Mrs. Alderks and Mrs Boyer's students came to school with a surprise! Their teachers were transformed into pirates. The class celebrated "Talk Like a Pirate Day" with pirate stories, songs and writing stories in pirate dialogue. Arrg!
In 6th grade students got to make paper airplanes.
Students were read a math story.
Cherry Creek was very lucky to have over 70 volunteers (some of them parents of students) from US Synthetic donate time and materials on United Way's Day of Caring. A large crew repainted lines and maps on the playground, as well as added more large graphics with shapes and the alphabet. Along with that, volunteers spent an hour in each classroom teaching students about math and reading, including doing a project and activity with each class. The students loved having the special visitors, the faculty and staff appreciated their time and donations and the school as a whole was cheered up from the inside out with all the service projects. A BIG Cherry Creek THANK YOU to US Synthetics!!
Capt. Biesinger leads Mrs. Sumsion's class in the pledge.
Captain Will Biesinger from the Utah Army National Guard's Special Forces and father of Emma, a 5th grader, came to visit the 6th graders at Cherry Creek Elementary on 9/11 for Patriot's Day. He led Mrs. Sumsion's class in the Pledge of Allegiance (which was very neat!) and then shared his experience of how he was a school teacher and after the attacks on 9/11 felt inspired that he had something to offer the military and joined to help fight for freedom in Afghanistan during Operation Enduring Freedom. After 6 years he became a captain. He explained about what is going on in Afghanistan and shared pictures of his time there, the people there and what school is like for children. Until 10 years ago girls were not even allowed to learn. Mostly, "school" is held under a tarp and they do their writing in the sand with their finger or a stick. Aren't we lucky to have cooled and heated classrooms with desks, chairs and the school supplies we need?
Students were able to ask questions about what kinds of food the Afghan people eat (they eat a lot of goat), his favorite part of Afghanistan (a valley that used to be full of danger and conflict and now peace has been restored), what he'll remember most about Afghanistan (the good people there) and many other great questions. Capt. Biesinger encouraged the students to read and learn all they can because knowledge is power! The way the Taliban prevents people from having power is by keeping them from learning. He taught that even as Americans have patriotism and love their country, so do many people all over the world, including the Afghan people. They love their country and fight for freedom too! We thank Capt. Biesinger for coming today and reminding us that there are more good people in the world than bad.
Mrs. Golding's class learned about nouns this week and created a class "Noun Town: Where people, places, and things live!"
We Can All Be a Hero!
#1 Turn off the TV. The average American watches 8 hours of TV a day. The average millionaire watches 8 hours of TV a WEEK.
#2 READ READ READ READ READ!
#3 Listen to and respect teachers, parents and others.
#4 You are not entitled to anything! He said children can expect 4 things from their parents: food, shelter, clothing and love. Other than that, everything else is a bonus, but NOT to be demanded nor expected.
#5 Do hard things. Work hard.
He finished the assembly answering questions from the students. We learned he hates One Direction due to the inappropriate lyrics in his opinion, doesn't own a TV (thus, doesn't have a favorite TV show), loves to read, favorite color is black, and has talked to Michael Jackon and Paul McCartney on the phone, thanks to his uncle Donnie Osmond's friendship with them. Students were able to purchase books, as well as pre- order copies of the new Michael Vey book.
and meeting Marley and his friends!
We enjoyed starting our rock unit today. Students were able to make observations and sketch the different types of rocks.


"Hello, is anybody in there?"
Santa (Natasha) Reindeer (Bridey) "Sure hope it snows soon!"
Well, what do you think? Don't I have a lot of furry friends? I haven't met them all up close, I met some of them on the internet. The internet is a wonderful place to meet friends, even for us dogs.
I do know Casey personally as well as Natasha, Bridey, Quincy, and Mayday.
Casey is a Standard Schnauzer and lives with her parents in New Jersey and I got to meet her and have a real date with her in Myrtle Beach. Casey was my first girlfriend and she'll always be number one with me.
Natasha and Bridey are two lovely girls who live near me in the Poconos of Pennsylvania. We have gone swimming together and for walks.
Quincy and Mayday are boy and girl Standard Schnauzers that live in North Carolina. They, along with their mom and dad have visited us at Myrtle Beach. When they go on trips they get to travel in a really neat motorhome. I really envy Quincy because he has a full time companion, Mayday. I told mom and dad that all I want for Christmas is my own furry companion.
This special message is for all my furry friends' parents: I'm hoping that you make sure that your pets are safe when they go for rides in your car. Make sure that they're wearing doggie seat belts and never, never lock them in the car by themselves if it's very cold or very hot outside. Also, never leave your furry kids in an unlocked car because if they're very cute or very handsome, someone might kidnap them. My mom said that someone tried to kidnap one of her furry kids years ago, but she returned to her unlocked car before the lady who was holding mom's dog in her arms, got away.
Also, your pets should always wear I.D. tags just in case they get lost. Mom says that I also have a microchip. Getting lost could be the worst thing that could happen to us if we couldn't find our way back home. There are only two words on the back of my I.D. tag.....HUGE REWARD! I think this means that I'm worth an awfully lot to my mom and dad. But, I knew that!


Scott Martin isn't just a talented caddie. He's also a remarkable photographer. This week, Scott is in St. Andrews, Scotland, caddying for Steve Flesch at the Senior Open Championship. Along the way — including the weekend over at Carnoustie — he's taken some great photos that he's shared to his Instagram account (@flyerscaddie). Here's a look.


The island of Hvar is a Croatian Island that is known for its important nautical location, its various historical periods, cultural and natural monuments. This Island of the Adriatic Sea is located between the islands of Brac, Vis and Korcula.
Hvar is considered one of the 10 most beautiful islands in the world. The climate is characterized by mild winters, and warm summers with the most sun year round, which is why it was named the Sunny Island.
On Hvar Island there is lot of nice restaurants where tourists can enjoy fresh fish and good wines. Some of the best Croatian wines come from Jelsa vineyards and cellars. Jelsa is located in a bay on the northern coast of the island of Hvar.
Beside Jelsa and Hvar town, there are some other historical small towns on island such as Stari Grad and Vrboska.
In this small area there are few cultural monuments on famous UNESCO list of world intangible heritage.


Fanny is available for public speaking events and speaking within the workplace.
Motivational Money Talks – fire up your passion to become an excellent money manager and financially free!
She delivers fun and interactive workshops of all aspects of improving our relationship with money and financial literacy.
Workshops for adults and young people.
Contact Fanny for fees or use the contact form below.


text:
Rilland-Bath – przystanek kolejowy w Rilland, w prowincji Zelandia, w Holandii. Został otwarty 1 stycznia 1872 roku. Znajduje się na linii kolejowej pomiędzy Roosendaal, a Vlissingen, pomiędzy przystankiem Krabbendijke, a stacją Bergen op Zoom.

Przypisy

Stacje i przystanki kolejowe w prowincji Zelandia

redpajama_set_name: RedPajamaWikipedia


We present a unified method to estimate current–voltage characteristics of insulators starting from ab initio electronic calculations of the properties of the dielectric material. The method consists of three stages: 1) computation of trap energy distributions for excess electrons by means of density functional theory, 2) computation of local electron mobilities from a multiple trapping electron transport model which includes trap filling effects and 3) macroscopic integration of the Poisson and current–field equations, using local electron mobility data from stage 2) to predict the current– voltage characteristics for a material of a given width. The only input to this procedure is the chemical composition of the insulating material. We compare our model results with experimental studies of the current–voltage curve of cross-linked polyethylene.


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text:
\section{INTRODUCTION}

One of the most important systems in stress response is hypothalamus-pituitary-adrenal (HPA) axis, because the released hormones lead to energy directed to the organisms. The HPA axis is organized into three distinct regions: the hypothalamus, pituitary gland and adrenal gland. It is a complex set of direct influences and feedback interactions among the three endocrine glands. These glands work together by producing and secreting, or responding to common hormones including corticotropin-releasing hormone (CRH), adenocorticotropin  (ACTH), and cortisol (CORT) \cite{Kyrylov_2005}. The dynamics of the HPA axis is very important, because cortisol overproduction leads to Cushing's disease;
cortisol underproduction generates Addison's disease.

During the past decade, the mathematical modelling of the HPA axis has been intensively studied \cite{Kyrylov_2005,Andersen_2013,Bairagi_2008,Conrad_2009,Gudmand_2014,Jelic_2005,Lenbury_2005,Markovic_2011,Pornsawad_2013,Savic_2005,Savic_2006,Vinther_2011}.
In 2005, Savic and Jelic \cite{Savic_2005} presented one of the mathematical models of HPA axis described by a system with three nonlinear differential equations with one delay.  Three variables have been considered: the concentration of $CRH$, the concentration of $ACTH$ and the concentration of free cortisol $CORT$. According to the results obtained by stability analysis, the system does not oscillate at all in the neighborhood of the equilibrium point. In 2006,  Savic et al. \cite{Savic_2006} considered the same model, but four time delays have been introduced. Once more, their results showed that the system describing the HPA axis does not oscillate in a neighborhood of the equilibrium points.

In 2011, Vinther et al. \cite{Vinther_2011} introduced feedback functions as generalized Hill functions, based on the receptor dynamics. They investigated the possibility of time delays as being capable of producing oscillations in accordance with the ultradian rhythm. By numercial simulations, oscillating solutions in a neighborhood of the equilibrium point have been observed.

In 2015, Kaslik and Neamtu \cite{EvaMiha_MMB} proved the occurrence of oscillating solutions in a neighborhood of the unique equilibrium point, by performing a Hopf bifurcation analysis, considering several distributed time delays and fractional derivatives in the minimal three-dimensional mathematical model previously analyzed in \cite{Vinther_2011}.

On the other hand, Gupta et al. \cite{Gupta_2007} and Sriram et al. \cite{Sriram_2012} incorporated expression of the glucocorticoid receptor (GR) in the mathematical model of the HPA axis and demonstrated that repeated stress and the level of GR concentration leads to a disorder; however, it is important to note that they did not consider time delays.

