---
abstract: |
    [**Abstract**]{} [ ]{}Based on Pontryagin Maximum Principle (PMP), this paper establishes a generalized PMP aiming at control system with with extra input/output terms. The paper details the adaptive target and gives a proof of the generalized theorem. Transformation and application of this specific method is showed and thereafter an example explained its feasibility.

    [**Keyword**]{} [ ]{}Pontryagin Maximum Principle; port-Hamiltonian Systems
author:
- |
    [ Yuanzun Zhao]{}\
    [Department of Mathematics]{}\
    [Peking University, Beijing 100871, China]{}\
    [email: lukesweet@163.com]{}
title: '**Generalized Pontryagin Maximum Principle in port-Hamiltonian Systems and Application** '
---

[**Introduction**]{}
====================

Optimal control, a crucial component of modern control theory, has already been generalized to many kinds of control systems. One of the most used method to deal with optimal control problems is Pontryagin Maximum Principle(PMP)[@qy1]. The core idea of PMP is to embed the target control system into a Hamiltonian system and transform the optimal requirement into a boundary condition[@qy2]. However, not all the problems can be solved through PMP.

Towards control problems with extra terms in the control equation or extra algebraic expression, which cannot be easily solved by classic PMP, it’s effective to embed the systems into port-Hamiltonian. The embedding method, analogous to handling of PMP[@An1], is called Pontryagin Maximum Principle for Port-Hamiltonian Systems and will be detailed in the following. All the conclusions is based on the port-Hamiltonian systems theory and is proved of its reliability and maturity.[@pa1]

[**Acknowledgement:**]{} I would like to thank Mr. Zhangju Liu for his useful advice and great encouragement.

[**port-Pontryagin Maximum Principle and Application**]{}
=========================================================

[**Generalized Optimal Control Problems in port-Hamiltonian Systems**]{}
------------------------------------------------------------------------

Consider the special control system described as follows: $$\dot{q}=F_u (q)+B(q)f',$$ $$e=A^{T}(q)(\dot q-B(q)f')$$ $q\in M,    u=u(t)\in U$, $f'=f'(t),e=e(t)$ is a continuous function in $N$, with initial conditions $$q(0)=q_0,$$ Given cost function $¦Õ:M\times U\times T^{*}N \rightarrow  \mathbb{R}$, the problem is to find a pair of control $u=\tilde{u}$ and input that minimizes $$J=\int_0^{t_1} \varphi(q(t),u(t),e(t)) dt.$$

This is a typical control problem in port-Hamiltonian system, with $B(q)f$ as a port of any kind. Notice that $f$ is a continuous input(different from $u$), that is, it cannot be simply viewed as a part of control. The basic idea dealing with control problems of this kind is dividing it into two parts: finding out the optimal $u$ for fixed $f$, and then finding out the optimal continuous $f$.

To solve the former part, we need to establish a generalized PMP aimed at the port. It’s required to embed the control system in a port-Hamiltonian system, just like PMP embedding control systems in Hamiltonian systems. While the latter part requires transformation and application of PMP.

The two parts are respectively discussed as follows.

[**Generalization to PMP in port-Hamiltonian system** ]{}
---------------------------------------------------------

We now consider embedding the optimal control problem in the following port-Hamiltonian system: $$\left\{
\begin{aligned}
&\frac{\partial q}{\partial t}=\frac{\partial H_u}{\partial p}+B(q)f'\\
&\frac{\partial p}{\partial t}=-\frac{\partial H_u}{\partial q}+A(q)f\\
&e'=B^{T}(q)\frac{\partial H_u}{\partial q}\\
&e=A^{T}(q)\frac{\partial H_u}{\partial p}
\end{aligned}
\right.$$ whereas $M\subset \mathbb{R}^n$ is a configuration space, $U\subset \mathbb{R}^l$ is admissible control set, $N\subset \mathbb{R}^k$ is admissible input set. $q\in M$ is the state of system, and $u(t)\in U$ is a preinstalled control, $A(q), B(q)$ is $n\times k$ transform matrixes depending on state $q$.

With Hamiltonian defined as $h_{u,f}(\lambda)=\langle \lambda,f_u (\lambda) \rangle, \lambda\in T^{*}M$, thereupon we have the following geometric statement of port-PMP: \[section\]

Given an admissible control $u=\tilde{u}(t),f=\tilde{f}(t)$, if (2.2),(2.3) have a solution $\tilde{q}(t)=q_{\tilde{u}(t),\tilde{f}(t)}(t)$, if\
$$\tilde{q}(t_1)\in \partial A_{q_0}(t_1),$$ here $A_{q_0}(t_1)$ indicates the attainable set from point $q_0$ in $t_1$ time, whatever $u(t)$,\
with $f(t)=\tilde f(t)$ fixed.\
Then there exists a Lipschitzian curve $\lambda_t\in T_{\tilde{q}(t)}^* M,t\in [0,t_1]$ in the cotangent bundle, such that\
$$\lambda_t\not\equiv0,$$ $$\frac{\partial \lambda}{\partial t}=-\frac{\partial h_u}{\partial q}+A(q)f,$$ $$h_{\tilde{u}(t),\tilde{f}(t)}(\lambda_t)+\int_0^{t} e(\tilde{u},\tau)f(\tau)+e'(\tilde{u},\tau)f'(\tau)d\tau$$ $$=\max_{u\in U}\{h_{u(t),\tilde{f}(t)}(\lambda_t)+\int_0^{t} e(u,\tau)f(\tau)+e'(u,\tau)f'(\tau)d\tau\}$$ for almost all $t\in [0,t_1]$

To prove the conclusion, a vector field depending on two parameters needs to introduced first:\
$$g_{\tau,u}={P_\tau^{t_1}}_*(F_{u(\tau)}-F_{\tilde u(\tau)}), \tau \in [0,t_1],u\in U$$

According to [@An1], $$q_u(t_1)=q_1\circ \vec{exp} \int_0^{t_1} g_\tau,u(\tau) dx$$

Thus we have the following lemmas:

\[Lem1\]Let $\Gamma \in[0,t_1]$ be the set of Lebesgue points of the control $\tilde{u} (\cdot)$. If $$T_{q_1}M=cone\{g_{\tau,u} (q_1)|\tau \in T ,u\in U\}$$ Then $$q_1\in intA_{q_0}(t_1)=A_{q_0}(t_1)\backslash \partial A_{q_0}(t_1)$$

The proof is in [@An1].

Now in the port-Hamiltonian System, we define a new flow $g^{P}$ $$g_{\tau,u,f}={P_\tau^{t_1}}_*((F_{u(\tau)}+B(q(t))f'(t))-(F_{\tilde u(\tau)}+B(q(t))f'(t)), \tau \in [0,t_1],u\in U$$

\[Lem2\]Let $\Gamma \in[0,t_1]$ be the set of Lebesgue points of the control and input $\tilde{u} (\cdot),\tilde{f} (\cdot)$. If $$T_{q_1}M=cone\{g_{\tau,u,f} (q_1)|\tau \in T ,u\in U\, f\in Q\}$$ Then $$q_1\in intA_{q_0}(t_1)=A_{q_0}(t_1)\backslash \partial A_{q_0}(t_1)$$

Define $\hat u=(u,f)$, $\hat u\in L^k\times C^{(1)l}\subset L^{k+l}$. Apply Lemma \[Lem1\] to $\hat u$ and we directly get the conclusion.

Now return to proof of the theorem. Let the endpoint of trajectory $q_1$ satisfies $q_1=\tilde{q}(t_1)\in \partial A_{q_0}(t_1)$. By Lemma \[Lem2\], if this condition holds, origin point $o_{q_1}\in T_{q_1}M$ belongs to $\partial cone\{g_{\tau,u,f} (q_1)|\tau \in T ,u\in U, f\in N\}$, so this set has a hyperplane of support at the origin: $$\exists \lambda^{E*}_{t_1}\in T_{q_1}^*M, \lambda^{E*}_{t_1}\not=0,$$ satisfies: $$\langle \lambda^{E*}_{t_1},g_{t,u,f}(q_1)\rangle\leq 0, \forall t\in[0,t_1],u\in U$$ Let $\lambda_{t_1}^*=\lambda^{E*}_{t_1}+\int_0^{t_1} A(q(t))f(t)dt$

thus it satisfies: $$\langle \lambda_{t_1}^*+\int_0^{t_1} A(q(t))f(t)dt,g_{t,u,f}(q_1)\rangle\leq 0, \forall t\in[0,t_1],u\in U$$ that is $$\langle \lambda_{t_1}^{E*},P_{t*}^{t_1}(F_u(q_1)+\int_0^{t}B(q)f'd\tau)\rangle\leq \langle \lambda_{t_1}^{E*},P_{t*}^{t_1}(F_{\tilde{u}}(q_1)+\int_0^{t} B(q)f'd\tau)\rangle$$ further, $$\langle P_{t}^{t_1*}(\lambda_{t_1}^{E*}),F_u(q_1)+\int_0^{t}B(q)f'd\tau\rangle\leq \langle P_{t}^{t_1*}(\lambda_{t_1}^{E*}),F_{\tilde{u}}(q_1)+\int_0^{t}B(q)f'd\tau\rangle$$

Then flow $P_t^{t_1}$ defines Lipschitzian curve $\lambda_{t}^*$ in $ T_{q(t)}^*M$: $$\lambda_{t}^*\triangleq P_t^{t_1*}\lambda_{t_1}^*+\int_0^{t}A(q(\tau))f(\tau)d\tau\in T_{\tilde{q}(t)}^*M$$

In terms of this covector curve, the inequation above reads: $$\langle \lambda_{t}^*-\int_0^{t} A(q)fd\tau, F_u(q_1)+\int_0^{t}B(q)f'd\tau\rangle\leq \langle \lambda_{t}^*-\int_0^{t} A(q)fd\tau, F_{\tilde{u}}(q_1)+\int_0^{t}B(q)f'd\tau\rangle$$ that is, $$\langle \lambda_{t}^*,F_u(q_t)\rangle+\int_0^{t}e'(u,\tau)f'(\tau)+e(u,\tau)f(\tau)d\tau\leq \langle \lambda_{t}^*,F_{\tilde{u}}(q_t)\rangle+\int_0^{t}e'(\tilde{u},\tau)f'(\tau)+e(\tilde{u},\tau)f(\tau)d\tau$$ which exactly equals to Hamiltonian maximum conditions: $$\begin{aligned}
&&h_{\tilde{u}(t),\tilde{f}(t)}(\lambda_t)+\int_0^{t} e(\tilde{u},\tau)f(\tau)+e'(\tilde{u},\tau)f'(\tau)d\tau,\\
&&=\max_{u\in U}\{h_{u(t),\tilde{f}(t)}(\lambda_t)+\int_0^{t} e(u,\tau)f(\tau)+e'(u,\tau)f'(\tau)d\tau\}\end{aligned}$$

Besides, since the curve is fixed once the terminal point is fixed, the following equation holds: $$\lambda_{t}^*\triangleq P_t^{t_1*}\lambda_{t_1}^{E*}+\int_0^{t}A(q(\tau))f(\tau)d\tau=\lambda_{t_1}^*\circ (\vec{exp}\int_t^{t_1}-\frac{\partial h_{u,f}}{\partial q}+A(q(x))fdx)^*-\int_t^{t_1}A(q(\tau))f(\tau)d\tau$$ that is, $$\frac{\partial \lambda_t^*}{\partial t}=-\frac{\partial h_{u,f}}{\partial q}+A(q)f\\$$

Thus, the existence of extremal curve is proved.

