack of happiness.


THE PRESIDENT OF THE UNION NICK DVORAK '16 CRAFTED his own brew and invited us to try it.
This past week I had the privilege of tasting Nick Dvorak's '16 Renssel-ale homebrewed beer. It is a wheat-based beer brewed with hops and citrus.
Upon pouring the Renssel-ale into my pint glass, I noticed its golden amber color and apparent carbonation. Raising the glass up to the light, I found the wheat beer to be slightly cloudy; however, its absorption remained translucent. It, just like any other wheat beer, maintained an appealing head about three centimeters in length, which dissipated after a couple minutes to a thinner film. This film was maintained by the brew's continuous and attractive carbonation stemming from the middle area of the glass. The overall look was inviting, with no sediment floating around and a dark, golden appearance.
Inhaling the beer's aromas, first through my nose then my mouth, I caught bready notes of wheat followed by a distinct sweetness—the citrus. I enjoy beers brewed with fruity elements, and this is no different. To feel out a better characteristic for Dvorak's beer, I took a couple more exploratory sniffs and detected a hoppy scent, which I find unique in wheat beers, since they usually are not brewed with hops. Finally, taking a sip, I tasted mainly a wheat beer flavor, followed by a slight citrus influence and faint hoppy bitterness. I was expecting more of a citrusy power, but I think over time its citrus flavor slowly diminished, while maintaining the same aroma. As for its bitterness, the brew's hoppy scent correlates with its hoppy taste: present but not overwhelming. Taking another sip of the homebrew, I let the golden liquid roll over my tongue, feeling its smooth texture and crisp carbonation. I relate the feel to a slight seltzer touch, with its bubbles noticeably felt on the tongue.
Overall, the Renssel-ale was a fantastic brew. I can see myself ordering this at the bar or having this in downtown Troy at say, Slidin' Dirty or The Shoppe. Though I do wish I had the chance to taste it fresh, the same brew poured into a pint glass months later still did the job. I really like the carbonation through the cloudy golden amber hue; it was attractive and gave a fresh-off-the-tap impression.
Noticing our review in the past weeks' Polys, President of the Union Nick Dvorak '16 sent over a note asking if Chris and I would like to sample his homebrewed beer. If you follow the RPI subreddit with a keen eye, you'd remember Dvorak, who goes by the handle /u/anonymoose, post about two and a half months ago about possibly starting a homebrew club.
Renssel-ale, as he calls it, is Dvorak's first batch of beer, finishing the product around the weekend of July 4. It's an American wheat ale, which is similar to a Hefeweizen.
After popping the top and pouring the beer into my trusty Superman pint glass, I noticed the aroma of honey and citrus, both of which the beer was brewed with. Also to note was its cloudiness, due to it being an unfiltered wheat beer, my personal favorite variety. On the tongue, it was lightly fizzy and fruity, yet slightly bitter. It was, in fact, reminiscent of Blue Moon, and it definitely had the fuller body Dvorak was looking for.
Wheat beers are rarely bitter, so this was a nice surprise.
Dvorak detailed the brewing process for me, saying it was made with citrusy hops, brewed at a constant 62 degrees with two weeks of primary and one week of secondary fermentation. It was conditioned in the the bottle for two weeks, as Hefeweizens are. He said that when fresh, the citrus was overpowering. After sitting in the refrigerator for a few months, the flavor, according to Dvorak, had mellowed out.
To hit the perfect 5, the beer could be a little more complex; I'd give this beer a 4.75. Combining my personal preference for wheat beers with a pleasant, but not overbearing, sweet touch, Dvorak's Renssel-ale deserves a high mark. He tells me plans to brew a red ale followed by a cider, and I definitely would like to sample each.
Suffice it to say, if politicking doesn't work out for him, Dvorak could easily have a future in brewing.


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text:
BUZZ ALDRIN, WHAT HAPPENED TO YOU IN ALL THE CONFUSION?
translated by Deborah Dawkin
Seven Stories Press ($30)
by Michelle Wallin
With the second man on the moon as his idol, thirty-something Mattias rarely seeks out the attention of the limelight. Preferring to live in the shadows, the humble narrator reveres Buzz Aldrin for his contributions to the Apollo 11 mission while allowing Neil Armstrong to revel in the glory. Wanting to do good in the world without everyone knowing, Mattias lives a quiet life in Stavenger, Norway as a florist for a small, financially struggling nursery, until life changes knock him out of orbit.
Johan Harstad's first novel to be translated into English, Buzz Aldrin, What Happened to You In All the Confusion? is an exquisitely crafted journey into one man's psyche. Ignoring the disintegrating relationship with his girlfriend Helle, the looming bankruptcy of the nursery where he works, and his growing desire to slip away unnoticed, Mattias lives in denial, refusing to see that hiding from the world doesn't save one from inevitable change.