With the aim of improving the mathematical model of the HPA axis described in \cite{Gupta_2007}, we include distributed time delays and  frac\-tional-order derivatives. On one hand, distributed time delays represent the situation where the delays occur in certain ranges of values with some associated probability distributions, taking into account the whole past history of the variables. In many real world applications, distributed time delays are more realistic and more accurate than discrete time delays \cite{Cushing_2013}. Distributed delay models appear in a wide range of applications such as, population biology \cite{Faria_2008,Ruan_1996}, hematopoiesis \cite{Adimy_2003,Adimy_2005,Adimy_2006,Ozbay_2008}, neural networks \cite{Jessop_2010}. On the other hand, the main benefit of fractional-order models in comparison with classical integer-order models is that fractional derivatives provide a good tool for the description of memory and hereditary properties of various processes \cite{Kilbas,Lak,Podlubny}.

The paper is structured as follows. Section 2 provides the mathematical model of the HPA axis, with the influence of the GR concentration, where we introduce distributed time delays to account for the time needed by the hormones to travel from source to destination, as well as fractional-order derivatives to account for the memory properties of the system. In Section 3, a local stability analysis of the system with distributed delays is provided. Numerical simulations are carried out and discussed in Section 4, followed by concluding remarks in Section 5.

\section{THE MATHEMATICAL MODEL}
The mechanism of the HPA axis can be shortly described as follows. Paraventricular nuclei (PVN) of hypothalamus generate corticotropin releasing hormone (CRH) which induces the adenocorticotropin (ACTH) production in the pituitary. Then, ACTH stimulates the adrenal cortex to produce glucocorticoids, which in turn suppress the production of both CRH and ACTH.

In formulating the mathematical model which describes the variation in time of the concentrations of the three hormones CRH, ACTH and CORT, as well as the glucocorticoid receptors GR, the following sequence of typical events is considered, according to the schema presented in Figure \ref{fig:0}.

\begin{figure}[htbp]
\centering
\includegraphics*[width=0.4\textwidth]{schemaHPA_GR.pdf}
\caption{A simple schematic representation of the HPA axis with negative feedback.}
\label{fig:0}
\end{figure}

CRH is secreted from the hypothalamus and released into the portal blood vessel of the hypophyseal stalk, and then transported to the anterior pituitary where it stimulates the secretion of ACTH. In our mathematical model, the evolution of the CRH hormone concentration in the hypothalamus is described by:
$$\dot CRH(t)=\displaystyle\frac{a_1}{a_2+\int_{-\infty}^th_1(t-s)CORT(s)ds}-a_3CRH(t),$$
where $a_1$ models a circadian production and stress term, $a_2$ is the inhibition constant, $a_3$ is the degradation rate of cortisol.

In the pituitary, cortisol enters the cells and binds the glucocorticoid receptor in the cytoplasm, causing the receptor to dimerize. This leads to the complex $GR\times CORT$ that inhibits the production of $ACTH$, modeled by:
$$\dot ACTH(t)=\displaystyle\frac{b_1CRH(t)}{b_2+GR(t)\int_{-\infty}^th_1(t-s)CORT(s)ds}-b_3ACTH(t),$$
where $b_1$ stands for a production term, $b_2$ is the inhibition constant, $b_3$ is the degradation rate of $ACTH$, and
$$\dot GR(t)=\displaystyle\frac{c_1\left(GR(t)\int_{-\infty}^th_1(t-s)CORT(s)ds\right)^2}{c_2+\left (GR(t)\int_{-\infty}^th_1(t-s)CORT(s)ds\right)^2}+c_3-c_4GR(t),$$
where $c_1$ is the dimerization constant, $c_2$ the binding affinity constant, $c_3$ the production constant and $c_4$ the degradation term for pituitary $GR$ production.

As for the evolution of cortisol concentration produced by the adrenal, the following equation is considered:
$$\dot CORT(t)=d_1\int_{-\infty}^th_2(t-s)ACTH(s)ds-d_2CORT(t),$$
where $d_1$ is a production coefficient and $d_2$ is the degradation rate of $CORT$.

Therefore, the four-dimensional mathematical model with distributed time delay is:
\begin{equation}\label{sysHPA4}
\begin{array}{l}
\dot CRH(t)=\displaystyle\frac{a_1}{a_2+\int_{-\infty}^th_1(t-s)CORT(s)ds}-a_3CRH(t),\\
\dot ACTH(t)=\displaystyle\frac{b_1CRH(t)}{b_2+GR(t)\int_{-\infty}^th_1(t-s)CORT(s)ds}-b_3ACTH(t),\\
\dot GR(t)=\displaystyle\frac{c_1\left(GR(t)\int_{-\infty}^th_1(t-s)CORT(s)ds\right)^2}{c_2+\left (GR(t)\int_{-\infty}^th_1(t-s)CORT(s)ds\right)^2}+c_3-c_4GR(t),\\
\dot CORT(t)=d_1\int_{-\infty}^th_2(t-s)ACTH(s)ds-d_2CORT(t),\\
\end{array}
\end{equation}
with the initial conditions $CRH(t)=\phi_1(t)$, $ACTH(t)=\phi_2(t)$, $GR(t)=\phi_3(t)$, $CORT(t)=\phi_4(t)$, $t\in(-\infty,0]$, where $\varphi_i$  are bounded continuous functions defined on $(-\infty,0]$, with values in $[0,\infty)$.

In system (\ref{sysHPA4}), the delay kernels $h_1,h_2:[0,\infty)\to[0,\infty)$ are probability density functions representing the probability that a particular time delay occurs. They are assumed to be bounded, piecewise continuous and satisfy
\begin{equation}\label{delay.kernel.properties}
\int_0^{\infty}h(s)ds=1.
\end{equation}
The average delay of a delay kernel $h(t)$ is given by
$$\tau=\int_0^{\infty}sh(s)ds<\infty.$$
Two important classes of delay kernels often used in the literature are worth mentioning:
\begin{itemize}
\item Dirac kernels: $h(s)=\delta(s-\tau)$, where $\tau\geq 0$. In this particular case, the distributed delay is reduced to a discrete time delay:
$$\int_{-\infty}^t x(s)h(t-s)ds=\int_0^\infty x(t-s)\delta(s-\tau)ds=x(t-\tau).$$
\item Gamma kernels: $h(s)=\displaystyle\frac{ s^{p-1}e^{-s/\beta}}{\beta^p\Gamma(p)}$, where $p,\beta>0$. The average delay of a Gamma kernel is $\tau=p\beta$.
\end{itemize}

On the other hand, we also consider the four-dimensional mathematical model with fractional-order derivatives of Caputo type and discrete time delays $\tau_1,\tau_2>0$:
\begin{equation}\label{sysHPA4.frac}
\begin{array}{l}
^cD^q CRH(t)=\displaystyle\frac{a_1}{a_2+CORT(t-\tau_1)}-a_3CRH(t),\\
^cD^q ACTH(t)=\displaystyle\frac{b_1CRH(t)}{b_2+GR(t)CORT(t-\tau_1)}-b_3ACTH(t),\\
^cD^q GR(t)=\displaystyle\frac{c_1\left(GR(t)CORT(t-\tau_1)\right)^2}{c_2+\left (GR(t)CORT(t-\tau_1)\right)^2}+c_3-c_4GR(t),\\
^cD^q CORT(t)=d_1ACTH(t-\tau_2)-d_2CORT(t),\\
\end{array}
\end{equation}
with the initial conditions $CRH(t)=\phi_1(t)$, $ACTH(t)=\phi_2(t)$, $GR(t)=\phi_3(t)$, $CORT(t)=\phi_4(t)$, $t\in(-\max(\tau_1,\tau_2),0]$, where $\varphi_i$  are bounded continuous functions defined on $(-\max(\tau_1,\tau_2),0]$, with values in $[0,\infty)$.

\section{STABILITY OF THE EQUILIBRIUM POINT}

In what follows we use the notations: $CRH(t)=x_1(t)$, $ACTH(t)=x_2(t)$, $GR(t)=x_3(t)$, $CORT(t)=x_4(t)$. The coordinates of the equilibrium point of systems (\ref{sysHPA4}) and (\ref{sysHPA4.frac}) are the positive solution of the following algebraic system:
$$
\left\{
\begin{array}{l}
a_1-a_2a_3x_1-a_3x_1x_4=0,\\
b_1x_1-b_2b_3x_2-b_3x_2x_3x_4=0,\\
c_4x_3(x_2x_4)^2-(c_1+c_3)(x_3x_4)^2+c_2c_4x_3-c_2c_3=0,\\
d_1x_2-d_2x_4=0.
\end{array}\right.
$$

\begin{proposition} $ $
\begin{itemize}
\item[(i)] The equation
$$
\begin{array}{l}
F(x):=c_4d_1^2(p_2x^2+p_1x+p_0)^3-(c_1+c_3)d_1^2x^2(q_1x+q_0)(p_2x^2+p_1x+p_0)^2+\\
\qquad\quad+c_2c_4d_2^2x^2(q_1x+q_0)^2(p_2x^2+p_1x+p_0)-c_2c_3d_2^2x^4(q_1x+q_0)^3=0,
\end{array}
$$
has at least one positive root;

\item[(ii)] An equilibrium point $E_0$ of systems (\ref{sysHPA4}) and (\ref{sysHPA4.frac}) has the coordinates $(x_{10}$, $x_{20}$, $x_{30}$, $x_{40})$, where $x_{20}$ is a positive solution of equation $F(x)=0$ and
$$x_{10}=\displaystyle\frac{a_1d_2}{d_2a_2a_3+d_1a_3x_{20}}\quad;\quad x_{30}=\displaystyle\frac{p_2x_{20}^2+p_1x_{20}+p_0}{x_{20}^2(q_1x_{20}+q_0)}\quad;\quad
x_{40}=\displaystyle\frac{d_1x_{20}}{d_4}
$$
\end{itemize}
\end{proposition}

In the case of the distributed time-delay system (\ref{sysHPA4}), considering the transformation:
$$
u_1(t)=x_1(t)-x_{10},\quad u_2(t)=x_2(t)-x_{20},\quad u_3(t)=x_3(t)-x_{30},\quad u_4(t)=x_4(t)-x_{40},
$$
the linearized system at an equilibrium point $E_0$ becomes:
\begin{equation}\label{14}
\begin{array}{l}
\dot u_1(t)=a_{11}u_1(t)+b_{14}\int_{-\infty}^th_1(s)u_4(t-s)ds,\\
\dot u_2(t)=a_{21}u_1(t)+a_{22}u_2(t)+a_{23}u_3(t)+b_{24}\int_{-\infty}^th_1(s)u_4(t-s)ds,\\
\dot u_3(t)=a_{33}u_3(t)+b_{34}\int_{-\infty}^th_1(s)u_4(t-s)ds,\\
\dot u_4(t)=b_{42}\int_{-\infty}^th_2(s)u_2(t-s)ds+a_{44}u_4(t),
\end{array}
\end{equation} where
$a_{11}=-a_3$, $b_{14}=-\displaystyle\frac{a_1}{(a_2+x_{40})^2}$, $a_{21}=\displaystyle\frac{b_1}{b_2+x_{30}x_{40}}$, $a_{22}=-b_3$, $a_{23}=-\displaystyle\frac{b_1x_{10}x_{40}}{(b_2+x_{30}x_{40})^2}$, $b_{24}=-\displaystyle\frac{b_1x_{10}x_{30}}{(b_2+x_{30}x_{40})^2}$, $a_{33}=-c_4+\displaystyle\frac{2c_1c_2x_{30}x_{40}^2}{(c_2+x_{30}^2x_{40}^2)^2}$,  $b_{34}=\displaystyle\frac{2c_1c_2x_{30}^2x_{40}}{(c_2+x_{30}^2x_{40}^2)^2}$, $b_{42}=d_1$, $a_{44}=-d_2$.