[**Application of PMP for port-Hamiltonian System and Transformation of Control**]{}
====================================================================================

[**Application of PMP for port-Hamiltonian System**]{}
------------------------------------------------------

PMP for port-Hamiltonian System is adaptive to control systems with either extra input or output. Input $B(q)f'$ in (2.1) corresponds to storage port and output $e$ in (2.2) can be either dissipation port or another storage. Analogously to application of PMP to classic control optimal problems, we introduce an extremal parameter $\nu$.

Consider the following optimal control problem: $$\begin{aligned}
&&\dot{q}=f_u(q), q\in M, u\in U\\
&&q(0)=q_0\in M\\
&&t_1 fixed\end{aligned}$$ and the cost function is defined as $$\hat{J}=\int_0^{t_1}\hat{\varphi}(q(t),u(t),e(t))dt,$$

We extend this control system as follows: $$\hat{q}=\left(
\begin{array}{c}
J_{q_0}(u)\\
q
\end{array}
\right)$$ and extend the corresponding vector field: $$\hat{f}_u(q)=\left(
\begin{array}{c}
\varphi(q,u)\\
f_u(q)
\end{array}
\right)$$

Thus we get a new control system: $$\begin{aligned}
&&\dot{\hat{q}}=\dot{f}_u(q), q\in M, u\in U\\
&&\dot{q}(0)=\dot{q}_0=\left(
\begin{array}{c}
0\\
q_0
\end{array}
\right)\\
&&t_1 fixed\end{aligned}$$ where $\hat{q}_0$ is a (n+1)-dimension random vector.

Notice that if $\tilde{u}$ is optimal control, then the following condition holds: $$h_{\tilde{u}(t)}(\lambda_t^*)=\max_{u\in U} \{h_{u(t)}(\lambda_t^*)$$ Then the terminal point satisfies: $$\tilde{\hat{q}}(t_1)\in \partial A_{\hat{q}_0} (t_1),$$ Therefore, PMP for port-Hamiltonian Systems can be applied to find the extremal curve.

[**Introduction of extremal parameter**]{}
------------------------------------------

When use PMP\* to solve optimal control problems, we need transform it into Hamiltonian equations through the Hamiltonian. However, directly using the previous Hamiltonian does not extinguish maximum from minimum of cost function. To make up the defect, we introduce new parameters $\nu$ and a new control $w$. Define $y=J_{q_0}(u)$, and consider the following system: $$\begin{aligned}
&&\dot y=\varphi(q,u)+w\\
&&\dot q= f_u(q)\end{aligned}$$

Then the extremal stochastic curve in origin system corresponding to the control $w(t)\equiv0$. As a result, it comes to the boundary of attainable set at $t_1$. Apply PMP to it.\
Define new Hamiltonian as follows: $$\hat{h}_{(w,u)}(\nu,\lambda^*)=\langle \lambda^*,f_u\rangle +\nu(\varphi+w)$$

The corresponding Hamiltonian system is $$\left\{
\begin{aligned}
&\frac{\partial \nu}{\partial t}=\frac{\partial \hat h}{\partial y}=0\\
&\frac{\partial y}{\partial t}=\varphi+w\\
&\dot\lambda_t^*=\vec h_{\tilde{u}(t)}(\lambda_t)
\end{aligned}
\right.$$

The first equation stands for $v\equiv constant$.

In terms of this system, Hamiltonian Maximum condition is: $$(\langle \lambda_t^*,f_{\tilde{u}(t)}\rangle+\nu\varphi(\tilde{q}(t),\tilde{u}(t)))=\max_{u\in U,w\geq0} (\langle \lambda_t^*,f_{u(t)}\rangle+\nu\varphi(\tilde{q}(t),u(t)))+\nu w$$ Since the maximum of original system is attained, there must be $\nu\leq 0$, thus we can set $\nu=0$ in the right hand of maximum condition: $$(\langle \lambda_t^*,f_{\tilde{u}(t)}\rangle+\nu\varphi(\tilde{q}(t),\tilde{u}(t)))=\max_{u\in U,w\geq0} (\langle \lambda_t^*,f_{u(t)}\rangle+\nu\varphi(\tilde{q}(t),u(t)))$$ So we prove the following conclusion:

If $u=\tilde u (t)$ is the optimal control for problem (3.9)-(3.11), that is, $\tilde u(t)$ minimizes $J(u)$. Define generalized Hamiltonian family: $h_{u,f}^\nu(\lambda)=\langle \lambda,f_u (\lambda) \rangle+\int_0^{t} e(\tau)f(\tau)+e'(\tau)f'(\tau)d\tau+\nu\varphi(q(t),u(t),e(t)), \lambda\in T^{*}M$£¬then there exists a stochastic Lipschitzian curve $\lambda_t\in T_{\tilde{q}(t)}^* M,t\in [0,t_1]$, and a number $\nu\in \mathbb{R}$ such that\
$$\begin{aligned}
&&\lambda_t\not\equiv0,\\
&&\frac{\partial \lambda}{\partial t}=-\frac{\partial H_u}{\partial q}+A(q)f,\\
&&h\nu_{\tilde{u}(t),\tilde{f}(t)}(\lambda_t)=\max_{u\in U}\{h^\nu_{u(t),\tilde{f}(t)}(\lambda_t)\},\\
&&\nu\leq0,\end{aligned}$$ for almost all $t\in [0,t_1]$

since pair $(\lambda_t^*,\nu)$ can be multiplied by any positive number, only abnormal case $\nu=0$ and normal case $\nu=-1$ need to be considered. Besides, when solving maximum problems, $\nu\leq 0$ becomes $\nu\geq 0$, that is, analogously abnormal cases $\nu=0$ and normal case $\nu=1$.

[**Example**]{}
===============

To demonstrate the method more specifically, we consider its application to classic Cheapest Stop Problem.

The original problem can be described as follows: A train moves on the railway. We start braking the train at certain initial location and speed. The goal is to stop it with minimum expenditure of energy, which is assumed proportional to the integral of squared acceleration.

Its mathematic statements is $$\begin{aligned}
&&\ddot x=u, \\
&&x(0)=x_0\\
&&\dot x(0)=v_0\\
&&t_1 fixed, x(t_1)=x_1, \dot x(0)=0,\end{aligned}$$ find $u=\tilde u$ minimizing $J(u)=\int_0^{t_1}u^2dt$.

Now consider that an auxiliary stopping device is introduced. The device is a slope that can be slowly uplifted at the entrance of station, simultaneously saving energy in gravitational form. The saved energy can be partially reused. Our new goal is to stop the train with minimum expenditure of cost, that is, energy used in stopping plus brake abrasion, minus energy that can be reused. The reuse ratio is defined as $R_u$, while the lifting of slope is measured by a continuous variable $f$. As we can see, with $f$ going up, $\dot x$ and $x$ is affected. The braked abrasion is assumed linear to the integral of output $e$.

Its mathematic statement can be organized as follows: $$\begin{aligned}
&&\left\{
\begin{array}{l}
\dot x_1=x_2\\
\dot x_2=u\\
\end{array}
\right.,x=\left(
\begin{array}{c}
x_1\\
x_2
\end{array}
\right)\in R^2, u\in R\\
&&x(0)=x^{(0)}\\
&&t_1 fixed,\\
&&\dot x=\left(\begin{array}{c}
x_2\\
u
\end{array}\right)+B(x)f\\
&&e_1=A(x)\dot x\\
&&e_2=B(x)\dot x\\
&&\hat J(u)=\int_0^{t_1}u^2+(e_1+e_2)fdt\rightarrow min.\end{aligned}$$ The system has two obvious output $e_1$ and $e_2$, thus be applied with PMP for port-Hamiltonian systems. Its generalized Hamiltonian is $$h_{u,f,t}^\nu(\xi^*,x)=\xi^*_1 x_2+\xi^*_2 u+\nu(u^2+(e_1+e_2)f)+\int_0^t(e_1+e_2)fd\tau, \xi^*=\left(
\begin{array}{c}
\xi_1^*\\
\xi_2^*
\end{array}
\right)\in T_{x(t)}^*R^2,$$ Thus it is embedded in a port-Hamiltonian systems: $$\left\{
\begin{aligned}
&\frac{\partial q}{\partial t}=\frac{\partial H_u}{\partial \xi}+B(q)f\\
&\frac{\partial \xi}{\partial t}=-\frac{\partial H_u}{\partial q}+A(q)f\\
&e=A^{T}(q)\frac{\partial H_u}{\partial p}\\
&e'=B^{T}(q)\frac{\partial H_u}{\partial q}
\end{aligned}
\right.$$ First consider abnormal case $\nu=0$: $$h_u^0(\xi^*,x)=\xi^*_1 x_2+\xi^*_2 u.$$ If maximum of $h_u^0(\xi^*,x)$ exists, there must be $E\xi^*_2\equiv0$. This means $\tilde u \equiv0$, which contradicts nontrivial requirement.\
Then consider the normal case $\nu=-1$: $$h_u^{-1}(\xi^*,x)=\xi^*_1 x_2+\xi^*_2 u-(u^2+(e_1+e_2)f).$$ Thus, $$\left\{
\begin{aligned}
\dot\xi_1^*=\frac{\partial\xi_1^*}{\partial t}=\frac{\partial h_u^{-1}}{\partial x_1}=0\\
\dot\xi_2^*=\frac{\partial\xi_2^*}{\partial t}=\frac{\partial h_u^{-1}}{\partial x_2}=\xi_1^*
\end{aligned}
\right.$$ Due to the Hamiltonian maximum generated by U, $$h_u^{-1}(\xi^*,x)=\xi^*_1 x_2+\xi^*_2 u-(u^2+(e_1+e_2)f).$$ $$\frac{\partial h_u^{-1}}{\partial u}=0$$ Thus we get $$\tilde u(t)=\frac{1}{2}\xi_2^*(t)=\alpha t+\beta.$$

The optimal control shall be linear. We can easily find the optimal control when put the conclusion into origin system. The control system with both control $u$ and input $f$ can be now transformed into a classic optimal problem with only continuous control $f$.

[**Conclusion**]{}
==================

The paper is focused on certain kind of extended control problems and give a feasible solution to the problems with output or input terms. Core idea of the solution is to divide the control systems into two parts and find the optimal control for fixed input/output. The theoretic basis of this method is PMP for port-Hamiltonian Systems which is introduced in the second section. The method, in essence, is a generalization of classic PMP since it’s obvious that the theorem regress to PMP when output/input become zero.