When Helle suddenly breaks off the relationship and the nursery closes, an opportunity to vacation in the Faroe Islands arises. Unfortunately, Mattias finds himself early in the trip on a deserted road with soaking wet clothes, a sore and bloody hand, a wallet full of cash, and no idea where he is or recollection of how he got there. A kindly man discovers the forlorn narrator lying on a bus bench and invites Mattias to stay at his halfway house, a place designed for people suffering from mental illnesses who aren't capable of living independently but who don't need to be institutionalized. Accepting the offer, Mattias finds a home on the Faroe Islands with a cast full of quirky characters: a girl who rides buses to get random men to fall in love with her; a psychologist who hoards the health records of patients; a scarred photographer who swears never to capture another Kodak moment.
With Mattias as his springboard, Harstad writes about mental illness without invoking the normal slew of stigmas. Mattias's straightforward narration about heartbreak, discontent, and unhappiness are emotional but Harstad's writing is far from sentimental. Rather than hide his despondency from loved ones and readers, we see a fresh look at a troubled man trying to make sense of his life and his place in it. Although the novel is pretty much a one-man show, the secondary characters have backgrounds that are eccentric enough to give the dramatic tone of the novel a comedic edge.
While rambling at times, Harstad's novel ultimately provides a thought provoking and insightful look at an individual, one with reactions and feelings to which readers are likely to relate. Mattias unravels his thoughts and allows us to understand his journey so that we, too, can comprehend what happened in the midst of his confusion, and perhaps put words to some of our own.
Click here to purchase this book at your local independent bookstore
Rain Taxi Online Edition, Fall 2011 | © Rain Taxi, Inc. 2011
This entry was posted in Uncategorized and tagged fall 2011 on November 11, 2013 by admin.


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M-JP-MHS
All students of the same study year.
One 120-minute lesson per week (with a 10-minute break)
Admitted to the main subject course.
Developing a broad understanding of jazz and pop history as well as the analytic skill to identify music based on its groove/arrangement/instrumentation.
Related to the main subject course (both involve musical analysis).
Each semester begins with several lectures providing a general introduction to various musical genres, styles and periods.
In subsequent lessons the students themselves prepare and give presentations (in pairs). They may choose from the following subjects:
Fall semester: Jazz
1. Pre-Jazz 1. (Precursor 1): African culture: General characteristics. The African musical heritage.
2. Pre-Jazz 2. (Precursor 2): Cultures of Western and Southern Europe: Classical music, popular music and marching music.
3. Slavery: The transatlantic slave trade. Music of the slaves. Different concepts of slavery arising from the different historical situation in Northern and Southern America and the Caribbean islands.
4. The city of New Orleans: New Orleans Jazz. The first recording.
5. Chicago Jazz: The Great Migration, Musicals, Tin Pan Alley (The Big Five) (N.Y.C.).
6. Swing, the big band era.
7. New Orleans Revival, Dixieland, jump and jive.
8. Bebop, CuBop, European jazz (e.g., Hot Club de France)
9. Cool jazz, west-coast Jazz.
10. Third stream (classical influences in jazz).
11. Hard bop, soul jazz, modal jazz.
12. Free jazz, actual improvisation and free funk.
13. Jazz rock, fusion, neo-bop.
14. Crossover, world music, retro jazz, acid jazz and other contemporary developments.
Spring semester: Pop
1. Country blues (Delta blues, Mississippi blues).
2. Classic blues and boogie-woogie.
3. City/urban blues, electric blues.
4. Rhythm and blues, jump and jive.
5. Rock 'n roll and rockabilly.
6. Beat (Merseybeat, London, Manchester) and surf music (California).
7. Soul (incl. Motown) and funk.
8. Folk rock, country rock and heavy metal ('Flower Power', New York underground scene).
9. Symphonic rock, progressive rock and glitter rock.
10. Reggae, ska.
11. Punk, new wave and disco.
12. Hip-hop, break dance and gangster rap.
13. Techno, house, jungle music and ambient (lounge) music.
14. Grunge, post-punk revival, trip hop, big beat and nu-Jazz (and contemporary developments still to come).
In their presentations, students sketch the cultural/historic background of their subject; they discuss how, why and when a musical style or movement emerged, and how it relates to broader cultural, historical and/or sociological developments. The musical styles are examined both as purely musical developments and in their broader cultural/historical context; in this way students will be better able to grasp the relationship between the different music-historical subjects.
The first three lessons of each semester take the form of lectures by the instructor, who discusses key elements in jazz and pop history and briefly describes their interrelationship.
In the subsequent lessons, the 14 subjects described under Content will each be discussed twice by the participating students, who, in pairs, prepare and give presentations about their subject. In other words: each presentation is given by two students; in case the number of students is higher or lower than 28, some presentations will be given by a single student/group of three students. In each of the 14 lessons, students give 45- to 60-minute presentations about two of the subjects. Both presentations are followed by a group discussion in which any gaps are filled and errors corrected.
In other words: each lesson encompasses one presentation, followed by a group discussion, and each student is involved in the preparation and actual reading of two presentations.
Masters of Jazz (DVD); educational series by Wynton Marsalis about the relation between jazz and classical music; listening material (cd); various books, including Ruud Kuyper: Jazz in stijl; and Fernand Tange: All that Jazz. History of Blues (DVD); History of Gospel (DVD). Video series: Bluegrass and Folk. History of Rock (DVD).
Preparing presentations in pairs.
Collecting listening materials.