The characteristic equation of (\ref{14}) is given by:
\begin{equation}\label{16}
\lambda^4+r_{3}\lambda^3+r_{2}\lambda^2+r_{1}\lambda+r_{0}+(s_{2}\lambda^2+s_{1}\lambda+s_{0})\left(\int_{-\infty}^0h_1(-s)e^{\lambda s}ds\right)\left(\int_{-\infty}^0h_2(-s)e^{\lambda s}ds\right)=0,
\end{equation} where
$r_3=-a_{11}-a_{22}-a_{33}-a_{44}$, $r_2=a_{11}(a_{22}+a_{33}+a_{44})+a_{33}a_{44}+a_{22}(a_{33}+a_{44})$, $r_1=-a_{33}a_{44}(a_{11}+a_{22})-a_{11}a_{22}(a_{33}+a_{44})$, $r_0=a_{11}a_{22}a_{33}a_{44}$, $s_2=-b_{42}b_{24}$, $s_1=-b_{42}(a_{21}b_{14}+a_{23}b_{34}-b_{24}(a_{11}+a_{33}))$, $s_0=-b_{42}(-a_{23}b_{34}a_{11}-a_{21}b_{14}a_{33}+b_{24}a_{11}a_{33})$.

If there are no delays, the characteristic equation (\ref{16}) is given by:
\begin{equation}\label{160}
\lambda^4+r_3\lambda^3+(r_2+s_2)\lambda^2+(r_1+s_1)\lambda+r_0+s_0=0
\end{equation}
Using the Hurwitz criteria  for equation (\ref{160}) we obtain:

\begin{proposition}
In the non-delayed case, if inequalities
\begin{equation}
r_3>0,\quad r_1+s_1>0,\quad r_0+s_0>0,\quad r_3(r_2+s_2)(r_1+s_1)>(r_1+s_1)^2+r_3^2(r_0+s_0),
\end{equation}
hold, then the equilibrium point $E_0(x_{10}, x_{20}, x_{30}, x_{40})$ of system (\ref{sysHPA4}) is locally asymptotically stable.
\end{proposition}

In the presence of different types of time delays, we analyze three cases, as follows.

\noindent\textbf{Case 1. Dirac kernels:} $h_i(s)=\delta(s-\tau_i)$, $i=1,2$.

In this case, denoting $\tau=\tau_1+\tau_2$, the characteristic equation (\ref{16}) becomes:
\begin{equation}\label{18}
\lambda^4+r_{3}\lambda^3+r_{2}\lambda^2+r_{1}\lambda+r_{0}+(s_{2}\lambda^2+s_{1}\lambda+s_{0})e^{-\lambda \tau}=0.
\end{equation}
If $i\omega$, with $\omega>0$, is a root of (\ref{18}) then $\omega$ satisfies the following equation:
\begin{equation}\label{19}
\omega^4-ir_{3}\omega^3-r_{2}\omega^2+ir_{1}\omega+r_{0}+(s_{2}\omega^2-is_{1}\omega-s_{0})(\cos(\omega\tau)-i\sin(\omega\tau))=0.
\end{equation}
Separating the real and imaginary parts of (\ref{19}) we obtain the system:
\begin{equation}\label{20}
\left\{
\begin{array}{l}
\omega^4-r_{2}\omega^2+r_{0}=(-s_{2}\omega^2+s_{0})\cos(\omega\tau)+s_{1}\omega\sin(\omega\tau)\\
-r_{3}\omega^3+r_{1}\omega=(s_{2}\omega^2-s_{0})\sin(\omega\tau)+s_{1}\omega\cos(\omega\tau).
\end{array}
\right.
\end{equation}
From this system, it follows that $\omega$ satisfies the equation:
\begin{equation}\label{21}
\omega^8+m_6\omega^6+m_4\omega^4+m_2\omega^2+m_0=0,
\end{equation} where $m_6=r_{3}^2-2r_{2}$, $m_4=r_{2}^2+2r_{0}-2r_{3}r_{1}-r_{2}^2$, $m_2=r_{1}^2-2r_{2}r_{0}-s_{1}^2+2s_{0}s_{2}$, $m_0=r_{0}^2-s_0^2$.

Denoting $z=\omega^2$, eq. (\ref{21}) can be rewritten as:
\begin{equation}\label{23}
z^4+m_1z^3+m_2z^2+m_0z+m_4=0.
\end{equation}
Let $z_0$ denote the smallest positive real root of equation (\ref{23}) and $\omega_0=\sqrt{z_0}$. Then:
\begin{equation}\label{31}
\cos(\omega_0\tau)=\displaystyle\frac{\Delta_1}{\Delta},
\end{equation} where
\begin{equation}\label{32}
\begin{array}{l}
\Delta_1=s_{2}\omega_0^6+(r_{3}s_{1}-s_{2}r_{3}-s_{0})\omega_0^4+(r_{0}s_{2}+r_{3}s_{0}-r_{1}s_{1})\omega_0^2-r_{0}s_{0},\\
\Delta=s_{2}^2\omega_0^4+(s_{1}^2-2s_{0}s_{2})\omega_0^2+s_{0}^2.
\end{array}
\end{equation}
 Therefore,
\begin{equation}\label{33}
\tau_j=\displaystyle\frac{1}{\omega_0}\left[\arccos\left(\displaystyle\frac{\Delta_1}{\Delta}\right)+2j\pi\right], j=0,1,2,...
\end{equation}

\begin{proposition} Suppose that $z_0=\omega_0^2$, and $\displaystyle\frac{dh(z)}{dz}\not =0$, where
$$h(z)=z^4+m_6z^3+m_4z^2+m_2z+m_0.$$ The sign of $Re\left[\displaystyle\frac{d\lambda(\tau)}{d\tau}|_{\tau=\tau_j}\right]$ is the same as that of $\displaystyle\frac{dh(z)}{dz}$. Therefore, the following transversality condition holds:
$$Re\left[\displaystyle\frac{d\lambda(\tau)}{d\tau}|_{\tau=\tau_j}\right]\not=0,$$
which corresponds to the occurrence of a Hopf bifurcation in a neighborhood of the equilibrium point $E_0$.
\end{proposition}

\noindent\textbf{Case 2. Mixed kernels:} $h_1(s)=\delta(s-\tau_1)$, $\tau_1>0$, $h_2(s)=a_{20}e^{-a_{20}s}$, $a_{20}>0$.

In this case equation (\ref{16}) becomes:
\begin{equation}\label{181}
\lambda^5+\alpha_{4}\lambda^4+\alpha_{3}\lambda^3+\alpha_2\lambda^2+\alpha_{1}\lambda+\alpha_{0}+a_{20}(s_{2}\lambda^2+s_{1}\lambda+s_{0})e^{-\lambda \tau_1}=0,
\end{equation} where $\alpha_4=a_{20}+r_3$, $\alpha_3=a_{20}r_3+r_2$, $\alpha_2=a_{20}r_2+r_1$, $\alpha_1=a_{20}r_1+r_0$, $\alpha_0=a_{20}r_0$ and $s_2$, $s_1$, $s_0$ above.

If $i\omega$, with $\omega>0$ is a root of (\ref{181}) then $\omega$ satisfies the following equation:
\begin{equation}\label{191}
-i\omega^5+\alpha_4\omega^4-i\alpha_3\omega^3-\alpha_{2}\omega^2+i\alpha_{1}\omega+\alpha_{0}+a_{20}(-s_{2}\omega^2+is_{1}\omega+s_{0})(\cos(\omega\tau_1)-i\sin(\omega\tau_1))=0.
\end{equation}
Separating the real and imaginary parts of (\ref{191}) we obtain that $\omega$ satisfies the equation:
\begin{equation}\label{211}
\omega^{10}+q_8\omega^8+q_6\omega_6+q_4\omega^4+q_2\omega^2+q_0=0,
\end{equation} where $q_8=\alpha_1^2+2\alpha_3$, $q_6=\alpha_{3}^2-2\alpha_{1}-2\alpha_1\alpha_2$, $q_4=\alpha_{2}^2+2\alpha_{0}-2\alpha_{3}\alpha_{1}-a_{20}^2s_{2}^2$, $q_2=\alpha_{1}^2-2\alpha_{2}\alpha_{0}-\alpha_{1}^2+2a_{20}^2s_{0}s_{2}$, $q_0=\alpha_{0}^2-a_{20}^2s_0^2$.