Up to now we can only make use of certain kind of port-Hamiltonian systems, specifically the ones with symplectic structure. It’s yet to be researched how general port-Hamiltonian systems can be connected to control problems. Though port theory, as a new subject, has been perfectly developed during the years, there are still blanks in its connection with classic subjects. Beyond doubt, there is great potential in this subject. Port-Hamiltonian theory stand a good chance to make improvement in not only control theory, but other applied fields.

[99]{} R. Bellman. Introduction to the Mathematical Theory of Control Processes. New York: Academic Press, New York, 1967. M. Bardi, I. Capuzzo-Dolcetta. Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Boston: Birkhauser, 1997. Andrei A. Agrachev, Yuri L. Sachkov. Control Theory from the Geometric Viewpoint. Heidelberg: Springer, 2004:167. A.van der Schaft and D.Jeltsem. Port-Hamiltonian Systems Theory: An Introductorty Overview. Foundation and Trends in Systems and Control, vol.1, no.2-3, pp.173-378, 2014. T. R. Bielecki, H. Jin, S. R. Pliska, X. Y. Zhou. Continuous time mean variance portfolio selection with bankruptcy prohibition. Math. Finance, 2005, 15: 213-244. D. Cuoco, J. Cvitanic. Optimal consumption choices for a ¡°large¡± investor. Economic Dynamics and Control, 1998, 22: 401-436. A. Bloch. Nonholonomic Mechanics and Control, Interdisciplinary Applied Mathematics. Heidelberg: Springer, 2003. M. Kawski. Combinatorics of nonlinear controllability and noncommuting flows. ICTP Lecture Notes Series, Mathematical control theory, 2002, 8: 222-311. Augner, Bjorn; Jacob, Birgit Stability and stabilization of infinite-dimensional linear port-Hamiltonian systems. Evol. Equ. Control Theory 3 (2014), no. 2, 207-229. Dirksz, Daniel A. Scherpen, Jacquelien M. A. Steinbuch, Maarten A port-Hamiltonian approach to visual servo control of a pick and place system. Asian J. Control 16 (2014), no. 3, 703-713. Macchelli, Alessandro Dirac structures on Hilbert spaces and boundary control of distributed port-Hamiltonian systems. Systems Control Lett. 68 (2014), 43-50. Seslija, Marko; Scherpen, Jacquelien M. A. van der Schaft, Arjan Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems. Automatica J. IFAC 50 (2014), no.2, 369-377.


1. Field of the Invention
The present invention relates to an image forming apparatus as a copier, a printer, a facsimile machine, or a compound machine thereof, and particularly to an image forming apparatus including a fixation device for fixing a toner image formed by an electrophotographic system to a transfer sheet.
2. Description of the Related Art
Recently, it has been made possible to obtain a large amount of image information and the like owing to a development of a communication network such as the Internet. In order to process such information, an image forming apparatus as a copier, a printer, a facsimile machine, or a compound machine thereof has been required more to have performance capable of forming a large amount of high-quality color images and the like at a high speed.
It is frequent that an image forming apparatus which forms an image by an electrophotographic system is used as such an image forming apparatus. In the above-described image forming apparatus, there is provided a fixation device for developing, by a toner, an electrostatic latent image formed based on the image information, and fixing an emerging toner image to a transfer sheet.
As the fixation device, there are known one which includes a fixing roller as a fixing member, and a pressure roller, each having a heater therein, and is constructed to form a pressure contact portion by bringing the fixing roller and the pressure roller into pressure contact with each other, one which is constructed to form a pressure contact portion by bringing a fixing roller member and a pressure roller into pressure contact with each other, in which the fixing roller member is formed by extending a fixing belt between a heating roller having a heater therein and a fixing roller, and the pressure roller is a pressure member also having a heater therein, and the like. In any of the above-described fixation devices, the transfer sheet to which the toner image is transferred is inserted into the pressure contact portion of the fixing roller and the pressure roller. Then, the toner is heated and pressurized by the pressure contact portion, is thus fused and adhered to the transfer sheet. Thereby, the toner is fixed thereto.
In order to fix the toner image formed on such a transfer material at a high speed by the fixation device with the construction as described above, for example, it is considered to raise a fixing temperature of the fixing member and to shorten a time necessary for the transfer material to pass through the pressure contact portion.
In order to raise the fixing temperature in a short time, it is considered to provide a high power heater in the fixation device, to increase the heater in amount and number, and so on. However, large power consumption is required when it is attempted to raise the fixing temperature in a short time, to increase the number and amount of the heater, and so on. Accordingly, there has been a problem in that, when it is attempted to provide a high speed and high image quality image forming apparatus, it is necessary to increase the power consumption of the entire image forming apparatus.
In this connection, it is necessary to control power consumption of the fixation device under operation in order to restrict the power consumption of the entire image forming apparatus within predetermined power consumption. For example, the following technologies have been proposed. In the first technology, priorities are given to an upper heat roller (a fixing roller) and a lower heat roller (a pressure roller), target temperatures are determined for the individual rollers, the heat roller having higher priority is operated first-based on the target temperature, the heat roller having lower priority is operated during a stop of energization of the heat roller having the higher priority, and both heat rollers are thus alternately operated so as not to be made to turn on simultaneously (for example, refer to JP-Tokukaihei-9-311580A). In the second technology, during a period from transfer of one image to an intermediate transfer body to transfer of the next image thereto, for example, the heat roller of either the fixing roller or the pressure roller is energized, and the two heat rollers are not energized simultaneously (for example, refer to JP-Tokukai-2000-19926A). In the third technology, the two heat rollers are alternately energized at a constant cycle (for example, refer to JP-Tokukai-2004-70056A). Moreover, in the fourth technology, in order to control the power consumption in conjunction with other devices than the fixation device, a dehumidifying heater for the transfer sheet is operated while the energization of the heater of the fixation device is being stopped, and the power consumption of the image forming apparatus is thus to be controlled (for example, refer to JP-Tokukai-2003-58024A).
However, in any of the constructions described in the above conventional technologies, the two heaters were always controlled to be energized based on the preset priorities while the image forming apparatus was being operated.
Specifically, the constructions described in JP-Tokukaihei-9-311580A, JP-Tokukai-2000-19926A, and JP-Tokukai-2003-58024A relate to the energization control for the two heaters in the fixation device, and the construction described in JP-Tokukai-2003-58024A relates to the energization control for the two heaters which are the dehumidifying heater and the heater of the fixation device. In any of the constructions, the priorities are preset for the two heaters, the heater having the higher priority is energized first, and the heater having the lower priority is energized while the energization of the heater having the higher priority is being stopped. In such a way, the control is always made so that the two heaters cannot be energized simultaneously, and the power consumption of the image forming apparatus under operation is thus controlled within the range of the predetermined power consumption.
Accordingly, the number of heaters for which the energization is controlled is increased to three or more, for example, in the case of providing the heaters to the following rollers for the purpose of fixing the toner image formed on the transfer material at the high speed. The rollers are the heat roller which heats the fixing belt of the fixation device, the pressure roller which forms the pressure contact portion abutting on the fixing belt and inserting the transfer material therethrough, an external heat roller provided so as to supply heat to the heat roller by abutting on the pressure roller as its surface temperature is less prone to rise owing to an elastic layer provided on the surface thereof, and the like. Moreover, when the operation state of the image forming apparatus is changed, for example, to warming up (WU), immediately after the start of paper feeding, under paper feeding, and standby, and in the case where it is required to perform the energization control for the heaters so as to make it possible to perform the optimum temperature control for the fixation device, which corresponds to the respective operation states, the heaters each having higher priority, for which it is necessary to preferentially perform the energization, are different depending on the respective operation states. Hence, there has been a problem in that it is impossible to perform the optimum temperature control for the fixation device in response to the operation state of the image forming apparatus within the range of the predetermined power consumption only by always making the control based on the preset priorities to avoid simultaneous energization of the two heaters.


Five weird Miami plants from our Homestead tour

Achiote seeds, also called annatto or bijol, are used for their bright red pigment.

Checking out the pulp and seed of a gac fruit.

Jade vine hangs at RF Orchids.

A vanilla blossom at RF Orchids.

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We took a field trip to RF Orchids, Fruit and Spice Park, and Andre’s Fish Farm in the Redland. We had a blast, and we learned a lot along the way, mostly about weird Miami plants that grow in our tropical climate — whether they should grow here or not. Here are five of the most unusual plants we learned about:

Vanilla orchid

There are more than 100 species of vanilla orchids in the world, but only five grow in the U.S., and they only grow in South Florida. The most well-known of these is vanilla planifolia, which is the tree-climbing plant that produces the vanilla bean we know from commercial vanilla, the seeds of which you’ll recognize as those little black flecks in your favorite vanilla ice cream.

Since the species of bee that pollinates the flower doesn’t live here, RF Orchids pollinates their vanilla orchid by hand. Workers use tall ladders to climb up to eye-level with the bloom on the one morning it opens, and ensure it’s pollinated before it closes forever the same afternoon. If a bloom isn’t pollinated, the blossom withers and dies, but if pollination is successful, the fruit of the plant develops over nine months into that long, fragrant brown pod that makes your desserts so delicious.

Zombie palm

The zombie palm, or zombia antillarum, is a small palm native to Hispaniola, but you can find them growing in South Florida too. They grow in clusters, with fan-like leaves, and their trunks are covered in long, spiky, needles.

A photo posted by The New Tropic (@thenewtropic) on Jan 31, 2015 at 10:02am PST

In some folklore, the palm is believed to have magical properties, RF Orchids owner Robert Fuchs told us. Some believe that a prick from the thorn of the zombie palm will put a person to sleep, he said. Others say that the thorns were used in certain Voudou rituals. One study cites sources saying the oil from the palm’s seeds could awaken a zombie, or that a house with a roof of thatched zombie palm leaves would protect its inhabitants from zombies.

Jade vine

The jade vine, or strongylodon macrobotrys, was one of the most striking plants we saw at RF Orchids, with an other-worldly turquoise color and unusually shaped flowers. The vine is native to the Philippines, where rainforest destruction has now made it an endangered species.

For years collectors and botanists had kept healthy jade vines in tropical gardens, but the plants would not produce seed. After a careful study of the the plant’s anatomy, horticulturalists learned to mimic bat behavior to successfully pollinate the plant.

The bats hang upside down to sample the jade vine’s nectar, and the plant gently brushes pollen onto the bat’s head while it drinks. The next plant the bat visits collects the pollen from the first before brushing its own pollen to be transported elsewhere. It is a great example of co-evolution in action; the plant and the bat have evolved to work perfectly in cooperation with each other.

Achiote

When we spotted the seed pods of the achiote tree, or bixa orellana, at Fruit and Spice Park, they looked like something out of a Dr. Seuss book. Clustered in clumps of 5 to 10 pods and covered in spiky red fur, the fruits hold a bright surprise inside.