Studying the backgrounds of the concepts discussed.
Assessment of the two presentations by the student.
An exam which consists of listening and analysis exercises: identifying genre(s), style, period, with argumentation. Background knowledge about the performers and/or composers.
Exam duration: 1.5 hour.
This exam tests the students' knowledge of jazz and pop history by means of questions from a sociological/historical perspective. For instance, questions may concern the history of the slave trade, the prohibition, the ways in which styles respond to or build on previous styles with different means. Grading: 5 points per question x 15: 75 points = 10; 67.5 = 9; 60 = 8; 52.5 = 7; 47.5 = 6; 40= 5; etc.
The student should have mastered the elements described under Aims.
The student has completed this module if he is awarded a minimum grade of 5.5 both semesters.
Lectures as well as both exams are assessed by the teacher, in writing.
The first six lectures (3x2) provide a general chronological introduction to the history of jazz and pop music. In subsequent classes, students give in total 14 presentations (mostly in pairs) about the history of jazz, blues, gospel and country and folk music; these presentations lead into group discussions about the subject.


TownePlace Suites Boston North Shore/Danvers is just 17 miles north of Boston, so it's easy to visit historical Massachusetts sites. Salem is just 6 miles away for more sightseeing, including the campus of Salem State University. Beverly's scenic beaches, eclectic shopping and lush green spaces are also within a short drive. If you're looking for entertainment right at the hotel, we have complimentary Wi-Fi and premium movie channels. You can choose the perfectly-sized suite for you as we have studio, one- and two-bedroom options available, all with separate living rooms. We also have fully equipped kitchens in our all-suite hotel, so you can whip up your family's favorite meals. Prefer to let someone else cook breakfast? Our complimentary breakfast buffet is full of delicious traditional favorites and healthy options every morning. Enjoy our free parking and slip into a peaceful night's sleep on our soft beds with stylish bedding and fluffy pillows at TownePlace Suites Boston North Shore/Danvers.
Stay active while on vacation with our fitness center with cardio equipment and our seasonal outdoor pool that is comfortably heated.
Bring all of your friends and family along for a wedding using our group booking options, or set up a room block for your conference or convention.
Don't leave your furry four-legged friend at home while you travel if you take advantage of our hotel's pet-friendly policy instead.


In other words, strategy is about: Writing a letter starting with DEAR MSD - (direction)-Where is the business trying to get to in the long-term – The visionE- (environment)- What external, environmental factors affect the businesses' ability to compete? Survival of the fittest is a phrase coined by Herbert Spencer. He wasn't referring to this fittest in the sense of the most highly trained and physically energetic but that those who are the most suited to their environment, i.e. those who adapt and change will survive. The environment around us changes, and if we don't change to match it, our business will not be fit.A – advantage- How can the business perform better than the competition in those markets? i.e. competitive advantage, your USPR - (resources - (What resources (skills, assets, finance, relationships, technical competence, leverage, facilities) are required in order to be able to compete? M - (markets; scope)- Which markets should a business compete in and what kind of activities are involved in such markets? Who are you target market and what is the best medium to reach themS -(stakeholders) -What are the values and expectations of those who have power in and around the business? E.g., your banks, customers, investorThe origin of strategy are military and concern the art of planning and winning wars A strategos was a general in command in the Greek army.Originally strategy - from the ancient Greek – strategia "generalship – was associated with planning and winning of ways.The word "strategy" is derived from the Greek word "stratçgos"; stratus (meaning army) and "ago" (meaning leading/moving).Strategy is an action that managers take to attain one or more of the organization's goals. Strategy can also be defined as "A general direction set for the company and its various components to achieve a desired state in the future. Strategy results from the detailed strategic planning process".A strategy is all about integrating organizational activities and utilizing and allocating the scarce resources within the organizational environment so as to meet the present objectives. While planning a strategy it is essential to consider that decisions are not taken in a vaccum and that any act taken by a firm is likely to be met by a reaction from those affected, competitors, customers, employees or suppliers.Strategy can also be defined as knowledge of the goals, the uncertainty of events and the need to take into consideration the likely or actual behavior of others. Strategy is the blueprint of decisions in an organization that shows its objectives and goals, reduces the key policies, and plans for achieving these goals, and defines the business the company is to carry on, the type of economic and human organization it wants to be, and the contribution it plans to make to its shareholders, customers and society at large. Features of StrategyStrategy is Significant because it is not possible to foresee the future. Without a perfect foresight, the firms must be ready to deal with the uncertain events which constitute the business environment. Strategy deals with long term developments rather than routine operations, i.e. it deals with probability of innovations or new products, new methods of productions, or new markets to be developed in future. Strategy is created to take into account the probable behavior of customers and competitors. Strategies dealing with employees will predict the employee behavior. Strategy is a well defined roadmap of an organization. It defines the overall mission, vision and direction of an organization. The objective of a strategy is to maximize an organization's strengths and to minimize the strengths of the competitors.Strategy, in short, bridges the gap between "where we are" and "where we want to be".
DebriefWhat did I want happen?What actually happen?What caused the gap – or what contributed to its success?What am I going to do about it next time?