Considering $z=\omega^2$, eq. (\ref{211}) can be rewritten as:
\begin{equation}\label{231}
z^5+q_8z^4+q_4z^2+m_2z+q_0=0.
\end{equation}
Let $z_0$ denote the smallest positive real root of equation (\ref{231}) and $\omega_0=\sqrt{z_0}$. Then:
\begin{equation}\label{311}
\cos(\omega_0\tau_1)=\displaystyle\frac{A_1}{a_{20}B_1},
\end{equation} where
\begin{equation}\label{321}
\begin{array}{l}
A_1=(\alpha_1\omega_0^4-\alpha_2\omega_0^2+\alpha_0)(s_2\omega_0^2-s_0)+(\omega_0^5+\alpha_3\omega_0^3-\alpha_1\omega_0)s_1\omega_0,\\
B_1=(s_1\omega_0-s_0)^2+(s_1\omega_0)^2.
\end{array}
\end{equation}
 Therefore,
\begin{equation}\label{331}
\tau_{1j}=\displaystyle\frac{1}{\omega_0}\left[arccos\left(\displaystyle\frac{A_1}{a_{20}B_1}\right)+2j\pi\right],  j=0,1,2,...
\end{equation}

\begin{proposition} Suppose that $z_0=\omega^2_0$,  and $\displaystyle\frac{dh(z)}{dz}\not =0$, where
$$h(z)=z^5+q_8z^4+q_4z^2+q_2z+q_0.$$ The sign of $Re\left[\displaystyle\frac{d\lambda(\tau)}{d\tau}|_{\tau=\tau_{1j}}\right]$ is the same as that of $\displaystyle\frac{dh(z)}{dz}$. Therefore, the following transversality condition holds:
$$Re\left[\displaystyle\frac{d\lambda(\tau)}{d\tau}|_{\tau=\tau_{1j}}\right]\not=0,$$
which corresponds to the occurrence of a Hopf bifurcation in a neighborhood of the equilibrium point $E_0$.
\end{proposition}

\noindent\textbf{Case 3. Weak gamma kernels:} $h_i(s)=ae^{-as}$, $a>0$, $i=1,2$.

The characteristic equation becomes:
\begin{equation}\label{451}
\lambda^6+\beta_{5}\lambda^5+\beta_{4}\lambda^4+\beta_{3}\lambda^3+\beta_{2}\lambda^2+\beta_{1}\lambda+\beta_0=0,
\end{equation}
where
$\beta_5=r_3+2a$, $\beta_4=2r_3a+r_2$, $\beta_3=2r_2a+r_1+a^2$, $\beta_2=r_0+2r_1a+r_2a^2+s_2a^2$, $\beta_1=r_1a^2+s_1a^2+2r_0a$, $\beta_0=r_0a^2+s_0a^2$.
Denoting
$$
\begin{array}{l}
D_1(a)=\beta_5\beta_4-\beta_3,\\
D_2(a)=\beta_5\beta_4\beta_3+\beta_5\beta_1-\beta_3^2-\beta_2\beta_5,\\
D_3(a)=\beta_5(\beta_5\beta_3\beta_2+\beta_5\beta_4\beta_0+\beta_2\beta_1-\beta_3\beta_0-\beta_5\beta_2^2-\beta_1\beta_4^2)-(\beta_3^2\beta_2+\beta_1^2-\beta_5\beta_2\beta_1-\beta_4\beta_3\beta_1),\\
D_4(a)=\beta_1\beta_3-\beta_0
\left|\begin{array}{cccc}
\beta_5&1&0&0\\
\beta_3&\beta_4&\beta_5&0\\
\beta_1&\beta_2&\beta_3&\beta_5\\
0&\beta_0&\beta_1&\beta_3
\end{array}\right|, \\
D_5(a)=\beta_0D_4(a)\\
\end{array}
$$
we obtain the following:

\begin{proposition}
\begin{itemize}
\item[(i)] If the conditions $D_1(a)>0$, $D_2(a)>0$, $D_3(a)>0$, $D_4(a)>0$, $D_5(a)>0$ hold, for any $a> 0$, the equilibrium point $E_0$  is locally asymptotically stable;

\item[(ii)] If there exists $a_{0}>0$ so that $D_4(a_0)=0$ and $D_1(a_0)>0$, $D_2(a_0)>0$, $D_3(a_0)>0$ and $\displaystyle\frac{dD_4(a)}{da}|_{a=a_0}\not =0$, a Hopf bifurcation occurs at $E_0$ as $a$ passes through $a_0$.
\end{itemize}
\end{proposition}

\section{NUMERICAL SIMULATIONS}

For the numerical simulations, we consider the scaled parameter values used in \cite{Gupta_2007}:
$$a_1 = a_2 = 0.1,~~a_3 = 1,~~ b_1 = b_2 = 0.1,~~ b_3 = 10, ~~c_1 = 1,~~c_2 = 0.001,~~ c_3 = 0.05,~~c_4 = 0.9,~~d_1 = d_2 = 1.$$
For these values of the system parameters, three
positive equilibrium states coexist because of the homodimerization
of the GR with cortisol: one equilibrium state with a low GR concentration which is asymptotically stable for any choice of time delays, one equilibrium state with a medium GR concentration which is unstable for any choice of time delays and one equilibrium state with a high GR concentration whose stability depends on the choice of time delays. According to \cite{Gupta_2007}, the low GR concentration represents the normal state, and
high GR concentration reflects a dysregulated HPA axis resulting in persistently low cortisol levels.

In the following, we investigate the stability of the equilibrium point with high GR concentration:\\
$$E_0:~~\bar{x}_{10}=0.66013~(CRH),~~\bar{x}_{20}=0.0514~ (ACTH),~~ \bar{x}_{30}=0.5481 ~(GR),~~\bar{x}_{40}=0.0514~ (CORT).$$

In the case of discrete time-delays: $h_1(s)=\delta(s-\tau_1)$, $h_2(s)=\delta(s-\tau_2)$, with $\tau_1=25$ min, $\tau_2=\tau-\tau_1$ min, we compute the critical value $\tau^\star=32.8043$ min, according to Proposition 3. Figure 2 displays the trajectories of system (\ref{sysHPA4}) for $\tau=\tau_1+\tau_2=31$ min and $\tau=\tau_1+\tau_2=33$ min, respectively. When $\tau=31$ min (below the Hopf bifurcation value), we observe that the trajectories of the system converge to the asymptotically stable equilibrium state $E_0$. On the other hand,  when $\tau=33$ min (above the Hopf bifurcation value), the trajectories of the system converge to the asymptotically stable limit cycle which appears in a neighborhood of $E_0$ due to the supercritical Hopf bifurcation.

\begin{figure}[htbp]
\centering
\begin{tabular}{cc}
\includegraphics[width=0.49\textwidth ]{fig_dirac1.pdf} &
\includegraphics[width=0.49\textwidth ]{fig_dirac2.pdf}\\
\end{tabular}
\caption{Trajectories of system (\ref{sysHPA4}) with discrete time-delays $\tau_1=25$ min and $\tau_2=6$ min (left) and $\tau_2=8$ min (right), considering an initial condition in a small neighborhood of $E_0$. }
\end{figure}

In the case of weak gamma kernels: $h_1(s)=h_2(s)=ae^{-as}$, with $a=\tau^{-1}$, the equilibrium state $E_0$ is asymptotically stable, for any $a>0$. Figure 3 shows the trajectories of system (\ref{sysHPA4}) for $\tau=50$ min, where the trajectories of the system converge to the asymptotically stable equilibrium state $E_0$.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.49\textwidth ]{fig_weak.pdf}
\caption{Trajectories of system (\ref{sysHPA4}) with weak gamma kernels with $\tau=a^{-1}=50$ min, considering an initial condition in a small neighborhood of $E_0$. }
\end{figure}

For the fractional-order model (\ref{sysHPA4.frac}) with $q=0.8$, we consider the discrete time-delays: $h_1(s)=\delta(s-\tau_1)$, $h_2(s)=\delta(s-\tau_2)$, with $\tau_1=25$ min, $\tau_2=\tau-\tau_1$ min. Figure 4 displays the trajectories of system (\ref{sysHPA4.frac}) for $\tau=\tau_1+\tau_2=39$ min and $\tau=\tau_1+\tau_2=40$ min, respectively. When $\tau=39$ min (below the Hopf bifurcation value), we observe that the trajectories of the system converge to the asymptotically stable equilibrium state $E_0$. On the other hand,  when $\tau=40$ min (above the Hopf bifurcation value), the trajectories of the system converge to the asymptotically stable limit cycle which appears in a neighborhood of $E_0$ due to the supercritical Hopf bifurcation. Numerical simulations show that, compared to the integer-order model with discrete time-delays, as the fractional order decreases, the critical value for the Hopf bifurcation parameter $\tau=\tau_1+\tau_2$ increases.

\begin{figure}[htbp]
\centering
\begin{tabular}{cc}
\includegraphics[width=0.49\textwidth ]{fig_frac1.pdf} &
\includegraphics[width=0.49\textwidth ]{fig_frac2.pdf}\\
\end{tabular}
\caption{Trajectories of system (\ref{sysHPA4.frac}) with discrete time-delays $\tau_1=25$ min and $\tau_2=14$ min (left) and $\tau_2=15$ min (right), considering an initial condition in a small neighborhood of $E_0$. }
\end{figure}

\section{CONCLUSIONS}
In this paper, we have considered a four-dimensional mathematical model that describes the hypothalamus-pituitary-adrenal axis with the influence of the GR concentration. Due to the fact that the involved processes are not instantaneous, we have incorporated distributed delays, and we have also taken into account fractional-order derivatives for the modelling of memory properties. This approach to the modelling of the biological processes is more realistic because it takes into account the whole past history of the variables, capturing the vital mechanisms of the HPA system. Sufficient conditions for the local asymptotic stability of the equilibrium points have been obtained and a Hopf bifurcation analysis has been undertaken. Numerical simulations reflect the importance of the theoretical results. As a direction for future work, this model can be generalized by considering general feedback functions to account for the interactions within the HPA axis.

\section{ACKNOWLEDGMENTS}
This work was supported by grants of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, project no. PN-II-RU-TE-2014-4-0270 (E. Kaslik) and project no. PN-II-ID-PCE-2011-3-0198 (M. Neam\c{t}u).