Achiote seeds are covered in a red-orange pigment that’s sold as achiote, annatto, or bijol, and used commonly to color cheeses and many Latin American, Carribbean and Filipino dishes. The pigment is often used in place of more expensive saffron in rice dishes. In some native cultures, the pigment was used for body paint and a natural lip stain, giving it the nickname “lipstick tree.”

A few of our fellow travelers tried on the “lipstick,” which was surprisingly permanent and turned more orange throughout the day.

Gac

Gac fruit is a softball-sized, bumpy melon that contains clusters of bright red, edible pulp around strange, flat seeds that resemble fossils or stones. The fruit grows natively in Southeast Asia on a vine that our Fruit and Spice park tour guide, Roger, warned us is highly invasive in South Florida.

The pulp of the gac fruit, while mild in taste, is used frequently at special occasions like Vietnamese new year or weddings to color and flavor a special sticky rice dish. The pulp contains up to ten times more beta-carotene than carrots as well as up to seventy times more lycopene than tomatoes. Its high antioxidant content has made gac a popular food and juice supplement. Here’s a bit more about it, from Fruit & Spice Park tour guide Roger Blanco.

Have you tried any of these fruits? Which ones did we miss? Let us know in the comments or on Facebook or Twitter.


Yerba Prima Men's Rebuild (colon cleanser) 1 Box

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046352001159

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Yerba Prima Men's Rebuild

Over thirty years ago, the Food for Health Institute, with Yerba Prima, developed the first Internal Cleansing Program. Now, we have developed an improved, more powerful Men’s Rebuild® Internal Cleansing System based upon over thirty years of experience and clinical research. Yerba Prima Internal Cleansing includes the latest knowledge from Ayurvedic, Chinese, European and Native American traditions in a complete cleansing program. Only Yerba Prima Internal Cleansing includes Great Plains® Bentonite for added detoxification.

Men today are exposed to high levels of stress, as well as unavoidable pollution, in our busy lives. It doesn’t matter if you are a bodybuilder, a weekend athlete or just out of shape. Anyone can benefit from the elimination of waste and toxins with internal cleansing. For vitality and better health, internal cleansing can help!

Men’s Rebuild® Internal Cleansing System combines 30 of the finest cleansing and vitalizing nutrients from the world’s great healing traditions. It really works and is simple to use, whether you are trying internal cleansing for the first time or are an experienced user. Our more concentrated and powerful three-part herbs and fiber program gives a gentle yet thorough cleansing of the colon and the entire body.

DIRECTIONS

The Men’s Rebuild® Internal Cleansing System consists of three products: Men’s Rebuild®, Herbal Guard® and Prima Cleanse®. Men’s Rebuild is an easy program to follow, whether you are cleansing for the first time, or are an experienced user. It provides a gentle, thorough, total body cleansing, plus protecting and rebuilding of the elimination systems.

Prima Cleanse*

Men’s Rebuild

Herbal Guard

Day 1

Evening

3

Take with food and at least 8 oz of liquid

Day 2

Morning

3

1

1

Take with food twice a day, morning and evening. Take each serving with at least 8 oz. (a full glass) of liquid. Drinking additional liquid is helpful.

Evening

3

1

1

Day 3

Morning

3

1

1

Evening

3

1

1

Day 4 Gentler Cleanse

Morning

3

1

1

Evening

3

1

1

Day 4 Stronger Cleanse

Morning

5

2

2

Evening

5

2

2

Day 5 and after Gentler Cleanse

Morning

3

1

1

Continue for one to five months

Evening

3

1

1

Continue for one to five months

Day 5 and after Stronger Cleanse

Morning

5

2

2

Continue for one to five months

Evening

5

2

2

Continue for one to five months

Ending The Program For Both Gentler and Stronger Cleanse

After finishing the Internal Cleansing System, daily use of a Yerba Prima fiber formula such as Colon Care or Daily Fiber® helps maintain a clean colon and healthy body.

Everyone should start with 3 Prima Cleanse capsules per serving. After Day 3, follow the Gentler Cleanse or the Stronger Cleanse. Continue to adjust the number of Prima Cleanse capsules to your body’s cleansing needs, since Prima Cleanse provides the most stimulating part of the program’s cleansing action. Most people will notice an increase in the frequency and/or volume of bowel movements. If the cleansing action is too strong, reduce the number of Prima Cleanse capsules until the desired cleansing action is reached. If the cleansing action is not strong enough, first increase your fluid intake, then increase the number of Prima Cleanse capsules until the desired cleansing action is reached. Take the number of Prima Cleanse capsules that will help produce one or more regular, easy, non-urgent bowel movements per day.

OTHER INGREDIENTS

Rice flour, cellulose, maltodextrin, USP Kosher gelatin capsule

WARNINGS & SIDE EFFECTS

Consult with your healthcare physician before taking. Keep out of reach of children.

Note: In the event of a pricing error or fraud alert, we may refuse or cancel any orders placed for that item in accordance with our Terms & Conditions. We will notify you of any cancellation. Also, because manufacturers continually change product specifications without notice. While we try our best to keep product descriptions up to date, they do not necessarily reflect the latest information available from the manufacturer. We are not responsible for incorrect or outdated product descriptions and/or images. It is your responsibility to know what products are legal or illegal in your country.

FDA: These statements have not been evaluated by the Food and Drug Administration. This product is not intended to diagnose, treat, cure, or prevent any disease.

More Information

Contact us

Have questions? Call us at 1-800-499-4810 or chat with us live.

Hours

Hours: 8am to 5pm CT Monday Through Friday

Location

181 West Crossroads Pkwy Unit F Bolingbrook IL 60440

About Us

Best Price Nutrition has been an online retailer since 2002 selling discount bodybuilding supplements, fat burners, muscle builders, pre-workouts and protein. You will find the best prices and fastest shipping worldwide on your supplement needs from our warehouse store.


Q:

Anyone get the MacPorts' Mercurial package to work with MercurialEclipse plugin?

I'm trying to get the Mercurial Eclipse plugin to use my MacPorts version of Mercurial (since I need to access a repo that's using the new dotencode format), but I can't get the Mercurial preference page under "Team" to save the changes. It will recognize "/opt/local/bin" as a valid directory for the "hg" executable, but when exiting the workspace the changes don't appear to be saved properly, since the next time I launch Eclipse, the old "/usr/local/bin" is back there again.
Has anyone else had problems with this? "/opt/local/bin/hg" is a symlink to "/opt/local/Library/Frameworks/Python.framework/Versions/2.6/bin/hg" on my system, but that file also contains a shebang ("#!") with the same path (duh!). Is that known to cause any problems on anyone else's machine?
Edit: Symlinking /usr/local/bin/hg to /opt/local/bin/hg works, but this doesn't fix the cause of the problem.
There are no errors being logged in the Eclipse Error Log view, other than "abort: requirement 'dotencode' not supported!" on startup. I.e. no errors on validating the settings or when saving the workspace.

A:

Do you have another version of hg in /usr/local/bin?  If not or if you no longer need it, you might be able to work around the issue by making a symlink:
sudo ln -s /opt/local/bin/hg /usr/local/bin/hg
sudo chmod -h g+rx,o+rx /usr/local/bin/hg