Keep moving and never give up. Life works in cycles and moves to a rhythm. You will have up and down. When you hit a slow point or things don't seem to be moving, don't give up, keep going. You are going to hit the wallThe act of holding firmly and steadfastly to a purpose, state, goal, or undertaking despite obstacles, warnings, or setbacks. Achieving your desired vision will not be easy. Then again, living a life of frustration, disappointment and continual under-achievement is not any easier.So why not opt for the former hard work instead of the latter?Be persistent. Nothing can replace it. The less talented will overcome the more talented, and the tortoise will beat the hare. You will need to be persistent, because achieving anything worthwhile takes time and effort. You may have to even face ridicule. Persistence will get you through.US president Calvin Coolidge hit the nail on the head when he said, nothing in the word can take the place of persistence. Talent will not; nothing is more common than unsuccessful men with talent. Genius will not; the world is full of educated derelicts. Persistence and determination alone are omnipotent.
SUMARISE AND TAKE QUESTIONS BEFORE ROUNDING UP WITH YOU GOT THE POWER! I want you to share one thing you plan on doing differently as a result of my presentation. I want you to also write 1 goal that you will achieve in a month. Give it to the person sitting next to you with your contact address; the person will post it to you on that date. What separates ordinary people from extra ordinary people is that little extra. When you make a decision today to ……., (summary of my topic/presentation) you will become extra ordinary and that is who you are. I challenge you to become one, because you can. I think the writer and mountain climber James Ullman summed it all up when he said something like, 'Challenge is the core and mainspring of all human action. If there's an ocean, we cross it. If there's a disease, we cure it. If there's a wrong, we right it. If there's a record, we break it. And if there's a mountain, we climb it. CONCLUSION/Top/You can start at the bottom and rise to the top/You can turn nothing into something/You can turn pennies into fortune and disaster into success/ Power/You Got the Power! To create magic in all areas of your life/You Got the Power! To be successful/You Got the Power! To set and achieve all your GOALS because YOU ARE A UNIQUE & MASTERPIECE CREATION /You have a unique talent, skills and capabilities/You have a unique voiceprint, palm print, footprint and fingerprint/You have a unique destiny that only you can fulfil/You have a unique history and never in the history of the world has someone like you existed/You have a unique genetic code. You have a unique DNA which can distinguish you from any other person living or dead. Some have even suggested that your DNA carries with it the wisdom of previous generations/Above all you are endowed with the seeds of greatness. -'YOU GOT THE POWER!
2. 5 Things to share I got five things I'll like to share with you today if applied will make 2013 your best year ever. So let's get started. I have not come here to impress but to express. To draw from within you the power you already possess. All you need to achieve your goals lies within you. Educate in Latin means - draw out. All the strategies that I will be sharing with you today are within you. I am just here to draw them out. I don't just want positive evaluation and bizarre behaviour for one week. I want you to be different three months from now. At the end of the seminar I want you to share one thing you plan on doing differently as a result of my presentation. That will be our summary. After all, what you receive to make a difference is more important than what I say. When you leave here today you will have solutions to how to set and achieve your goals.
3. My Story Permit me to introduced myself properly I am a study in doggedness and an example of how anyone can overcome adversity to succeed and thus become an inspiration to others. Born in Islington, North London and taken to Nigeria when I was two years old. I got an early jolt in life, when barely eight, my father died. From then life became a struggle. At 10 years old I acquired the thirst to achieve from hawking cold drinks and biscuits on the streets of Lagos to support my mother who sold all her personal belongings to send me to school. In Nigeria I had a varied and interesting career in the entertainment industry from being a Promotions Manager to an Artiste Manager.
4. My Story To conquer poverty, which was my greatest fear when I was growing up, I relocated to London in January 1996 thinking that London's roads are littered with gold and silver. When I arrived I was shocked to discover that a crook had stolen my birth certificate and used it to collect my National Insurance card, credit card, and even opened a bank account. I also discovered I was purportedly married except the crook forgot to invite him. Everywhere I went, I was told somebody was bearing my name. At a stage the authorities did not know who the real Dayo Olomu was. With a strong desire to succeed backed with clarity, action, self belief and my faith, I overcame these obstacles and that little boy who celebrated his 10th birthday at a bus garage in Lagos whose identity was stolen when he came back to live in London is now a social entrepreneur; business improvement consultant, success strategist, corporate trainer, lifestyle business coach and a motivational speaker, a television personality, an agent of positive change and most importantly a husband and a father.
8. Survival of theFittestHerbert Spencer - published Theprinciples of biology in 1864.By fittest, of course, Spencerdidnt have in mind the commonlyused meaning of the word now,i.e. the most highly trained andphysically energetic. The fittestreferred to here are those animalswhich are the most suited to theirenvironment, i.e. those which arebest fitted to survive.The Current Climate is very clear– We must be adaptable tochange.
9. CARBS•How many of you know what carbohydrates do to the body? .•Carbohydrates provide your body with energy•Some might be wandering what has CARBS got to do with making 2013 the bestyear of your life in business. You will know in a minute.•I would like to share with you 5 Indispensable Strategies for Business Excellencethat has helped me in my business. It helped me to achieve my long term goal ofhaving one of my products in more than 100 countries less that 2 years of setting thegoal.•The principles that I will be sharing with you today is called is CARBS.