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Pandemic resilience and government support are top priorities for airport sector
Willis Towers Watson and Airport Operators Association (AOA) partner on leading airport conference to focus on issues facing the industry.
LONDON, 12 November, 2020 –The AOA Annual conference held in partnership with Willis Towers Watson (NASDAQ: WLTW), a leading global advisory, broking and solutions company, provided the aviation industry with a timely forum to present their strong and unified voice in the current challenging times.
With high profile speakers such as the Secretary of State for Transport, The Rt Hon Grant Shapps MP and Shadow Transport Minister, Jim McMahon MP, alongside industry leaders, including CEOs from a wide number of airports, the conference focused on the aviation sector and UK government's response to COVID; the sector's role in powering the UK economy; whilst the industry commits to delivering a sustainable aviation sector for a net zero world.
With airports in the UK facing an approximate £83m loss per week and not expected to fully recover until 2024/25, the conference highlighted the urgent need for a customised government strategy to support the industry's survival post-COVID, alongside the sector's opportunity to build back better and greener, as the UK's aviation industry pioneers the path to decarbonisation.
Our ongoing partnership with the AOA, as well as our growing Airport Risk Community ensures we can provide a collaborative and critical business platform to discuss the current and emerging risks."
Karen Larbey,
Director of Strategy and Planning, Transportation Industry, Willis Towers Watson
Karen Larbey, Director of Strategy and Planning, Transportation Industry, Willis Towers Watson, said "We were delighted to partner with the AOA to deliver their annual conference. In such a challenging business environment, it is essential to work together in a spirit of true collaboration, across the aviation ecosystem. Our Airport Risk Community brings together airports and industry stakeholders to discuss how best to tackle the major risks such as the current COVID-19 pandemic and climate risk, which are having a significant impact on airport resilience. Our ongoing partnership with the AOA, as well as our growing Airport Risk Community ensures we can provide a collaborative and critical business platform to discuss the current and emerging risks that threaten the aviation industry's future growth."
Karen Dee, Chief Executive, Airport Operators Association, said "2020 has been an enormously challenging year for UK airports: passenger numbers suffered a dramatic decline because of lockdown and then quarantine measures and, of course, revenues followed suit. In such circumstances AOA felt it was essential to bring the sector together both to share experiences and to plan a pathway to recovery. We were delighted that, with the support of our Corporate Partner, Willis Towers Watson, we were able to provide such a great line up of speakers and reach so many of our members. We look forward to continuing this important partnership."
The event was attended by well over 500 attendees made up from the Willis Towers Watson Airport Risk Community as well as members of the Airport Operators Association and is part of Willis Towers Watson's ongoing strategy to bring global connectivity to the airport sector.
About Willis Towers Watson
Willis Towers Watson (NASDAQ: WLTW) is a leading global advisory, broking and solutions company that helps clients around the world turn risk into a path for growth. With roots dating to 1828, Willis Towers Watson has 45,000 employees serving more than 140 countries and markets. We design and deliver solutions that manage risk, optimize benefits, cultivate talent, and expand the power of capital to protect and strengthen institutions and individuals. Our unique perspective allows us to see the critical intersections between talent, assets and ideas — the dynamic formula that drives business performance. Together, we unlock potential.
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Whitaker Studio
The Joshua Tree Residence
Need somewhere to live? If you happen to have a few Shipping Containers, no problem, contact https://www.whitakerstudio.co.uk/ and they can create something really cool. The one featured in the link below is called the Joshua Tree Residence and is something quite extraordinary. My favourite is the Hechingen Studio ... but then again black always was my favourite tonal value...
The Hechingen Studio - https://vimeo.com/168088526
The Hechingen Studio
The Frank Lloyd Wright Foundation
The Frank Lloyd Wright Foundation is a must visit site and place for fans of his work, The foundation is in their own words dedicated to "preserving Taliesin and Taliesin West for future generations, and inspiring society through an understanding and experience of Frank Lloyd Wright's ideas, architecture, and design."
On a personal note, I've always admired the work of this modern renaissance man whose work has influenced many. HIs story is an interesting and sometimes intriguing read, filled with great achievements, great art and great tragedy...
http://franklloydwright.org/
Fallingwater - Sketch by Frank Lloyd Wright
Fallingwater in Summer - Courtesy of the Western Pennsylvania Conservancy
Morris House - Unbuilt - Sketch by Frank Lloyd Wright
Ellen Jewett - Natural History Surrealist Sculptures
Ellen Jewett is a talented sculptor with a flair for the beautiful. Working from her Canadian studio, she sculpts creatures which are a gorgeous combination of flora and fauna and a feast for the eyes. Ellen's sculptures are handmade and created from materials which avoid toxic components. They are made of clay set over a light metal armature. Painted in acrylic, mineral and oil pigments with glass eyes inserted for realism, some are quite beautiful, whilst others are otherworldly but not quite nightmarish.
See more of her work at ellenjewettsculpture.com | DeviantArt | Etsy
Hello all, welcome to Gadgets, Geeks and Gizmos; a blog about really cool and wonderful stuff. It is also about the people who make this stuff. Here, I and other contributors will post links, images and stories which feature the weird, wonderful and crazy stuff which geeks and gadgeteers simply love.
I trust this will become a place where folk come to discover and share in the things which make me feel good, or sometimes just simply make me stop and appreciate life.
I trust you'll enjoy the experience and please feel free to share anything you think should be part of the journey.


Good airflow and sunlight penetration help "Granny Smith" trees produce numerous apples.
Homegrown "Granny Smith" apples from your own fruit tree (Malus x domestica "Granny Smith") provide years of juicy treats if properly maintained. Although fertilizing, soil amendments and watering should be the main strategies for cultivating productive "Granny Smith" trees, the spacing between the trees for a home orchard must be considered so each one can grow and produce fruit with vigor.
Growing to at least 20 feet, standard size "Granny Smith" trees are the traditional plants that likely come to mind when most people envision a home orchard. However, planting multiple trees in your yard requires a minimum of 30 feet between each plant. Their spreading canopies intertwine and cause shading problems for lower branches if they're planted close together, and your fruiting prospects decline as the shade grows deeper. Large spaces between the trees allows light penetration to practically all branches for optimum fruit growth.
Nurseries sell smaller apple trees created by controlling the rootstock height for almost every cultivar. "Granny Smith" apple trees are available in semi-dwarf varieties that only grow to a 15-foot height. The spacing for these trees is significantly smaller compared with the standard size trees -- only 18 feet of space between each apple tree is required. Not only is light penetration at its peak with this spacing, air circulation within the limbs is perfect for good leaf transpiration. Water evaporation through the leaves helps the tree cultivate its fruit and foliage growth for a healthy "Granny Smith" tree.
Perfect for small yards, the dwarf "Granny Smith" apple tree only grows to 10 feet. Spacing is directly related to this shorter tree height, and only 8 feet is needed between each tree for peak growth and health. Structural shading, however, is a consideration not applicable to the larger trees. When you decide on a planting location for your orchard, observe the surrounding buildings, such as your home or a detached garage. During the fall, winter and spring months, the sun's angle may create a largely shaded area across a portion of the garden. Your fruit trees must not be trapped in these shady areas or the fruit quantity and quality will suffer.
The open space between the trees may tempt you to plant grass or other ground covers. However, you should leave the area below the tree canopies free from manicured ground cover. Your "Granny Smith" apple trees have feeder roots that spread horizontally out from the trunk in search of water and nutrients. Adding grass on top of the roots creates an instant competition for energy supplies. Mulch the trees' bases with organic or inorganic materials, such as wood chips or landscaping rocks, to retain a healthy soil structure.
Rodriguez, Amy. "How Far Apart to Plant Granny Smith Trees?" Home Guides | SF Gate, http://homeguides.sfgate.com/far-apart-plant-granny-smith-trees-46495.html. Accessed 21 April 2019.


Lay the bacon strips on a cutting board and place a piece of tuna in the center of each; season with salt and pepper. Fold the bacon around the tuna and secure with toothpicks.
In a large nonstick skillet, heat 1 tablespoon of the olive oil until shimmering. Add the tuna and cook over moderately high heat, turning once, until the bacon is crisp and the tuna is still pink inside, about 6 minutes.
Meanwhile, in a medium bowl, whisk the remaining 2 tablespoons of olive oil with the vinegar; season with salt and pepper. Toss in the frisée and avocados and transfer to plates.
Remove the toothpicks from the tuna and cut each piece in half. Arrange the tuna over the frisée and serve right away, drizzling any remaining dressing left in the bowl over the fish.