**2 + 5*x**2 - x**2) + 5*x**3 - 4*x**3 + 0*x**3.
-2*x**3
Expand (-2*h**5 - 3*h**3 + 3*h**3)*(2 + 2 - 6) + 19 - 14*h**5 - 19.
-10*h**5
Expand -r**5 - 4*r**3 + 4*r - 4*r + (-6*r**4 + 4*r**4 + 0*r**4)*(r - 2*r + 3*r) + 4*r**4 - 4*r**4 + r**5 + 0*r**5 - r**5 - r**5 + 2*r**5 - r**5 + 0*r**5.
-5*r**5 - 4*r**3
Expand (4 - 1 - 1)*(-4*y + 4*y - 5*y)*(0*y + 0*y + y**2).
-10*y**3
Expand (5 - 1 + 1)*(15*l**3 + 6*l**3 - 6*l**3) - l**3 - 3*l**3 + 2*l**3.
73*l**3
Expand (-119 + 119 + 40*c)*(-4*c**4 - c**4 + 6*c**4).
40*c**5
Expand n - 3*n**2 + n + 9*n + (3*n**2 + n**2 - 3*n**2)*(-3 + 0 + 5).
-n**2 + 11*n
Expand (u**2 + 4*u**2 - 4*u**2)*(-5*u**2 - 1 + 1)*(4*u + 0*u - 1 + 3).
-20*u**5 - 10*u**4
Expand (-2 - 3 + 3)*(t - 4*t + t)*(2 - 3 + 2).
4*t
Expand (-2*p + 2*p - 3*p**3)*(0*p**2 - 4*p + 2*p - p**2).
3*p**5 + 6*p**4
Expand (0*m + 0*m - 5*m)*(-m**2 - 3*m**3 + m**2).
15*m**4
Expand 50 - 11*p**3 + 2*p**2 - 50 + (4 - 4 - p**2)*(5*p - 4*p - 2*p) + 3*p**3 - 4*p**3 - p**3.
-12*p**3 + 2*p**2
Expand ((-3 + b + 3)*(3*b - 2*b - 2*b) - 8 - 5*b**2 + 8)*(5*b**2 + b**2 - 5*b**2).
-6*b**4
Expand (-4 + 2 - 1)*(3 - 5 + 0 + i).
-3*i + 6
Expand (-3*q**2 - q**2 + 5*q**2)*((-q - 3*q + 2*q)*(2 - 1 + 1) + q - 2*q + 2*q).
-3*q**3
Expand -23*b**3 + 16*b**3 - 4*b**2 + 2*b**2 + b**3 - b + b + (0*b**2 + b**2 - 3*b**2)*(4 + b - 4).
-8*b**3 - 2*b**2
Expand (-7 - 5 - 3)*(-5*k + 2*k + k).
30*k
Expand (-5*s - 2*s + 5*s)*(3*s**4 - s**4 + s**4) - 4*s**5 + 6 - 6 + 2*s**5 + 0*s + 0*s + (-s + 3*s + 0*s)*(-s**4 + 0*s**3 + 0*s**3) - s**5 + 0*s**5 - s**5.
-12*s**5
Expand -2*y**4 + 2*y - 2*y + 5*y**4 - 2*y**4 + 0*y**4 + (-y + 4*y + 0*y)*(3*y**3 - 3*y**3 + 2*y**3).
7*y**4
Expand (4 + 0 - 2)*(-2 + 1 + 0)*(-29*j - 12*j**2 + 29*j).
24*j**2
Expand (2 + 2 - 3)*(1 - 7*f - 1) + 2*f + 1 - 1 + (-1 + 4 - 6)*(1 + f - 1).
-8*f
Expand ((-2 + 4 + 1)*(-3 + 0 + 1) + 0 + 2 - 4)*(2*q - 5*q + 4*q).
-8*q
Expand 0*o + 0*o + 5*o**2 + (0 - 2*o + 0)*(2*o + o + o + 1).
-3*o**2 - 2*o
Expand -a**3 + a**3 + 3*a**3 + (20*a**3 + 2*a**3 - 3*a**3)*(2 - 4 + 3).
22*a**3
Expand (0*j - 2*j**3 + 0*j)*((-4 - 2 + 1)*(-2*j + 2*j**2 + 2*j) + 0*j**2 + j**2 + 0*j**2).
18*j**5
Expand (1 - 1 - t)*((-t - t + t)*(-1 + 1 + 1) - 3*t + t + 4*t + (1 + 0 - 3)*(0*t + 3*t - 2*t) + t - 2*t + 0*t - t - 2 + 2).
3*t**2
Expand (-2*k + 2*k - 4*k)*(-2*k**3 + 3*k**3 - k**2 - 3*k**3).
8*k**4 + 4*k**3
Expand (-4 + 2*w + 4)*(-1 - 3 + 3)*(0*w + 2*w - 3*w).
2*w**2
Expand 0*x**4 - 2*x**4 + x**4 + (-x + x + x**2)*(6*x**2 - 2*x**2 - 2*x**2) - 2*x**4 + 2*x**4 + 2*x**4 + 2*x**4 + 0*x**4 + 0*x**4 + x**4 - 2*x + 2*x.
6*x**4
Expand (-1 + 1 - j**2)*(-5 - 1 + 0)*(-4 - 1 + 4).
-6*j**2
Expand (33 - 10 - 11)*(-b + 0*b + 3*b).
24*b
Expand (0 + 2 - 3)*(0 - 5 + 3)*(5*r**3 + 2*r**3 - 3*r**3).
8*r**3
Expand (4 - 4 - h**2)*(-14 - 4 - 2) + (h + 0*h - 2*h)*(4*h + h - 3*h).
18*h**2
Expand 14*x**2 - 7*x**2 - 41*x**2 + (2 - 1 + 1)*(2*x**2 - 3*x**2 + 0*x**2).
-36*x**2
Expand (-3*f + 3*f + 2*f)*(f - 6*f + 2*f)*(4 - 4 + 7).
-42*f**2
Expand (-4*w + 3*w - 12*w)*(1 - 5*w**4 - 1).
65*w**5
Expand (-3 + 2 + 0)*(1 - 2*m**2 - 1) + (3*m - m - m)*(-m - 5*m + 10*m) + 2*m**2 - 3*m**2 - 2*m**2.
3*m**2
Expand (-3*v**3 - 6*v**3 + 2*v**3)*(7*v - 4*v + 7*v).
-70*v**4
Expand (-f + 4*f - f)*(1 + 5*f + 10*f - 10*f) - 2*f**2 + f**2 - f**2.
8*f**2 + 2*f
Expand 0*d**4 - 1 - d**4 + d**2 - 3 + (-3*d**2 - 2*d**2 + 3*d**2)*(d**2 + d**2 + 0*d**2).
-5*d**4 + d**2 - 4
Expand -2*b**3 + 5*b**3 - b**3 + (4 + 4 - 6)*(-4*b + 3*b + 4*b)*(-b**2 + 2*b**2 - 3*b**2).
-10*b**3
Expand (2 - 2 + 2)*(-5*f + f + 2*f) + f + 3*f - 3*f - 8*f + 0*f + 13*f - 1.
2*f - 1
Expand (-3*i + 2*i + 2*i)*(5*i - 4*i - 2*i) + (5*i**2 - 6*i**2 - i**2)*((2 + 2 - 2)*(-1 + 3 + 0) - 1 - 1 + 3 + 2 - 4 + 0 + 3 + 1 - 6).
-3*i**2
Expand (-4 - 2 + 3)*(4*d + 4 - 4) + 1 + 0 - 5 + 2*d.
-10*d - 4
Expand (-4*w + 4*w + 2*w**2)*(3 + 0 + 0).
6*w**2
Expand (l**2 - 2*l**2 + 2*l**2)*(3 + 6 + 0) - 3*l**2 - l**2 + 3*l**2 + (0 + 2*l + 0)*(-2*l + 2*l + l).
10*l**2
Expand (5*o**2 - o**2 - 5*o**2)*(-6*o + 3*o + o) + 4*o**3 + 4*o - 4*o - o + 2*o**3 + o - o + o + 3 - o**3.
7*o**3 + 3
Expand (5 - r - 5 + (0*r - 2*r + 0*r)*(-4 + 3 + 0) + (0 + 3 - 2)*(0 + 0 + r) - 4*r + 5*r + 0*r)*(5 + 0 - 3).
6*r
Expand (3 - 4 + 2)*(-3*w + 2*w + 3*w) - 2*w + 9*w + w - 2 + 2*w + 2 - 1 + 2 - 3*w + 2*w.
11*w + 1
Expand ((0 - 1 + 3)*(r - 5 + 5) + 0*r - r - 2 + 8*r)*(2*r**3 - 4*r**3 + 4*r**3).
18*r**4 - 4*r**3
Expand -9 + 3 + 3 + 3*s + 4*s - 2*s + 0*s + 1 - 1 + s + (-1 + 2 - 3)*(-s + 0 + 0).
8*s - 3
Expand (0*r**3 + r**3 - 3*r**3)*(-180*r - 2 + 78*r + 75*r).
54*r**4 + 4*r**3
Expand -3 - g**2 + 3 + (0*g - 2*g + 5*g)*(-7*g + g + g).
-16*g**2
Expand (-2 + 3*d + 2 + (2*d + 4*d - 4*d)*(-5 + 1 + 2) - 2*d + 2*d - 2*d)*(-d + 0*d + 0*d).
3*d**2
Expand (-n**2 + n**2 - 2*n**2)*(-2 - 1 - 3)*(8*n**2 + 11*n - 11*n) - 2*n**4 - n**3 + n**3.
94*n**4
Expand (0*f**2 + 0*f**2 + f**2)*(-1 + 6 - 4)*(-8 + 9 - 21).
-20*f**2
Expand (-2*a + 0*a + a)*(1512 - 1512 + 22*a).
-22*a**2
Expand (2*v + 2*v**2 - 2*v)*(-6*v + 78 - 78)*(v + 0 + 2*v + 2).
-36*v**4 - 24*v**3
Expand 4*t**3 - 2*t**4 - 4*t**3 + (2*t**3 + 0*t**3 - t**3)*(-1 + 1 + t) - 5*t**4 - t**4 + 4*t**4 + 6*t**3 - 6*t**3 - t**4.
-4*t**4
Expand (12 + 2 + 1)*(6 - 4 - 3)*(b + 4 - 4).
-15*b
Expand (0*u + 2*u - u)*(3 - 3 + 4*u + (0 + 1 + 1)*(-2*u + u + 3*u)).
8*u**2
Expand (-3*q + 4*q + 2*q + 1)*(-2*q**3 - 3*q**3 + 4*q**3) + (0 + 2 - 1)*(2*q**3 - 2*q**3 + 2*q**4) + 4*q**4 - q**4 - q**4 + 0*q**3 - 2*q**4 + 0*q**3.
-q**4 - q**3
Expand (-9*w**2 - 8 + 8)*(3*w - 2*w + w) + w**3 + 3*w**2 - 3*w**2 - 3*w**3 + 0*w**3 + 2*w**3.
-18*w**3
Expand 0 - n**5 + 0 + (0*n - 2*n**4 + 0*n)*(-n - 2*n + 2*n) + 6*n**5 + 3*n**5 - 3*n**5.
7*n**5
Expand -11*s**4 + 37*s**3 - 37*s**3 + (0 + 0 - s)*((-1 + 1 - 2*s)*(1 - 2*s**2 - 1) + 2*s**3 + 4*s - 4*s + s - s**3 - s).
-16*s**4
Expand (6*q**5 + q**5 - 3*q**5)*(-4 + 2 + 1) - 2 - q**5 + 2 - q**5 + 0 + 0 + (-3*q**2 + 3*q**2 + q**3)*(-2 + 2 + q**2) - 5*q**5 + 2*q**5 + q**5.
-7*q**5
Expand -4*u**4 + 2*u**2 - 5*u**4 + u**4 + 4*u**3 + u**4 - 4*u**3 + (-2*u - 5 + 5)*(3 - u**3 - 3).
-5*u**4 + 2*u**2
Expand (r**3 + 2*r**4 - 3*r**3 - 1 + 0)*(-3*r - 4*r + 6*r).
-2*r**5 + 2*r**4 + r
Expand c**4 + 3*c - 3*c + 0*c**4 + 8*c**4 + 3*c**4 - 4 + 4*c**4 + 4 + (0 + 0 + 2*c)*(c**3 + 2*c**3 - 2*c**3).
18*c**4
Expand -4*p**2 + 5*p**2 - 6*p**2 + 3*p - 3*p - p**2 + (-2*p + 2*p - 2*p)*(2*p + 2*p - 2*p).
-10*p**2
Expand (62*r - 28*r - 15*r)*(-r - 1 + 1)*(-4 - 1 + 4).
19*r**2
Expand 2*s**2 + 0*s**2 + 0*s**2 + 4*s**2 + 0*s**2 - 5*s**2 + (3*s - 3*s - 2*s)*(-12 + 12 - 7*s).
15*s**2
Expand (2*o - 2*o - o)*(-2*o**4 - 5 + 5) + (-16*o**2 - 27 + 27)*(2*o**3 - 6*o**3 + 3*o**3).
18*o**5
Expand (-3*y + 0*y + 0*y)*((1 + 3 - 3)*(-2 + 5 - 1) + 3 - 2 - 3 - 5 - 2 + 6 - 2 + 4 + 0).
-3*y
Expand (0 + 3 - 4)*(u**4 - 3*u**4 + 5*u**4) + 5*u**4 + 4*u**4 - 4*u**4.
2*u**4
Expand h**3 + 0 + 0 - 2*h**3 + 2*h**3 - 2*h**3 + (1 - 1 - h**2)*(-1 + h + 1) + 3*h**3 + 3*h - 3*h + (h + h + 0*h)*(-h**2 - 2*h**2 + 4*h**2).
3*h**3
Expand (66*m - 41*m**2 - 66*m)*(0 - m + 0).
41*m**3
Expand (-1 - 2 - 5)*(-2 + a**2 + 2).
-8*a**2
Expand (-14 + 14 + x**2)*(6*x + 15 - 15).
6*x**3
Expand (0*x + x + 0*x)*(-1 - 12*x**2 + 1) + 3*x**3 - 1 + 1.
-9*x**3
Expand (5*l**2 - 16*l + 16*l)*(l**2 + l - l).
5*l**4
Expand (k - 2*k - k)*(5 - k - 5)*(-2*k**2 - 6 + 6).
-4*k**4
Expand -h + 25*h + 3*h + 2*h + h - 4*h + (5*h + 0*h - 3*h)*(-3 + 1 + 0) + (4 - 3 + 1)*(4 - h - 4) - h - 4*h + 3*h - 2*h + 6*h - h.
21*h
Expand -5*z - z + 4*z + (-z + 3*z - z)*(-2 - 5 + 6) - z + 2*z - 2*z + 4*z - 5*z + 0*z + (-3 + 3 + z)*(-1 + 1 + 2) + z + 2*z - 2*z.
-2*z
Expand -s**5 - s**3 + s**3 + (-6*s**2 + 6*s**2 + 4*s**3)*(-5*s**2 + 3*s**2 + s**2).
-5*s**5
Expand (-3*g + 2*g**2 + 3*g)*(-5 + 5 + g**2) + (-2*g - 2*g**2 + 2*g)*(g**2 + 4*g**2 + 9*g**2).
-26*g**4
Expand (-2*u**2 + 2*u - 2*u)*(-u**2 + 5*u**2 - 5*u**2) + (u**4 + 3*u**4 - 5*u**4)*(-3 + 4 + 1) - u**4 + 2*u**4 - 2*u**4.
-u**4
Expand (4 + 0 - 2)*(3*u**4 - 5*u**4 + 3*u**4) + 3*u**3 - 3*u**4 + 7*u**3 + 5*u**4.
4*u**4 + 10*u**3
Expand (2 - 9 - 2)*(4 - 4 + 4*n)*(-3 + 7 + 0).
-144*n
Expand 4*x**2 - 4*x**2 + x**3 + (0*x**2 + 2*x**2 + x**2)*((2 + 2 - 8)*(-1 - x + 1) - 2*x - 1 + 1).
7*x**3
Expand (2*j - 3*j + 2*j)*(6*j - j - 4*j) + 0*j**2 - 2*j**2 + j**2 + (-3*j - 2*j + 4*j)*(-6*j + 4*j + 0*j) + 4*j**2 + 2*j**2 - 2*j**2.
6*j**2