14. My Purpose & Passion 1. My purpose in life is to use my creativity and enthusiasm to make a positive difference in the world, to serve God, to transform lives and connect people to their destiny. 2. My passion is adding value to lives, helping to grow people, productivity, performance and profit. 3. My core belief is that we are all endowed with the seeds of greatness. 4. My fulfilment is seeing the results of my principles and strategies being transformed into peoples lives. 5. My core values which underpin everything I do revolve around 5Fs: Faith, Family, Fitness, Fairness and Friendship 6 My motto is if you want to obtain something youve never had in your life, you most be ready to do things youve never done before in your life.
15. My mission, vision and legacy 7. My brand value is to offer value for money, quality products and services with an element of fun. 8. My mission is to inspire and empower people and organisations to reach higher levels of achievement and peak performance 9. My Long term goal is to help 1 billion people around the world to achieve their goals by 2020. 10. My vision is to become a leading global brand in the personal development industry and business building industry. 11. My legacy is, when I get to the end of my life, I want to know that my life counted for something, that long after I have left this world, somehow my impact lived on. I want to know that I have done all that I could to make this world a better place, by positively enhancing the lives of those around me and helping thousands, if not millions, to become who they desire to be and achieved what they thought was impossible. I want to know that I gave everything my best shot. I want it to be on record that I maximised my potential and stretched myself to the limit. Most importantly I want to know that I serve God and that I am a good husband and father.
40. Why People Don't Take Action The reason why people do not take action is – FEAR such as • Fear of Ridicule • Fear of rejection. • Fear of making decisions. • Fear of change. • Fear of confrontation. • Fear of loss. • Fear of success. • And of course the big one – fear of failure!
43. Action Cures Fear To conquer the fear of public speaking I joined Toastmasters International. It was the summer of 2003 when I walked into a pub in Croydon. It was the meeting of the Toastmasters Club. When I saw how the people spoke so eloquently there, I asked myself: when will I be able to do this? It took me three months my first engagement as a speaker. But I did it at last and I am still doing it. Today I am not only an advanced toastmaster but I am also a competent leader and the charter president of a toastmasters' club.
44. Action Cures Fear I spent my birthday of 2006 with Tony Robbins attending his Unleash the Power. Firewalking is the act of walking barefoot over a bed of hot embers or stones. The Firewalk is the dramatic highlight of Unleash the Power Within, the introductory three-day seminar given by personal development guru Tony Robbins. Designed to be both a challenge to the participants and a symbol of the change they can make to their lives, it also served as a very effective marketing tool for Robbins' pricey products and seminars. This is where sane humans prance across several yards of smoking-hot, burning coals while their fellow higher achievers and some tribal drummers chant on. And most don't burn their feet, including me. During a fire-walking event, you almost always see a large, glowing bed of burning coals. The bed may be 10 feet long or so. And the glowing coals are real. People actually do walk across the red-hot coals in bare feet.
45. Action Cures Fear I remember the first time I did bar bending in 2007: I was introduced to this by Tosin Ogunnusi, Head of Motivational Training & Personal Development at ThinkTraining Consultancy. Tosin & I stood 6 feet apart, rested each end of a 6 foot long Iron bar in the soft spot located in the front of our throats, just under our Adams's apple. We looked into each other's eye and concentrated on both our current power, as well as having drawn up former powerful images of ourselves by the instructor. We uttered the: Yes, Yes, Yes, I was ready: on the count three, we began to walk towards each other. UNBELIEVABLE! Yes, right in front of our eyes and throats, that 6 foot long once staff iron bar bent into a U shape between us, the belly of the U iron bar touching the ground. What a glorious and exciting illustration that our minds have incredible powers, if only we can channel it. My message to you today for you who fear that you can do something, take action, feel the fear and do it any way.
47. Done is Better Than PerfectFacebook's Founder Mark Zuckerberg wrote a letter to prospectiveshareholders in which he said, "We have the words ‗Done is betterthan perfect' painted on our walls to remind ourselves to always keepshipping".
53. Review ……a retrospective analysis of what you have just done Review actual performance/progress and goals against planned performance At the beginning (or end) of each month, review your progress for the past month, and set your goals for the coming month. Set easily achievable goals — it's better to set your sights low (at least at first) and achieve them than to set them too high and fail. Monthly goals should be mini-goals of your overall yearly goals. At a set time each week (Mondays work for me), review your progress for the last week, and set goals for the week. These goals should be mini- goals for your monthly goals. For each of these goals, list a few action steps. Then schedule the action steps throughout the week (one step per day is ideal).
59. You! You!! You!!! If the three most important words in real estate are location! Location!! Location! the three most important words in achieving your success in life are, YOU! YOU!! YOU!!! You must believe in yourself. It is said that people succeed when others do not believe in them. Rarely does a person succeed when he does not believe in himself. You have to have self belief to get anywhere in life. According to Venus Williams, the Olympic gold medallist and professional tennis champion, ―you have to believe in yourself when nobody else does. That's what makes you a winner‖. The size of your success is determined by the size of your belief. - David Schwartz - The Magic of Thinking Big When I was writing my book ―4 indispensable Strategies for Success‖ the first person I told said to me, ―Dayo, you must be a joker and a dreamer. What do you know?‖ But I believed in my ability to make it happen and today the book is now a best seller in UK and Nigeria. When no one believed in me, I believed in myself and achieved more then anyone thought possible.