text:
Writer Sings the Blues
Writer doldrums are usually transient and can serve as story fodder if you know how to manage them. Terri Coduri Viani shares inspirational tips from her writing tribe on how to overcome your writer blues.
Terri Coduri Viani
"I don't know what makes a writer, but it probably isn't happiness."
Ouch. Stinging words from William Styron snap the writer's psyche like the business end of a rat-tailed towel. We are not, as he said, known for being a bunch of "happy chuckleheads." But Styron also pointed out that this pervasive melancholy - a mood Paul McCartney called "an important color in writing" - is what makes us good at what we do. Empathy, understanding, and imagination open us to the world; they also leave us vulnerable to its too-rough edges. Add to those showbiz vicissitudes and social media posts that make us believe everyone but us has a three-picture deal, and we have a powerful prescription for a rising case of the writer doldrums. Public Service Announcement for anyone living in captivity with a writer: these doldrums are often characterized by Luddite levels of computer avoidance or Olympic face-plants onto the couch followed by endless scrolling through Shondaland. However, if you find your writer staring out the window eating handfuls of Captain Crunch from the box, there's no need to worry. This is known as "working."
On the good news front, writer doldrums are usually transient and can serve as story fodder if you know how to manage them. I asked my writing tribe how they deal with their writer doldrums, and here's what they said:
Music: Writer/producer Diana Lanham says music recently brought her out of a month's long case of the writer doldrums. "While listening to music for a future shoot, I heard a song that completely inspired me. And just like that, I got my writing mojo back. In a week, I finished a complete short screenplay." So put on your favorite artist or find a new one. Whichever you chose, blast it. Dancing optional.
Get Out: Tug on those trainers and go for a walk. Judy Bloom said a good writer is always a people watcher, so get out of your own head and notice the world around you.
Talk to Friends: Our first instinct is to seek out writer pals for a little commiserating but approach this with caution. Two writers commiserating can often deepen the blues until both of you are crying into your copies of Save the Cat. Find non-writer friends with a different perspective who can help you see the forest for the trees.
Help the Writing Community: Offer notes on a script or shout out someone's good news. "I'm a big believer in what you put out in the world comes back to you," says screenwriter Guy Crawford. "When someone posts they got a manager, a contest placement, a general meeting or anything like that, I feel joy for them. I try to share [their good news] and by doing so remind myself everyone may be trying to get to the same place, but the path is different. By championing other writers I'm fueling my own soul at the same time."
[Creativity in the Time of Chaos]
If your writer blues are entrenched, you may need to go deeper than walks and Twitter shoutouts. An extended social media break might be the thing or trying a different creative art. Draw or knit or bake (I'm a fiend for cupcakes. DM for address). And - important! - remember your sense of fun and play. Into The Script blogger, life coach, and script consultant Olivia Brennan offers this advice:
"Creating is an extension of ourselves. When we're burnt out, stuck in a never-ending pit of low self-esteem, rejection - maybe all of the above, that's when we know we haven't been prioritizing ourselves as human beings. As Jurassic Park taught us, life finds a way, and sometimes, it's going to make creating a bit of a challenge. What can you do in the next moment that will make you feel better and make the process feel more comfortable? You have to make time to play and not make it all about the end result."
[Six Things Writers Can Do To Manage Fear and Envy]
Most of all, give yourself time and grace to work through those doldrums without feeling guilty or ashamed. Writer blues have nothing to do with how much you love writing or your dedication to the craft. They're just another part of this funny old thing we call the writing life.
Learn more about the craft and business of screenwriting from our Script University courses!
writing inspirationScreenwriting
Terri Coduri Viani got her screenwriting start on Disney/ABC's hit show, Brand Spanking New Doug. After Disney, she freelanced in New York City before moving to New England to write for The Westerly (RI) Sun and The Stonebridge Press rural newspaper group. Her scripts have been finalists in both the New England Film Fellowship Contest and the PAGE International Screenwriting Awards, as well as placing on The Bitch List 2020, and at Stowe Story Labs and the Austin Film Festival. She is an associate member of the WGA, West, and a Script Magazine contributing writer. In her childhood, she lived and traveled all over the world including Saudi Arabia and the Soviet Union, and spent her high school years at an all-girls boarding school in the British countryside. She currently resides in Connecticut with one husband and three cats and credits her around-the-world upbringing for her love of offbeat worlds and characters as well as her deep understanding of the human desire for a place to call home. Instagram and Twitter: @tcviani
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Hello Coffee/Cocoa/Tea Crafty Friends… Welcome to the Coffee Loving Cardmakers and Little Acres Creations Collaboration Blog Hop!
Today both design team is sharing their coffee/cocoa/tea themed projects showcasing the new stamp, Cafe Dreamers stamp set from Little Acres Creations. And I have 2 cards to share with you today.
My first card is a mixed media card. I created the night sky background with Gelatos. I scribble the shades of blues and black Gelatos on a watercolor paper and blended them with baby wipe. Then, I added some white acrylic paint with fan brush.
I stamped the sentiment with Versafine Clair Nocturne and Mini MISTI. And I dry it with craft heater because this is a pigment ink that dries slowly. With Mini MISTI, I can arrange the 2 sentiments on the card and I bend the top shaped like an arch.
I added the finished background panel on a card base with dries-clear adhesive glue.
I stamped mouse sitting on the cup image twice, one I stamped on a green patteren paper and one I stamped on a white cardstock with Versafine Clair Nocturne. I dried them with craft heater so I can add colors immediately.
I fussy cut the cup and cut off the mouse then I added some black Gelato and blend it with baby wipe. For the mouse, I colored it with Grey watercolor pencil, and pull the colors with watercolor brush, then I fussy cut the mouse. I added the mouse on the cup with dries-clear adhesive glue.
I added the cup on the card with 3D adhesive. And I added some clear star sequins and more white stars that I drew with White UniBall Gel Pen.
On my second card, I tried the no-line coloring technique. It is a challenge for me. I stamped the image on a white cardstock with Antique Linen Distress Ink using Mini MISTI.
I colored the image with Prismacolor Premier Colored Pencils and Prismacolor Colorless Blender Pencil. I added some shadow at the bottom of the cup with Watercolor pencils and watercolor brush. And then I cut it with one of the Fancy Frame Dies – Craftin Desert Divas.
I stamped the sentiment on a white cardstock with Versafine Clair Cheerful and trimmed it with paper trimmer.
I added the flower patterned paper on the card base as the background, and then I added the polkadots and brown stripe paper strips on the card with dries-clear adhesive glue.
I wrapped some natural twine ribbon on the colored panel and added on the card with 3D foam tape, and then I added the sentiment also with the 3D foam tape.
Thank you so much for stopping by my blog today! I hope you all enjoy the blog hop and the projects. Have a fabulous day!
Pingback: Coffee Loving Cardmakers + Little Acres Creations Blog Hop! | Coffee Loving Cardmakers!
Oh Helen, these are FABulous!
Such pretty cards! Both are completely different, and equally beautiful!
So dreamy! Love both cards, Helen!
Hi Sweet One! Love the background on your first card and the second is just sweet!
Wonderful! These cards are just beautiful.
Great cards Helen!! The sky on the first one is stunning, and the second so bright and pretty!!
Such gorgeous cards! I love the gradient of blues for the sky! So deelish!
WOW – Helen! Both cards are gorgeous!!
Great cards, Helen! I love the watercolor background with the dark sky and stars. The second card is very sweet!
wowza! two completely different cards and both are beautiful! fantastic job!
LOVE both of your creations!! That nighttime sky you created with the Gelatos! I haven't tried those yet… I think I must! Gorgeous.. and your no line coloring! So beautiful! And love the mix of feminine and beautiful papers!
Pretty cards! I especially like the swirling galaxy you created!
Loving the sentiments and both your cards are so different…the starry nite time background is gorgeous, and love the soft colors in the other card. Fun and adorable cards.
Adorable cards and I love the rose background. So pretty and these mice are adorable.
Oh my my all tome favorite is the one with the flowers and the pinks. I love pink and Spring so this one is my fav. Both are precious but the pink one has my heart. Beautiful cards Helen.
This is adorable! You are so talented, and I always enjoy seeing your amazing creativity. Your art makes me happy, happy, happy!
Thanks so much for sharing with us. It's always so nice to have you play along with us.
http://www.karen-mycuprunnethover.blogspot.com – I hope you will stop by to visit me!
Both cards are wonderful. So glad you shared with us at Die Cut Divas.


This house / villa (property) of 224 m² (about 2408 ft²), built in 1920, on 3 levels, with a land size of 2825 m² (about 0,70 acres) comprises 12 rooms. It is provided with a parking lot. Heating : individual electric.


Updated at 4:30 p.m. Wednesday: Revised to include information about the Bell County case.
Six cases of the measles have been confirmed in Texas in recent days, health officials say.
The Texas Department of State Health Services confirmed a case in Bell County on Tuesday, a day after five cases were announced — three in Harris County, one in Galveston County and one in Montgomery County. Five of those involve children.
The three Harris County patients are two boys younger than 2 and a woman who is between 25 and 35 years old. The cases are the first in Harris County this year. The last was in Houston in 2018, according to the county's health department.
In Galveston County, the confirmed case is a boy between 1 and 2 years old who was tested Jan. 28. Health officials say the case is part of the cluster in the region.
The Montgomery County case is a girl, the Houston Chronicle reported.
The Bell County case involves a child who is not school-aged and is too young to be vaccinated, according to the county health department.
Officials have not released the identities of any of the patients.
"We know there's a link between two of the Houston-area cases, and public health is investigating to determine whether the others are linked or whether they occurred independently," Texas Department of State Health Services spokesman Chris Van Deusen said.
Two of the children had recently been immunized and "likely were exposed to measles before receiving the vaccine or before the body could mount a full immune response," Van Deusen said.
The Chronicle reported that four of the children had gotten the first of the two vaccines, though the state health department could not confirm that. County officials were working to confirm that the woman had been vaccinated.
The Centers for Disease Control and Prevention recommends children get two doses of the measles, mumps and rubella vaccine — one between 12 and 15 months and the second between ages 4 and 6 — to be fully protected against measles.
"While this is a relatively small number of cases, it's a good time to make sure you and your children have gotten the recommended two doses of measles vaccine," Van Deusen said.
According to the CDC, two doses of the vaccine are 97 percent effective against the measles, while one dose is 93 percent effective — and vaccinated people who still get the disease tend to have a milder illness.
The agency recommends that adults with no evidence of immunity get at least one dose of the vaccine. Doctors can test for immunity, but the CDC says that may cost more and require additional doctor's visits, and that there's no harm in getting another dose of the vaccine.
Which North Texas cities were named among anti-vaccine 'hotspots' in national study?
There were nine confirmed cases of measles in Texas last year.
Across the country, nine other states reported cases of the measles in January, according to the CDC. In Washington, 50 cases have been confirmed this year.
Outbreaks have also been reported in New York state and New York City, where 64 cases have been confirmed in the Orthodox Jewish community in Brooklyn since October.
Measles can spread when travelers bring measles into the U.S. It is further spread in communities where groups of people are unvaccinated, according to the CDC.
It typically takes about two weeks from the time of exposure to the virus for a rash to develop, but it can take up to three weeks. People are contagious from four days before they get the rash to four days after it appears and should seek medical treatment and isolate themselves at home.
The rash begins on the face as flat, red spots and spreads down the neck and trunk to the rest of the body.
Other symptoms include a fever higher than 101 degrees, cough, runny nose and red, watery eyes.
Anyone with these symptoms who thinks they may have been exposed to the virus should call their health provider in advance of a visit so precautions can be taken to prevent exposure to staff and other patients.
Updated at 12:26 p.m. and 1:02 p.m. Feb. 7 to revise the headline to summarize the total number of measles cases involved and to include information in the article about ensuring immunity in adults, as well as testing for immunity.