Benefits and threats of new technologies.
In this paper first the effect of new hardware and software technologies on threats to data integrity and usage integrity is considered. Next the potential is considered of new technical facilities for improving the protection. It is concluded that the increasing risks for data and usage integrity are not counter balanced at present by new protection measures. A concerted action is proposed to face this problem. Especially action is proposed to develop methods for quality assurance of software, for access control in networks and to improve data/usage integrity around PC's.


The Indianapolis Colts are sitting at 7-6 right now and are in the middle of a tight playoff race for the 6th seed in the AFC. Led by quarterback Andrew Luck playing at an MVP level, the Colts’ offense has carried the team most of the season as the young defense learned a new system under defensive coordinator Matt Eberflus. As the season has progressed though, the young defense led by DROY front runner Darius Leonard has essentially turned the corner and is now the 9th ranked defense in the NFL in terms of DVOA.

To add some stats for context, the Colts’ defense has 14 sacks in their last four games played and is top ten in sacks for the season in the NFL. Over the past four weeks, the defense has given up only 15 points per game along with only giving up 275 total yards per game. The Colts are also a top five rush defense in all of football this year in terms of yards per rush.

So what has contributed to this defensive outburst the last four weeks or so by the Colts? Well let’s look at some film and find out.

1.) Blitzing the Quarterback

The Colts’ defense was shredded earlier in the season by offenses because they couldn’t get home with four man rushes. Quarterbacks would sit in the pocket and wait and wait until an open outlet emerged downfield. As a result, the defense was gashed by mediocre quarterbacks such as Sam Darnold, Derek Carr, and Blake Bortles— mediocre may be a stretch for Bortles. The frustration only grew when the Colts registered no sacks against the Raiders and Jaguars (first meeting).

After that first Jaguars game though, Defensive Coordinator Matt Eberflus decided to get aggressive and creative with his blitz calls. The Colts have registered 14 sacks over the last four games with players such as Kenny Moore II and Darius Leonard contributing on the sack sheet. The main area where this has really taken effect is on third downs. Instead of just sitting back on third downs, Eberflus has elected to send a lot of pressure in recent weeks. The early returns on this change in decision making have been great.

The first clip here shows exactly how creative Eberflus has been with his blitzes. He brings a total of nine (!!!!) guys into the box here to confuse quarterback Marcus Mariota. He does decide to drop back two of those players into coverage but still brings seven guys on the play. On top of bringing a safety— Mike Mitchell— and a corner— Kenny Moore II— on this blitz, Eberflus also stunts Jabaal Sheard inside to get a favorable match-up against the center. The resulting play is Moore and Sheard combining for the half sack.

Here Eberflus again shows a heavy box with six players lined up over the Dolphins’ front. He drops back both Anthony Walker and Clayton Geathers at the snap of the ball but brings both Leonard and Moore off the edge. As a result, Leonard is left with an easy match-up with the running back on the right side of the screen. Leonard is able to beat the back just as quarterback Ryan Tannehill tries to escape the pocket and he ends up with yet another sack on the season. Bringing both Leonard and Moore on blitzes has been a staple of Eberflus’ in recent weeks.

Last clip here is a perfectly drawn up blitz that DeShaun Watson fails to recognize at all. Eberflus puts so much motion into this blitz that it is no wonder that Moore was able to have a free rush at the quarterback. The first movement has Sheard racing across the line on a big stunt, forcing the offensive tackle to look inside. Then, Geathers races inside and forces the running back to step up and block him on the play. These two motions essentially set up that Moore won’t be seen by any blocker on the play, giving him a free rush. Perfectly schemed up blitz by Eberflus.

2.) Dominating the Trenches

The defensive line has been a bit of a worry for the Colts this season. Denico Autry and Margus Hunt both stood out early in the season but injuries to both players slowed up their promising starts. Promising young players Jihad Ward and Hassan Ridgeway both have also been slowed by injuries and Ward was placed on IR earlier in the year. Al Woods and Grover Stewart have both been underwhelming. Kemoko Turay and Tyquan Lewis have also both dealt with injuries and some rookie inconsistencies.

The last couple weeks however, have been much different. Autry and Hunt have both returned to their dominant early year form as Autry has notched five sacks in his last two games. Sheard has solidified the left side of the line as a strong rotation of Kemoko Turay, Tyquan Lewis, and Al-Quadin Muhamad have held down the right side. This healthy group of guys have really played dominant football in recent weeks.

Our first clip here is a big third down play late in the game against the Jaguars. The Colts are down 3-0 at this point and the defense needs a stop here to keep the game a one score game for the offense. The defensive line— led by Autry, Hunt, and Sheard— gets immediate penetration and blows up the play in the backfield for the big loss. This was a huge stop right here and the defensive line absolutely dominated the Jaguars’ offensive line.

When the Colts have needed a play the last few weeks, the defensive line has delivered. In the fourth quarter down by a score against the Dolphins, Hunt makes this huge stop to give the ball back to the offense. Hunt has seemingly returned to his early season dominance as he has looked much healthier the last couple weeks. His quickness and strength are on full display here and he changes the momentum of the game with one big tackle. Lewis also does a nice job of getting past the tight end and getting into great position to make a play.

I could have picked any number of plays from the Colts’ win this past Sunday to conclude this section but I chose to highlight the star of the last couple games. Autry has been on a tear in recent weeks and he didn’t slow down at all against the Texans, winning Defensive Player of the Week Honors for the AFC. Here he is way too quick for the Texans offensive line as he gets the sack. The Colts’ defensive line in general though has been simply outstanding the last couple games.

3.) Role Players Settling in

The Colts’ defense has been a bit of a revolving door this year at multiple positions. At third cornerback, the Colts have rolled out guys like Chris Milton, Lenzy Pipkins, and Nate Hairston. At SAM linebacker, they’ve tried Najee Goode, Skai Moore, and Zaire Franklin at times this year. At defensive end, there was an early year rotation of Carroll Phillips and even Tarrell Basham early in the year. All of these guys however, did not pan out at those spots and it led to inconsistent play on the defense for weeks.

In recent weeks however, the defense has settled into certain guys filling those roles and they have been playing extremely well. Quincy Wilson has settled into the third corner spot and has looked much more disciplined and confident lately. Al-Quadin Muhammad is one of the more underrated players on this roster and his run defense has definitely improved in recent games. Rookie 7th round linebacker Matthew Adams has settled in nicely at SAM backer in recent weeks and his playing time has increased each week.

Once heralded as a major bust on Chris Ballard’s draft resume, Wilson is turning doubters into believers with his play in recent weeks. He looks much more comfortable in a zone defense and is actively looking to make plays on passes. He is playing much more physical as well and is much more active in run defense. With Wilson sliding into that third corner spot, the rotation of him, Pierre Desir, and Moore have built up a lot of chemistry the last couple of games. Here, Wilson (bottom of the screen) makes an excellent read in zone to intercept Marcus Mariota.

Defensive end Al-Quadin Muhammad may not be a player who is talked about often, but he is making a name for himself this season. With Sheard, Turay, and Lewis being the big names in the defensive end rotation, the Colts needed one more guy to step up and be a big piece in the rotation. Muhammad has filled in nicely as a base run defender and he has actually offered some decent traits as a pass rusher as well. His run defense though in recent weeks has really caught my eye. Here he slides through the Texans’ defensive line and makes a big tackle for a loss. The solidified rotation at the defensive end spot has led to better play from all four guys in recent weeks.

Last but certainly not least is Matthew Adams. After not earning any defensive snaps in his first five games of the year, Adams has worked his way into being a key player on defense. He has logged over 40% of defensive snaps played in back to back weeks and brings a new level of intensity and physicality to every snap. With him really filling that SAM backer spot, the linebacker core appears to be filled for the near future with three guys all under 24 years old. He makes the game easier for Leonard and Walker when he is on the field and he also makes some plays on his own. Here are two of my favorite highlights from him on the year.

4.) Confidence

The most important thing though for any defense is confidence. Early in the year, the team obviously struggled with confidence with guys filtering in and out of the lineup and injury issues. For a young team learning a new system, the players did seem lost at times early in the year as well.

That all changed though these last few games. With Eberflus letting these young players get after the quarterback more, they are playing much more relaxed and confident. With the defensive line getting healthy and stronger, they are playing with enough confidence to go out and dominate the opposition’s offensive line. With role players being solidified in spots that helps themselves and their teammates succeed, the whole defense is playing with more chemistry and confidence. All of these factors above are making a young, aggressive defense more confident. Look at the clips above if you want film of that confidence.

Final Thoughts

Overall, its easy to fall in love with how this defense has played of late. Season long contributors such as Leonard, Walker, and Moore have continued their strong play. The real difference though is now the entire defense is stepping up and playing with more aggression and confidence. As a result, instead of just Luck carrying this team to the playoffs, the defense is holding up their end of the bargain.

A lot of credit needs to go to defensive coordinator Matt Eberflus for this turnaround as he has really been putting players in positions to be most successful in recent weeks. With his newly found aggressive play-calling, these defenders are obviously getting after it more as well.