67. Persistence is Important. The act of holding firmly and steadfastly to a purpose, state, goal, or undertaking despite obstacles, warnings, or setbacks. Achieving your desired vision will not be easy. Then again, living a life of frustration, disappointment and continual under-achievement is not any easier. So why not opt for the former hard work instead of the latter? Be persistent. Nothing can replace it. The less talented will overcome the more talented, and the tortoise will beat the hare. You will need to be persistent, because achieving anything worthwhile takes time and effort. You may have to even face ridicule. Persistence will get you through. US president Calvin Coolidge hit the nail on the head when he said, nothing in the word can take the place of persistence. Talent will not; nothing is more common than unsuccessful men with talent. Genius will not; the world is full of educated derelicts. Persistence and determination alone are omnipotent.
68. Ordinary & Extra Ordinary People What separates ordinary people from extra ordinary people is that little extra. When you make a decision today to go extra mile and apply what you have learnt today from tomorrow you will become extra ordinary and that is who you are. I challenge you to become one, because you can. I think the writer and mountain climber James Ullman summed it all up when he said something like, ‗Challenge is the core and mainspring of all human action. If there's an ocean, we cross it. If there's a disease, we cure it. If there's a wrong, we right it. If there's a record, we break it. And if there's a mountain, we climb it.
71. You Got The Power You have a unique talent, skills and capabilities You have a unique voiceprint, palm print, footprint and fingerprint You have a unique destiny that only you can fulfil You have a unique history and never in the history of the world has someone like you existed You have a unique genetic code. You have a unique DNA which can distinguish you from any other person living or dead. Some have even suggested that your DNA carries with it the wisdom of previous generations. Above all you are endowed with the seeds of greatness.' YOU GOT THE POWER!
72. You Got The Power!


South Carolina was a significant state during the Revolution, in that more battles were fought here than in any other state in the union. One of the most important, if not the single most important, battle during the Revolution was fought at King's Mountain. Here British commander Patrick Ferguson camped out to snuff out the Americans. Ferguson personally picked this mountain because he thought that the Americans would not be able to defeat him here.
Originally, the forest surrounding King's Mountain was filled with towering trees with hardly any underbrush. This made it easy for the British to spot American troops. But the adverse was true as well. The Americans, coming from Tennessee, North Carolina, Georgia, and South Carolina hid behind trees and slowly inched their way up to the British stronghold. The Americans were repelled several times, but their fortitude proved stronger than that of the British and they commanded the mountain in only an hour of fighting.
Ferguson was killed at this battle along with a good number of his British troops. The Americans won the battle and sent couriers to Washington to inform him of their success. This significantly turned the tide of the war in the states. This battle prompted Cornwallis to start his trip into North Carolina towards Yorktown.
After the defeat of the British at King's Mountain, the Americans won the day again at Cowpens. Afterwards, the Americans headed north to the Dan River before forcing the surrender of Cornwallis at Yorktown.


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Alt-Right Elite: Donald J. Trump's World of Architecture
Alt-Right Elite: Donald J. Trump's World of Architecture - The Knoxville Mercury
In Architecture Matters by George Dodds December 21, 2016 leave a COMMENT
While campaigning, Donald J. Trump liked to broadcast Elton John's "Rocket Man" and "Tiny Dancer," much to the chagrin of Mr. John. For the 65,476,535 Americans who cast votes on Nov. 8 (48.1 percent and counting), David Byrne's "Burning Down the House" was more apt. That said, on Jan. 20, 2017, Trump will be the first president since Thomas Jefferson with such close ties to the architectural world, albeit more as a collector than designer. But since this leader of the Alt-Right Elite is soon to become Leader of the Free World, it's worth getting some sense of his past relation to architecture before he burns down any more houses.
The Italians have an expression for people like Mr. Trump—several of them actually. But the only one I can use in this venue is "Nato con una camicia." The direct translation of which is "born with a shirt," which essentially equates to being born with a silver spoon in one's mouth. (Yet another trait he shares with Mr. Jefferson.) As Mr. Trump worked his way up from the top, he built a domain of perception—aka: a brand—based on an empire of building with other people's money. You have to hand it to him; never has anyone achieved so much having done so little for so many for so long.
The results of the November 2016 election cycle demonstrated much to those interested in learning from such an unprecedented phenomenon. Chief among these lessons was the tone-deafness of America's left-leaning leaders. More astounding still, many of the brightest political observers of our generation continue their hearing impaired commentaries, learning little from seismic events.
Writing in the wake of Italy's failed referendum causing the resignation of Prime Minister Matteo Renzi, in his Dec. 5 New York Times column, Roger Cohen voices a claim made by many: "Democracies, it is clear, have not been delivering to the less privileged, who were disenfranchised or discarded in the swirl of technology's advance." Yet, like so much of liberal post-election self-flagellation, this is not only facile, it is also simply at odds with the facts. When such smart and level heads as Mr. Cohen get something so obviously wrong, one really begins to worry.