In a sluice box these man made crevices, or riffles as they called in a sluice, trap the gold so it can be recovered by the prospector. Building a sluice box: Building a sluice box is something that gold miners have done for many years.
Gold Creek Rifles - 108 S Fork Gold Creek Rd, Carlton, Washington 98814 - Rated 4.9 based on 17 Reviews "The best there is! ... Gun Store · Outdoor & Sporting Goods Company · Gun Range. Price Range $ Hours 8:30 AM - 6:00 PM. Open Now. People. 382 likes. 1 visit. ... Greg taught me everything I know about building rifles. April 28, 2018.
Rock Gold Separation Process,Gold Shaking Table In Hard Rock Gold Our factory has accumulated rich experience in the mineral processing equipment . is big channel support structure, table deck has 38 Riffles available. Get Price Gold Pan Plastic. Contact Supplier.
· Riffles Gold Washing Gold Pan,Top-quality Plastic Gold Panning Kit . Gold Extracting. Material: plastic. ... River Sand and sea sand from Malaysia for Export .. low price per ton black silica sand quartz granules for building sand .. Gold Supplier. Quotation More. ... Tianjin Yandong Mining Co., Ltd. Add to Favorites. Sand for .
That is a special small section of riffles which catch most of the gold near the head of the sluice. ... If this is the case with your gold, after the final dry cleanup procedure is completed, your gold is ready to be weighed and sold or displayed or stored away in a safe place.
A box is running right when you fill the front with gravel (and hopefully some gold). When the box has finished running the gravel down onto the riffle area of the box, the space fills between the riffles, you can start to look for the last of the gravels to leave the front of the box.
building gold riffles ksf co in - zpvsp. Building A Gold Dry Washer jdpolymers Building A Gold Dry Washer. 190 Dry Washer The Dustless Dry Washer applied to the drywasher fan but not to the riffles for more shake, and less gold blown.
Building a sluice box for gold prospecting is a fairly simple project, and is a fun way to spend the winter in preparation for the mining season. How to Use a Sluice for Gold - wikiHow Rinse the material out of your sluice into your bucket using lots of water.
Home Gunsmithing Building a Custom Bolt Action .223 Rifle with a Blackheart International Action Building a Custom Bolt Action .223 Rifle with a Blackheart International Action. ... The Blackheart International action has the following specifications: ... velocity of Federal 69 grain Gold Medal was 2920 fps and Asym 75 was 2887 fps.
· I can see myself building one of these and strapping it on my fourwheeler when I go on long trips up north around Pinochle and Eureka. ... Homemade Sluice Box ... You need this ___/__/__/__/ Gold will drop behind the riffles and stick.


text:
Q: Frequency of characters in text A method to return the frequencies of repeated characters

*

*The answer is always the number of all characters in text, not repeated characters! Can I know how to edit it?
public static int freq(String in ) {

  int frequency = 0;
  char[] alphabet = "abcdefghijklmnopqrstuvwxyz".toCharArray();
  for (int j = 0; j < 25; j++) {

    for (int i = 0; i < in .length(); i++) {
      if (alphabet[j] == in .charAt(i)) {
        ++frequency;
      }
    }
  }

  return frequency;

}

redpajama_set_name: RedPajamaStackExchange


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text:
Q: Skew-symmetric matrix mapping vector to orthogonal vector I am trying to prove that if $-a^2,-b^2$ are distinct non-zero eigenvalues of $M^2$ where $M$ is a real square skew-symmetric matrix, then there exist orthogonal vectors $\mathbf{v},\mathbf{v}',\mathbf{w},\mathbf{w}'$ such that:
$$M\mathbf{v}=a\mathbf{v}'\qquad M\mathbf{w}=b\mathbf{w}'$$
$$M\mathbf{v}'=-a\mathbf{v}\qquad M\mathbf{w}'=-b\mathbf{w}$$
My ideas:
$M$ has purely imaginary eigenvalues. Let $\mathbf{u}$ be an eigenvector of $M$ and let $M\mathbf{u}=ia\mathbf{u}$ for $a$ real. Then $M^2\mathbf{u}=-a^2\mathbf{u}$. In the same direction, $M\mathbf{r}=ib\mathbf{r}$ gives $M^2\mathbf{r}=-b^2\mathbf{r}$. Since $M^2$ is symmetric we know that $\mathbf{u},\mathbf{r}$ are orthogonal.  So I thought setting $\mathbf{v}=\mathbf{u},\;\mathbf{v}'=i\mathbf{u},\;\mathbf{w}=\mathbf{r},\;\mathbf{w}'=i\mathbf{r}$ would work (this satisfies the conditions above), but the problem is that $\mathbf{v},\mathbf{v}'$ are not orthogonal (and $\mathbf{w},\mathbf{w}'$ are not either). Am I on the right track at least?

A: I think that you should start from the eigenvectors of $M^2$ to be sure you find real vectors (the question implicitly asks for real things). So take $v$ and $w$ as eigenvectors of $M^2$ with respective eigenvalues $-a^2,-b^2$ and take $v'$ and $w'$ given by the condition
$$M\mathbf{v}=a\mathbf{v}'\qquad M\mathbf{w}=b\mathbf{w}'
$$
Then you can prove that $v$ and $v'$ are orthogonal. You should then also prove that $v$ and $w'$ are orthogonal which comes from the fact that also $v'$ and $w'$ turn out to be eigenvectors of $M^2$.


Students braved snow and below-freezing temperatures to watch the Irish battle the Brigham Young University Cougars on Saturday in the last home football game of the season.
Senior Laura Stangler said her last student game-day experience was very bittersweet.
The traditional senior marshmallow fight occurred during halftime, Stangler said. Most of the marshmallows stayed in the stands, but a few fell on the field.
Stangler said she appreciated the special seniors-only traditions after the game, as well.
Emotions in the senior section were "all over the place," Stangler said.
Senior Patrick Schmitz said he felt the game was a great bonding experience for the senior class.
Because it was their last game as students, Schmitz said he and his friends tried to participate in as many game-day traditions as possible.
Freshman Kaylee Correa said Brigham Young fans did not have a noticeable presence on campus.
Watching the seniors' marshmallow fight was enjoyable, Correa said.
Correa said the snow and cold greatly affected her game-day experience.
Contact Catherine Owers at [email protected].


Open House. Open House on Sunday, June 28, 2015 1:00 pm - 4:00 pm Fabulous executive townhome in North Delta at Capella in Sunstone!! Super location with a great yard!! Don't miss this one.
Please visit our Open House at 21 10595 DELSOM CRES in Delta.
Open House on Sunday, June 28, 2015 1:00 pm - 4:00 pm Fabulous executive townhome in North Delta at Capella in Sunstone!! Super location with a great yard!! Don't miss this one.
CAPELLA at SUNSTONE, one of Polygon's best colections of executive townhouse residences in North Delta. The exclusive unit offers 2,200 sq.ft., main floor offers open-plan with warm laminate flooring, gourmet kitchen with granite countertops, stainless steel appliances, nook area and family room, also offered are living and dining rooms. Upstairs you'll find 3 good size bedrooms highlighted by the master bedroom with huge walk-in closet. Large private backyard invites outdoor entertaining. Basement area has large entertainment size flex room, double garage. Luxury clubhouse offers swimming pool, exercise room, gym. Even your own lake. This is a must see. Book your showing today, give us a call.
I have listed a new property at 21 10595 DELSOM CRES in Delta.


text:
Training: the Answer to Every Siege Against One's Professio...
Training: the Answer to Every Siege Against One's Profession
Theory by itself can only go so far. In order to grow professionally, people need to practice and train relentlessly. This is especially crucial for a world that is constantly evolving and the skill sets needed in the labour market are changing by the day, writes Tadesse Tsegaye (seetadnow@gmail.com), a polyglot with experience in multicultural-cum-institutional settings in resources management.
The Greek mathematician Euclid's Elements, written in the third century BC, was a collection of theorems and problems that formed the basis for geometry. Yet, much of it owes a great debt to the work of earlier mathematicians.
Did he copy their work?
No, but he might have received his training from the pupils of Plato in Athens. A great believer in constantly training oneself to reach mastery, Euclid is said to have told a ruler that "there is no royal road to geometry" when asked if there was not an easier way to learn it.
And yet, it is this crucial key to professionalism that higher learning institutions do not emphasise. They assume that their students can imagine a practical application of every theory they learn in class and use this knowledge to compete in the job market. Unfortunately, following college, it is routine work that welcomes many of us. Pieces of training were hard to come by and from the few available, some used to be wasted. Years ago, a friend told me how training opportunities for professional growth would be lapped up by the training manager himself, who never missed a chance to attend such events where some snacks are available.
Neither is it unheard of for heads of institutions in Ethiopia to send themselves abroad at every opportunity for pieces of training that would have served their subordinates better.
This all came to me as I watched a recent interview of a walking testimonial of the essence of training. He was an army Brigadier who had no idea what it meant to be an officer before he joined the army's officer-training establishment in Harar. After graduating, thanks to his merit, he was selected to join further training, which attaches great emphasis to physical endurance and self-discipline.
The man fares even better on the battlefield. He became one of Ethiopia's most admired army officers when, among others, he broke a six-month siege through a narrow pass. His unquenchable thirst for knowledge and eagerness to think outside the box have always been epitomised through his relentless push to train his army units.
Tesfaye Habtemariam (Br. Gen.) not only left a legacy on the battlefront, but he also contributed to the continuous growth of his men. As far as he was concerned, practice and constant training were needed to ensure the professionalisation of his unit and their success in their missions.
Institutions may provide employees with trainings, which is necessary to assist in achieving their mission and accomplishing their goals through developing a plan. It may include training needs assessment, an action plan showing goals, objectives, and methods by which the strategy can be realised. Hence, they may designate a recognised point of contact within the company to handle this and other training-related duties and responsibilities.
However, training is not a duty and responsibility to be left only to a specific section. It is as key as transforming oneself from a manager to a leader through continuous improvement and workers through attending trainings aimed at enhancing or increasing their work skills and abilities after a thorough identification of skills needed and those no longer necessary.
No doubt, it looks like we are facing a siege of our own given the day's challenges with advances in technology. As a leader, one is judged by the number of least effective workers reporting to oneself, which determines the fate of the institution. This does not need to be the case. But there is no "royal road" to mastering the skills of one's profession, and this is through relentless practise and training.
PUBLISHED ON Oct 02,2021	[ VOL 22 , NO 1118]
Tadesse Tsegaye (seetadnow@gmail.com), a polyglot with experience in multicultural-cum-institutional settings in resources management.
Fortune News | Mar 02,2019
Addis Welcomes Nation's Fifth Advocates' Training Centre
Verbatim | Mar 14,2020
"We need every drop of the Nile."
Training Aircraft Crashes, Kills Pilot
Commentaries | Jul 03,2021
As Ethiopia's Economy Opens Up, Law Firms No Longer Defile the Legal Profession
View From Arada | Oct 16,2021
For Every 'Aha,' Society Moves Forward
International Stories | Apr 16,2020
'Every scenario on the table' in China Virus Outbreak: WHO's Tedros
Gov't Invests in Standard Agency's Training Academy
Films Review | Mar 23,2019
How to Train Your Dragon, and Lose It
Japan to Finance Kaizen Training Centre
Fortune News | Aug 24,2019
Center Emerges to Train Leather Specialists