The defense may not be perfect and still has it’s fair share of struggles— please learn how to defend screens better— but it has drastically improved the last few weeks. They are playing much more aggressive and confident and the defensive line is absolutely dominating the trenches each week. They will have to keep up this strong play the next two games however as Ezekiel Elliott and Saquon Barkley roll into town. I personally like the defense’s chances though.


The present invention relates to billboards or other large displays. Billboards are a type of outdoor advertising found, for example, along major highways. The name refers to large, outdoor steel-framed signs, which in some installations are mounted on poles or on a base to be elevated above the ground. Most often, the artwork (which in the present application includes broadly advertising materials or other content to be displayed) forming the sign is printed on large poster sheets, which are affixed to the face of the billboard. There are hundreds of thousands of billboards in the United States, generating billions of U.S. dollars in revenues.
A billboard frame is typically constructed from steel beams and supports the artwork. If the billboard is to be illuminated at night, typically lighting equipment is mounted in front of the billboard on poles to shine light back towards the billboard. Standard sizes for a large steel frame assembly include 20 feet high×60 feet wide (6.1×18.3 m), 20 feet high×48 feet wide (6.1×14.6 m), 14 feet high×48 feed wide (4.2×14.6 m), and 10 feet high×36 feet wide (3×11 m). The front of the steel frame is covered with a backing material, known as a facing. The artwork is affixed to the facing. The artwork is either preprinted on paper or vinyl sheets that are pasted onto the facing, or in some cases, the art is painted directly onto a plywood or canvas facing.
Billboards designed to display advertising at night have traditionally been illuminated from the front by lamps mounted in front of, and below, the billboard, which shine light back towards the billboard face. Due to the limitation of lamps, the quality of nighttime illumination has been relatively poor. Particularly because billboards are used mostly for advertising purposes, it would be desirable to provide a billboard which can be used at night but with a lighting arrangement better than the current designs.
There are increasing needs for large area displays as digital display technology and billboard print technology improves, which place increase requirements on backlight systems that are low cost and convenient to set up.


The Northwoods League features some of the best college baseball talent in America. As it turns out, it’s also home to some of the biggest and best tirades — even orchestrated ones — that you’re ever going to find.

Witness the epic meltdown from 6-year-old “Coach Drake” of the Kalamazoo Growlers.

On Wednesday evening, the “coach” took strong exception to an umpire’s outfield call during the Growlers game against the Wisconsin Woodchucks. What followed was a bat-throwing, bucket of balls dumping, dirt kicking, and hat throwing rant that would have made Billy Martin proud.

Watch:

6-year old Coach Drake LOSES it after ejection. pic.twitter.com/S9W0Xuj5fo — Kalamazoo Growlers (@kzoogrowlers) July 16, 2019

Now, so no one gets the impression that Coach Drake is just a complainer, here he is last week giving a pep talk to his pitcher and players on the mound.

Watch:

The CUTEST mound visit ever.

Meet Coach Drake.#SCtop10 pic.twitter.com/hJoCnGCMsu — Kalamazoo Growlers (@kzoogrowlers) July 9, 2019

“In that video, the broadcaster states that Coach Drake has the most ejections in Northwoods League, and it would not be long after that game that he picked up another one,” CBS Sports reported.

It’s unclear what kind of fine the league will issue for Coach Drake for his seriously disruptive conduct.

Follow Dylan Gwinn on Twitter @themightygwinn


67 F.2d 605 (1933)
In re S. W. STRAUS & CO., Inc. (RODELLI et al., Interveners).
Nos. 160, 186, 187.
Circuit Court of Appeals, Second Circuit.
November 6, 1933.
*606 Baker & Obermeier, of New York City (Joseph J. Baker and Oscar S. Rosner, both of New York City, of counsel), for appellant bankrupt.
Nathaniel L. Goldstein, of New York City (Abraham J. Halprin, of New York City, of counsel), for appellant receiver Schultze.
Archibald Palmer and Samuel L. Chess, both of New York City (Sydney Basil Levy, of New York City, of counsel), for appellees intervening creditors.
Before L. HAND, SWAN, and AUGUSTUS N. HAND, Circuit Judges.
SWAN, Circuit Judge.
S. W. Straus & Co., Inc., is a New York corporation which was formerly engaged in the business of dealing in investment securities. A so-called Martin Act suit was instituted against it in a state court, and on March 3, 1933, a decree was entered therein, with the corporation's consent, appointing permanent receivers, who were later succeeded by Louis F. Schultze as sole receiver. On the same date, March 3, 1933, and after the state court *607 decree had been made, an involuntary petition in bankruptcy was filed against S. W. Straus & Co., Inc., by three of its creditors. Both the alleged bankrupt and receiver, Schultze, appeared in this proceeding and obtained successive extensions of time until August 1st to plead to the petition. In the meantime two ex parte orders of intervention were obtained, one by Rodelli and the other by Weischedel, Glazier, Wiand, and White, upon intervening petitions, each of which alleged that the petitioner was a creditor of the bankrupt. Rodelli also obtained an ex parte order for examination of the bankrupt's officers and other witnesses under section 21a of the act (11 USCA § 44 (a). Thereafter the bankrupt moved to vacate the three orders aforesaid, and has appealed from an order entered August 2d denying this motion.
Determination of the bankrupt's appeal turns upon whether the interveners are shown to have had provable claims in bankruptcy. If they have, they were entitled to intervene by virtue of section 59f of the Bankruptcy Act (11 USCA § 95 (f); if they have not, then they should have been denied intervention. See In re New York Tunnel Co., 166 F. 284 (C. C. A. 2); In re Neve Drug Stores, 48 F.(2d) 693, 696 (C. C. A. 2). It is the contention of the bankrupt that it appears on the very face of the intervening petitions that the petitioners are not creditors.
This contention must be sustained as to Rodelli. He alleges that he purchased from Straus-Manhattan Co., Inc., five of its bonds, "the payment of principal and interest on the said bonds, pursuant to a trust indenture and pursuant to a direct agreement with your petitioner, having been guaranteed by S. W. Straus & Co., Inc., the alleged bankrupt herein." He alleges that interest on said bonds fell due June 1, 1933, and that both Straus-Manhattan Company and the bankrupt defaulted in the payment of it. Had the petition said no more, it could be taken as asserting a claim founded upon a "direct agreement" with Rodelli by which the bankrupt guaranteed payment of the principal and interest of the Straus-Manhattan bonds purchased by him. But the succeeding paragraphs make it clear that the agreement upon which Rodelli is relying is an agreement between the bankrupt and Straus-Manhattan Company. By this agreement, it is alleged, the former agreed to purchase from the latter on or before December 1, 1933, at not less than par value, "the entire amount of the deposited collateral held by the Trustee as security for the issue of the first mortgage convertible collateral trust bonds, of which your petitioner is a holder." It is then alleged that "this agreement is, in effect, a guarantee on the part of S. W. Straus & Co., Inc., that interest will be paid as it becomes due and the principal will be paid on or before December 1, 1933." It is further alleged that there was an anticipatory breach of the bankrupt's "contract of guarantee and repurchase and default in interest payment of June 1st, 1933, and that such breach establishes the liability of the alleged bankrupt." Reading the petition as a whole, it is impossible to accept the contention of Rodelli's counsel that it alleges two agreements  one, a direct guaranty of payment of principal and interest; the other, the agreement with Straus-Manhattan Company, which is "in effect a guarantee." We think the claim is founded solely on the latter agreement. If so, no provable claim is alleged on the part of Rodelli. The promisee is Straus-Manhattan Company. Laying aside any question of anticipatory breach, and assuming a breach and that the trustee under the mortgage securing the issue of bonds could sue as a third party beneficiary, this would not avail Rodelli. Without any allegation that the trustee has failed in its duty in this regard, no individual bondholder could have any right to sue. Hence Rodelli's petition showed no facts from which it appears that he is a creditor of the bankrupt, and the order appealed from was erroneous in not vacating the ex parte order of intervention previously granted him.
It is otherwise as to the intervening petitions of Weischedel, Glazier, Wiand, and White. They all contain substantially similar allegations. Each petitioner alleges that he purchased from the bankrupt bonds of another corporation in reliance upon the bankrupt's representations that they were first mortgage bonds and were guaranteed by it, that these representations were false and fraudulent, and that the bonds are of only nominal value and practically unmarketable. By reason thereof it is charged that the purchase price paid to the bankrupt is held for the use and benefit of the petitioner, and payment thereof has been demanded and refused.
The bankrupt contends that each petition alleges a pure tort claim for unliquidated damages caused by fraudulent misrepresentations. Such a claim is, of course, not provable in bankruptcy. Schall v. Camors, 251 U. S. 239, 40 S. Ct. 135, 64 L. Ed. 247. It is true the allegations are sufficient to charge liability in tort for fraud, but they are also sufficient to show liability in contract. One *608 who sells a bond with an absolute representation that it is secured by a first mortgage, may well be found to have given a warranty to this effect. See Burtch v. Child, Hulswit & Co., 207 Mich. 205, 174 N. W. 170; Menard v. Clarence E. Thompson & Sons, 90 Conn. 30, 96 A. 177; 9 C. J. 60. That a claim on a warranty is provable, even though in case of fraud there might be an independent claim purely in tort, is expressly stated in Grant Shoe Co. v. W. M. Laird Co., 212 U. S. 445, 449, 29 S. Ct. 332, 53 L. Ed. 591. We believe that the petitions sufficiently allege a breach of warranty.
But in any event they sufficiently allege a quasi contractual liability for unjust enrichment. Such a claim is provable. See Crawford v. Burke, 195 U. S. 176, 187, 25 S. Ct. 9, 49 L. Ed. 147; Schall v. Camors, 251 U. S. 239, 251, 40 S. Ct. 135, 64 L. Ed. 247; Cawthon v. Banco-Kentucky Co., 52 F.(2d) 851 (D. C. W. D. Ky.). It is urged that the petition cannot be treated as asserting a claim for recovery of the purchase price of the bonds because there is no offer to return them. In a suit in equity the decree may make suitable provision for restitution. In re American Knit Goods Mfg. Co., 173 F. 480 (C. C. A. 2); MacNamee v. Bankers' Union, 25 F. (2d) 614, 618 (C. C. A. 2); Williston, Contracts, § 1460. Proceedings in courts of bankruptcy are in the nature of proceedings in equity, so that the failure to tender restitution before the filing of the petition in bankruptcy is not fatal to the existence of provable claims by the interveners. In re Bancunity Corp., 36 F.(2d) 595, 598 (D. C. S. D. N. Y.). Our own decision of In re Neve Drug Stores, 48 F.(2d) 693, is cited as contrary to this view. It should not be so construed. As the opinion indicates, the acts of the bankrupt were treated as creating only tort claims, but the facts are stated so briefly as not to present clearly the situation which was under consideration. Klein's answer alleged the making of an agreement to sell his store for part cash and part shares of stock in the Neve Drug Stores (the bankrupt), and charged that "thereafter" the bankrupt and others by fraudulent acts caused the stock to depreciate, so as to cheat Klein out of a large part of the consideration which he received for the sale of his store. This is quite different from the case at bar. Here the fraud induced the purchase, and a claim in rescission is suggested by the allegation that the purchase price is held for the use of the petitioner. There was no error below in refusing to vacate the order of intervention granted to Weischedel and the three other interveners.
Since, as we have held, Rodelli was not shown to be a creditor, it was erroneous to grant his petition for an examination of witnesses under section 21a, and the bankrupt's motion to vacate such order should have been granted. It appears from the record that Weischedel also obtained an order for examination of witnesses, but the validity of this order is not before us, because the bankrupt's motion was directed only to Rodelli's order for examination and the order of August 2d from which the bankrupt has appealed is likewise so limited.
For similar reasons we cannot consider the bankrupt's argument as to the insufficiency of the petition in bankruptcy. So far as appears, the bankrupt has never moved to dismiss the petition, nor has it appealed from the denial of the receiver's motion to dismiss. In No. 160 the order appealed from must be modified in accordance with the views above expressed.
We turn now to the appeals of receiver, Schultze. On July 28th he obtained an ex parte order permitting him to intervene and answer the petition for adjudication. On July 31st he filed an answer denying the bankrupt's insolvency and the commission by it of an act of bankruptcy as charged in the petition. The bankrupt itself filed a similar answer. Thereafter counsel for Rodelli moved for vacation of the order allowing the receiver to intervene. The motion was joined in by Mr. Kaye, one of the attorneys for the petitioning creditors. On September 18th an order was entered granting the motion. This is the order on Appeal in No. 187.
Section 18b of the Bankruptcy Act (11 USCA § 41 (b) provides that: "The bankrupt, or any creditor, may appear and plead to the petition within five days after the return day, or within such further time as the court may allow." If this section be deemed exclusive, no one other than a creditor (except the bankrupt himself) may contest the petition for adjudication. This view was intimated in Re Columbia Real Estate Co., 112 F. 643, 647 (C. C. A. 7), but has not generally prevailed. In re Meyer, 98 F. 976, 980 (C. C. A. 2), intervention by assignee for benefit of creditors. As to intervention by equity receivers, In re Hudson River El. Power Co., 173 F. 934, 956 (D. C. N. D. N. Y.), affirmed on other grounds (C. C. A. 2) 183 F. 701, 33 L. R. A. (N. S.) 545; In re Morosco Holding Co., 296 F. 516, 520 (D. C. S. D. N. Y.); Blackstone v. Everybody's Store, 207 F. 752, 756 (C. C. A. 1); Struthers Furnace Co. v. Grant, 30 F.(2d) 576 (C. C. A. 6); Wood v. *609 Natural Soda Products Co., 31 F.(2d) 110 (C. C. A. 9). Cf. In re Bankshares Corp., 50 F.(2d) 94 (C. C. A. 2). Assuming, therefore, that it is within the District Court's power to permit a state court receiver to intervene to contest adjudication, the exercise of such power is clearly discretionary. See Blackstone v. Everybody's Store, supra. Cf. Gratiot County State Bank v. Johnson, 249 U. S. 246, 250, 39 S. Ct. 263, 63 L. Ed. 587. In the case at bar the bankrupt is itself putting up a defense to adjudication; the presence of the receiver appears to be unnecessary and to have resulted largely in a duplication of motions and orders. All the above-cited authorities allowing the receiver to intervene were, with the exception of In re Morosco Holding Co., cases where the bankrupt himself was not contesting adjudication. Under the circumstances of the present case, we see no reason to think that discretion was abused in excluding the receiver from participation.
The remaining appeal, No. 186, is from an order entered September 20, 1933, denying the receiver's motion to dismiss the petition in bankruptcy as insufficient upon its face. As appears from the record in No. 187, on September 18th the court had vacated the order authorizing the receiver to intervene. Technically it may be true, as the appellees urge, that this abated any pending motion of the receiver and requires either affirmance of the order or dismissal of the appeal in No. 186. But, as the sufficiency of the petition to support an adjudication is almost certain to arise again in the course of these proceedings, it seems expedient to express our views on this question, and, as they lead to an affirmance of the order, to affirm on this ground rather than on the more technical one first suggested.
The petition in bankruptcy charged as the only act of bankruptcy the giving of preferences to unknown creditors in unknown amounts, aggregating $2,500. Except in stating a different aggregate sum, it is identically like the petition held insufficient by this court in Re Gaynor Homes, 65 F.(2d) 378. Hence the petition was subject to dismissal had the objection been taken in time. But, as our previous decisions indicate, such a petition gives the court jurisdiction, and the defect is one which may be waived by answer and going to trial. Bradley v. Huntington (C. C. A.) 277 F. 948. Whether it would be waived by answer alone was there left open and is the question presented in the present appeal. Here it appears that both the bankrupt and the receiver answered the petition without reserving any objection to the sufficiency of the petition. The reason for holding a petition which follows the general language of the statute so vague as to be subject to demurrer or motion to dismiss is that it subjects the bankrupt to the danger that the petitioning creditors may prove against him acts of bankruptcy which they did not challenge by their pleading, and there is no way for him to tell what they did mean to challenge. See In re Fuller, 15 F.(2d) 294 (C. C. A. 2). Hence he should take the objection before answering, or should at least reserve it in his answer as was done in Re Gaynor Homes, supra. If the bankrupt answers without such reservation, it may be taken that he is satisfied with the pleading and is able, despite its vagueness, to admit or deny its allegations. In general, demurrers come too late after an answer has been filed, and we see no reason why this general rule should not be applied to pleadings in bankruptcy proceedings. Indeed, there is especial reason why the bankrupt should move seasonably, for the passage of four months may prevent an amendment to correct the defective petition by specifying with precision the act of bankruptcy which the petitioners intended to challenge. In re Fuller, supra; cf. Harney Shoes, Inc., v. Nat. Fabric & Finishing Co., 44 F.(2d) 517 (C. C. A. 1). Holding, as we do, that the defect was waived by answer, we find it unnecessary to consider whether the order might also be sustained under the doctrine applied in Re Standard Aero Corp., 270 F. 779 (C. C. A. 3).
We find no error in Nos. 186 and 187, and the orders involved in those appeals are affirmed. In No. 160 the order is modified as above indicated; and the appellant is awarded one-half its appellate costs to be recovered from Rodelli.