If we indeed live in a post-truth era, I choose to ignore it for the sake of argument. Facts and figures demonstrate that in the United States, the underprivileged have fared far better under the Obama administration than at any time since The Great Society, despite what the Republican-held House and Senate have tried to do to them. Over 13 million more have health insurance today than several years ago owing to the Affordable Care Act (Obamacare). Unemployment is at record lows, as are mortgage rates. But as Bill Murray's character, Tripper, chants in Meatballs, "It just doesn't matter."
Calm and shrewd stewardship at the executive level pulled President Bush's Reign of Error economy back from the brink. Meanwhile, House Republicans blithely passed 60 perfunctory bills to repeal all or part of Obamacare. During that same time, owing to unprecedented nominal legislative activity, the passing of resolutions to name U.S. post offices accounted for an average of 15 percent of all congressional productivity.
One area, sadly, where employment numbers are way down (and will stay so) is in coal mining, but this has nothing to do with imaginary illegal aliens or Secretary Clinton's inexplicable choice of DSL over high-speed cable. It has been a trend since the end of the World War II and will continue, not because of globalization or new digital technologies, but because of longstanding lower demand and because strip mining and mountaintop removal have permanently replaced the subterranean coal miner.
What Mr. Cohen ought to have been talking about, therefore, was not the failure of liberal democracies to deliver to the underprivileged, but the perception of that failure. Managing the domain of perception is where Mr. Trump excels and the left has truly lost its way. And as everyone knows, perception always trumps reality, just as it trumped Mr. Cohen and convinced coal miners in places like Clay County, Ky. (America's poorest county, which voted for Mr. Trump by as much as 90 percent) to shoot themselves in both feet by backing a candidate who will strip them of access to one of their most basic human rights: affordable medical care. But it seems that this, too, just doesn't matter.
Renderings are the sole property of New World Design Ltd., Chicago, Ill. All rights reserved.
New World Design created several photomontages of flying gilded pigs to cover the massive and controversial TRUMP sign on the Chicago Trump Tower.
What does matter (to architects, at least) is that very little of what The Trump Organization (TTO) has built approaches the level of architecture, which is clear to anyone well versed in the topic. It is more accurate to think of his buildings as Depreciating Monetary Delivery Systems. Among the TTO-built exceptions are Arthur Erickson's hotel in Vancouver, Canada, and Chicago's Trump® Tower (2008) by Adrian Smith of SOM in Chicago (largely funded by George Soros, back when Mr. Trump was still a card-carrying Democrat). The other exceptions are all previously existing landmarks, which he marks with his brand, from discrete buildings to vineyards to endangered 4,000-year-old Scottish dunes.
The former Bank of Manhattan Trust Building at 40 Wall St. (1929-30) is an elegant Art Moderne/Art Deco tower that, until the Chrysler Building's antenna was completed in 1931, was the tallest building in the world. It now goes by the poetic moniker, "The Trump® Building." There must be several floors of New York's Trump® Tower packed with round-the-clock staffers whose only job is to invent new names for Mr. Trump's properties. As of this writing, excluding golf courses, there are no fewer than 25 major buildings branded Trump®.
The infamous MacLeod House & Lodge in Northeastern Scotland is the only one of his 15 resort hotels unbranded, and for good reason. If traveling anywhere near Balmedie, Scotland, it's probably best to let the natives assume you're from Toronto, Calgary, or Drumheller. The only thing the locals dislike more than Mr. Trump is comparing the Jacobite Rebellion to the British invasion of the Falklands. He promised to spend $1.5 billion, build a large hotel complex, and employ thousands; instead he destroyed "Scotland's Amazon," employed relatively few, spent 1/30th the sum promised, and gave them the one thing Scotland desperately needed: another golf course.
There is a perception in our country that to be wealthy is to have good taste; you would think much of what we see in places like Palm Beach, Las Vegas, and most upper-middle class suburbs would have long ago demonstrated the inverse. Similarly, Americans tend to believe that bigger is better; if any of the survivors of the Titanic were still around, they would tell a different story. Yet, we continue to get bigger and more tasteless buildings from the likes of Mr. Trump. During an interview while campaigning, he explained that what made one of his new building projects (that he is branding, not building) so much better than anything he had branded before was that instead of two towers, this one would have three. "It will be amazing!" It's just this kind of razor-sharp reasoning that makes one curious about the acceptance rate at Penn's Wharton School of Business back in the 1960s.
Mr. Trump's "renovation" of Mar-a-Lago hints at what he may do to the White House—not with its power, but the building. It will certainly be the smallest of his homes. Have you seen the Drottningholm Palace or the Kremlin? The private family quarters on the second floor will certainly be cramped for a man with so many wives and multi-generational children. Additional levels of living space, a few new bathrooms here, a few bedrooms there, and closets—lots of closets. Not since Warren G. Harding has there been a president-elect entering his first term with more baggage in need of closets.