/**
 * DSS - Digital Signature Services
 * Copyright (C) 2015 European Commission, provided under the CEF programme
 *
 * This file is part of the "DSS - Digital Signature Services" project.
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */
package eu.europa.esig.dss.validation.timestamp;

import java.io.Serializable;

/**
 * This class represents XAdES Include tag in case of IndividualDataObjectsTimeStamp
 */
public class TimestampInclude implements Serializable {

	private static final long serialVersionUID = 8557108386646000784L;

	private String uri;
	/* The referencedData attribute shall be present in each and every Include element, and set to "true". */
	private boolean referencedData;

	public TimestampInclude() {
	}

	public TimestampInclude(String uri, boolean referencedData) {
		this.uri = uri;
		this.referencedData = referencedData;
	}

	public String getURI() {
		return uri;
	}

	public void setURI(String uri) {
		this.uri = uri;
	}

	public boolean isReferencedData() {
		return referencedData;
	}

	public void setReferencedData(boolean referencedData) {
		this.referencedData = referencedData;
	}

}


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Parador De Corias

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Overview

Parador De Corias is a 4-star property that provides visitors with a picnic area, a swimming pool and a library. Offering accommodation in the 4-story building, the hotel combines Roman architecture and modern facilities.

The city center is about 10 minutes on foot. A 55-minute drive to Ponferrada.

Guests may find Piornedo Village within 47 km and La Braña within 25 km of the property.

60 km to Asturias airport.

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Parador De Corias offers 76 soundproof rooms that come with a magnificent view of the mountain and such facilities as climate control, flat-screen television, a safe, a personal computer and a trouser press. They feature bathrooms with a hairdryer, a bidet and bath sheets.

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Contemporary dishes are served in the lounge restaurant.

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Residents will benefit from laundry, room service and shopping service.

This offer includes a stay in a Standard Double Room with a buffet breakfast.
For stays on 24 and 31 December the offer also includes a special dinner held on those evenings, a New Year's Eve party with free bar and party bags.

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Media:Flat-screen TV

Room Description:

This offer includes a stay in a Double or Twin Room with Extra Bed with a buffet breakfast.
For stays on 24 and 31 December the offer also includes a special dinner held on those evenings, a New Year's Eve party with free bar and party bags.

Standard Double Room

Room size:

370 sq. feet

Max occupancy:

2 persons

Bed type:

1 Double bed

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Room Facilities:

Bathtub

Air conditioning

— Less+ More

General:Work desk

Dressing area

Soundproofed windows

Parquet floor

Bathroom:Bathroom

Hair dryer

Towels

Bidet

Toilet

Dining:Mini-bar

Media:Flat-screen TV

Room Description:

This double room has a soundproofing, air conditioning and minibar.

Standard Twin Room

Room size:

370 sq. feet

Max occupancy:

2 persons

Bed type:

2 Single beds

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Room Facilities:

Bathtub

Air conditioning

— Less+ More

General:Work desk

Dressing area

Soundproofed windows

Parquet floor

Bathroom:Bathroom

Hair dryer

Towels

Bidet

Toilet

Dining:Mini-bar

Media:Flat-screen TV

Room Description:

This large double or twin room features a flat-screen TV, a desk and a private bathroom with free toiletries and a hairdryer. There is an extra bed available.

Double or Twin Room Extra Bed

Room size:

370 sq. feet

Max occupancy:

2 persons

Bed type:

3 Single beds

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Room Facilities:

Bathtub

Air conditioning

— Less+ More

General:Work desk

Dressing area

Soundproofed windows

Parquet floor

Bathroom:Bathroom

Hair dryer

Towels

Bidet

Toilet

Dining:Mini-bar

Media:Flat-screen TV

Room Description:

This triple room features a soundproofing, air conditioning and minibar.

Double or Twin Room Extra Bed

Room size:

360 sq. feet

Max occupancy:

3 persons

Bed type:

3 Single beds

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Room Facilities:

Bathtub

Air conditioning

— Less+ More

General:Work desk

Dressing area

Soundproofed windows

Parquet floor

Bathroom:Bathroom

Hair dryer

Towels

Bidet

Toilet

Dining:Mini-bar

Media:Flat-screen TV

Room Description:

This triple room has air conditioning, soundproofing and minibar.

Junior Suite

Room size:

220 sq. feet

Max occupancy:

2 persons

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Room Facilities:

Bathtub

Air conditioning

— Less+ More

General:Work desk

Dressing area

Soundproofed windows

Parquet floor

Bathroom:Bathroom

Hair dryer

Towels

Bidet

Toilet

Dining:Mini-bar

Media:Flat-screen TV

Room Description:

This suite features a minibar, soundproofing and air conditioning.

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Availability

Your departure date was more than 30 days after your arrival date.Bookings can only be made for a maximum period of 30 days.Please enter alternative dates and try again.