No doubt Mr. Trump sees its wealth of white classical detailing as mere substrate awaiting gold leaf. The Blue Room (restored by Jackie Kennedy) could use a few more colors, and the East Room (home to state dinners and the venue for awarding the Presidential Medal of Freedom) could profit from a few water features and a retinue of gilded putti.
Already on the drawing boards no doubt are the Trump® White House Penthouses, which—after a proper amortization vigil—could easily be flipped into condos. Who knows, the White House could actually turn a profit. So many air rights, so little time. The Clinton administration's Lincoln Bedroom kerfuffle seems quaint.
Not long after the election, many high-profile critics of Mr. Trump radically realigned their positions for personal gain. So, too, did entire industrial sectors, along with professional advocacy groups such as the American Institute of Architects, the latter demonstrating as an institution what Philip Johnson said of himself, quoted in a 1977 New Yorker interview: "Whoever commissions buildings buys me…. I'm for sale. I'm a whore." Mr. Johnson was responsible for re-skinning the former Gulf and Western Building (1969) in Manhattan for Mr. Trump shortly after Trump acquired it in 1994. The architecture critic of The New York Times at the time characterized the results as "a 1950s International Style glass skyscraper in a 1980s gold lamé party dress…."
I've known several non-whore architects in my life, many of whom practice here in Knoxville. As for the self-proclaimed whore and leading figure in the American Nazi party throughout much of the 1930s, Mr. Johnson's aphorism does a disservice to sex-industry workers. That the president-elect continues to pimp the Trump® brand even during the transition ought to surprise no one. It just doesn't matter. After all, unlike Jefferson, at least Mr. Trump hasn't slept with any of his slaves. But who knows, perhaps those tax returns will reveal more than we think. There may yet be a Sally Hemings in one of his many closets, which could go a long way to explaining his purchase of a vineyard in Albemarle, Va.
In the meantime I vote for David Byrne to perform "Road to Nowhere" at the inauguration. I suspect Elton John would prefer it to belting out "Goodbye Yellow Brick Road."
…Where the dogs of society howl
You can't plant me in your penthouse
I'm going back to my plough…
About the Author Most Recent Stories
George Dodds
George Dodds' Architecture Matters explores issues concerning the human-made environment, primarily focused on Knoxville and its environs. He has been teaching and publishing commentaries on the practice and history of architecture, urbanism, and landscape architecture for over 30 years. He has practiced in Detroit, Philadelphia, and Washington, D.C., has lectured internationally, and has served on the editorial boards of several journals. Since 2000, he has been on the faculty of architecture at the University of Tennessee.
Pro Bono Publico: Why Does a Bank Building Look Like a Suburban House?
An Art Untrue: Difficult Lessons From the New Walnut Street Garage
The Delible Lightness of Building
What Should We Do With the James White Parkway?


Hey Heidi here, ready to start the Holiday Craft series 2014, I was planning to start tomorrow Monday November the 3rd, but tomorrow I will be having a special post, that I hope you won't miss.
If you follow me on Flickr, you probably already had seen many of my 2014 holiday cards. I going to start the series with a very special card that I made using a very cute stamp set: The Alpine Carolers from Mama Elephant, I want to start with this card because I want to enter it to the Mama Elephant and me November challenge, which, is all about holiday cards.
Instructions and supplies are below.
I used the picture frame from the "Instalove" creative cuts from Mama Elephant to created a window (see picture above), if you have a window die that would fit your carolers you could used it, if not this is how you could created your own window. I distress it a little bit using "old paper" distress ink.
For the back ground I stamped two times the skyline of buildings from the "Central Park" Stamp set from Mama Elephant, I use black and grey ink for that. I also used some "broken china" distress ink to create the appearance of sky, and then I used a light yellow marker to fill in the windows on the buildings.
I die-cut some snowy hills using the "Landscaping Trio" creative cuts dies, from Mama Elephant and sponge a little bit the edges with light blue ink.
I used the very lightest part of the falling snow stencil from SSS to create some falling snow with texture paste.
I stamped, colored (with Copic markers), and die cut the carolers, from the Alpine Carolers" stamp set from Mama Elephant, I chose the tree carolers to resemble my own family (my husband my little boy, and I), and placed them on the snow.
I also stamped, color, and fuzzy cut some ornaments from the same stamp set, to decorate my window. I placed all of my elements on the scene and adhered them using little dots of liquid adhesive.
I stamped the "From my family to yours" sentiment from the "Alpine carolers" stamp set, and created a little banner with it, which I sponged with a little bit of "old paper" distress ink.
I pop the window over my scene with some foam adhesive.
Finally I adhered the window with the scene to a red note card that I stamped with a brick background.
Thanks for stopping by, your kind comments make my day happier!
What a sweet scene, love the added baubles at the top of the window sill! So glad you could join us at Mama Elephant & Me!
Such a cute card! Love the winter scene you created!
Woow great idea to make a windows scene. So cute!


This Single thick square silver cake card measures 8" and is ideal for lighter sponge cakes that need a hidden support or simply for your gateaux and desserts. Also ideal for multi tiered sponge Wedding cakes.
This 8" single thick Square cake card is ideal for presenting your celebration cakes and desserts.