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Doctor Who Interactive Google Doodle Celebrates 50th Anniversary
Posted byLarry Fire November 23, 2013 Posted inGames, Television & Streaming, Web SiteTags:50th Anniversary, Doctor Who Interactive Google Doodle, Game, Television & Streaming
In honor of the 50th anniversary of Doctor Who, Google has created an interactive Google Doodle based on the series — a Whodle! — and launched it today on their home pages around the world.
The doodle serves as an interactive game where you play as each of the eleven doctors in a race against time against a Dalek. As the Doctor, you need to collect all the letters of "Google" and bring them back to the TARDIS, while the Dalek is after you. But don't worry, if you die, you'll just regenerate to the next incarnation of the Doctor, though before that you'll have a Dalek on you shouting its signature phrase, "Exterminate!". The interactive game includes authentic sound effects from Doctor Who, provided to the Google Doodle creators by the BBC.
As part of the 50th anniversary, The Day of the Doctor, which stars Matt Smith and Jenna Coleman and will see guest appearances by David Tennant, Billie Piper, John Hurt, and many more, airs on Saturday, November 23, 2013 at 7:50pm GMT on BBC One in the UK and at 2:50pm EST on BBC America in the U.S.
An Adventure In Space And Time will air on BBC America on Friday, November 22 at 9PM ET/PT, with Doctor Who: The Doctors Revisited – The Eleventh Doctor, a special featuring current doctor Matt Smith, airing on November 24, 2013 at 8pm ET/PT on BBC America, which will be doing a marathon that day of Smith's top 11 episodes as voted by the fans.
What's Your SuperHero Name?
The 50 Funniest Stand-Up Specials of All Time


What is a NATE-Certified HVAC Technician and Why Do You Need One?
When you need your heating or air conditioning repaired, if you're not familiar with the company, you're at the mercy of whoever's ad caught your eye. So you can hold your breath and hope they're amazing at their job, or you can choose someone with credentials to back up their claims.
NATE stands for North American Technical Excellence, and it ensures just that. They are the country's largest non-profit certification organization for HVAC technicians. So what's the big deal about this certification?
Today's HVAC systems are increasingly technologically sophisticated. The NATE certification tests are nationally recognized and developed and supported by all segments of the heating ventilation and air-conditioning industry, according to their website.
Proper installation and maintenance of your HVAC system – When someone is dealing with complex technology in today's HVAC systems, you want your tech to be the best in their field. This certification ensures you're getting the best of the best, with the most up-to-date training available.
Fewer warranty returns and callbacks – When it comes to the comfort, health benefits and safety your heating and cooling system provide, the last thing you want is a warranty return or a call back to fix something that wasn't done correctly the first time. NATE-certified techs do things correctly the first time around so that you don't have to worry about workmanship defects.
The most efficient service – NATE-certified techs have proven their knowledge and their commitment to their profession, so it's no wonder they provide the best customer service. They've worked hard to achieve this certification, so it's no wonder they're willing to go the extra mile for their customers.
Peace of mind for consumers – You wouldn't go see a doctor without an MD hanging on the wall. That piece of paper certifies that you're in good hands. This is the MD of our profession. This certification lets you rest easy knowing your investment in your HVAC system is in good hands.
Up-to-date knowledge and advice – Just like all the technology around us, HVAC systems are ever-evolving. NATE-certified techs get up-to-date education about this changing technology so they know the best available options to install in your home.
Peak efficiency for you system – Having a properly installed and maintained system can save you money on your utility bills because it's running at peak efficiency.
NATE has been certifying technicians for over 20 years. Back in 1997, there was a major issue in the HVAC business. HVAC manufacturers were receiving returns of equipment that weren't defective because it was improperly installed. This cost everyone money, from the manufacturers and companies to the consumers.
NATE was developed to help get the proper training to people in the field and ensure quality for consumers.
There are over 34,000 certified techs in North America and that number is growing all the time.
In a booming industry that projects major growth, it's important to have a gold standard for training and certification. According to the U.S. Bureau of Labor Statistics Occupational Outlook Handbook, the industry was projected to grow 15 percent by 2026.
All of our technicians at W.G. Speeks are NATE certified because quality matters to us! Contact us today to have our skilled technicians help you!


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Search underway for Polk County man accused of stabbing man on July 4
Posted: Jul 6, 2019 / 07:10 AM EDT / Updated: Jul 6, 2019 / 08:20 AM EDT
POLK COUNTY (WFLA) – The Polk County Sheriff's Office needs your help locating a man who is considered very dangerous.
24-year-old Rudy Gonzalez, Jr is accused of repeatedly stabbing a Lake Wales man on the July 4th holiday.
The victim was airlifted, and he is in critical but stable condition.
Gonzalez Jr. has a violent criminal history. In 2016, he was convicted on two separate cases of battery domestic violence, including battery on a pregnant woman.
Rudy Gonzalez Jr is 5'7", 150 lbs. If you have any information on his whereabouts, please contact the Polk County Sheriff's Office immediately at 863-678-4115 or 863-298-6200.
More Polk County Stories
by Staci Dasilva / Jul 18, 2019
POLK COUNTY, Fla. (WFLA) - The story of a Polk County man going from millionaire to murder victim will once again be told to a national audience.
This weekend, BET's show "Murder in the Thirst" will highlight the life and death of Abraham Shakespeare.
After emotional plea, Florida board approves mandate for CPR training for bus drivers
LAKELAND, Fla. (WFLA) - The Florida Board of Education voted unanimously Wednesday to require bus drivers and attendants to be certified in CPR and first aid, following an emotional plea from the parents of a teenager who died after a chaotic bus ride in Polk County.
"She was just a joy," said her mother, Denise Williams. "She could go into a room and smile and bring out the best in you. She was bigger than life."
Bicyclist killed after being struck by 2 cars in Lakeland
POLK COUNTY, Fla. (WFLA) - A bicyclist died Tuesday after he was struck by two vehicles in Lakeland, authorities said.
The Polk County Sheriff's Office said Mitchell Johnson, 35, of Lake Wales was riding his bike on the far right side of Galloway Road, heading north, when he was struck from behind by a 2008 Lincoln MKZ.


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Impulse noise, Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), mean filter, median filter, Improved progressive switching median filter (IPSMF).
Jayanta Das, Bhaswati Das, Jesmine Saikia and S.R.Nirmala, "Removal of Salt and Pepper Noise Using Selective Adaptive Median Filter", International Conference on Accessibility to Digital World (ICADW), Conference date 16-18 Dec. 2016, © IEEE.
Raghuram Kunsoth and Mantosh Biswas, "Modified Decision Based Median Filter for Impulse Noise Removal", International Conferecence on Wireless Communications, Signal Processing and Networking (WiSPNET), 2016.
Pei-Eng Ng and Kai-Kuang Ma, Senior Member, IEEE, "A Switching Median Filter With Boundary Discriminative Noise Detection for Extremely Corrupted Images", IEEE Transactions on image processing, vol.15, no. 6, June 2006.
Mr.N.KrishnaChaitanya and Mr.P.Sreenivasulu, "Removal of Salt and Pepper Noise Using Advanced Modified Decision Based Unsymmetric Trimmed Median Filter", International Conference on Electronics and Communication Systems (ICECS), 2014.
Archana Singh, Sanjana Yadav and Neeraj Singh, "Contrast Enhancement and Brightness Preservation using Global-local Image Enhancement Techniques", Fourth International Conference on Parallel, Distributed and Grid Computing (PDGC), 2016.
Zhou Wang and David Zhang, "Progressive Switching Median Filter for the Removal", IEEE Transactions on circuits and systems—II: Analog and digital signal processing, vol. 46, NO. 1, January 1999.
Soon Ting Boo, Haidi Ibrahim and Kenny Kal Vin Toh, "An Improved Progressive Switching Median Filter", International Conference on Future Computer and Communication, 2009.
S. Esakkirajan, T. Veerakumar, Adabala N. Subramanyam, and C. H. PremChand, "Removal of High Density Salt and Pepper Noise Through Modified Decision Based Unsymmetric Trimmed Median Filter", IEEE Signal Processing Letters, vol.18, no.5, May 2011.
Thomas A. Nodes and Neal C. Gallagher, "Median Filters: Some Modifications and Their Properties", IEEE Trans. Acoust., Speech and Signal Processing, vol. ASSP-30, pp.739-746, April 1987.
T. Loupas, W. N. Mcdicken, and P. L. Allan, "An Adaptive Weighted Median Filter for Speckle Suppression in Medical Ultrasonic Images", IEEE Transactions Circuit Systems, Vol. 36, No. 1, pp. 129-135, 1989.
Sung-Jea KO and Yong Hoon Lee, "Center Weighted Median Filters and Their Applications to Image Enhancement", IEEE Transactions on circuits and systems, vol.38, No. 9, pp. 984-993, 1991.
Shuqun Zhang and Mohammad A. Karim, "A New Impulse Detector for Switching Median Filters", IEEE Signal Process. Lett., vol.9, no.11, pp.360-363, Nov.2002.
K. S. Srinivasan and D. Ebenezer, "A New Fast and Efficient Decision-Based Algorithm for Removal of High-Density Impulse Noises", IEEE Signal Processing, Letter, vol.14, no.3, pp.189-192, March 2007.
Raymond H. Chan, Chung-Wa Ho, and Mila Nikolova, "Salt-and-Pepper Noise Removal by Median-type Noise Detectors and Detail-preserving Regularization", IEEE Transactions on Image Processing, vol.14, no. 10, pp.1479-1485, oct. 2005.
Akanksha C. Thawale, Ruhina Quazi, " A Review on Noise Removal Using Modified Global-Local Filters", International Journal of Scientific Research in Science and Technology(IJSRST), Print ISSN : 2395-6011, Online ISSN : 2395-602X, Volume 4, Issue 3, pp.110-116, January-February-2018.


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text:
Tom Hodgins: Beaufort County's Marine Patrol
Author: Craig Hysell
Nine years ago, Sergeant Tom Hodgins found himself standing before the Interview Board of the Beaufort County Sheriff's Office. When they asked Hodgins why he wanted to be a cop, the retired Navy man of 22 years asked if he could answer that question with a question of his own. "Go ahead," came the reply.
"What's your favorite color?" asked Hodgins.
"Yellow."
"Why is yellow your favorite color?" The Board didn't have an answer. "That's the same reason I wanted to be a cop," Hodgins says today. "I don't know why, I'm just attracted to it."
The Marine and Beach Patrol Unit of the Beaufort County Sheriff's Office is a fairly new addition to its police force. "I had no knowledge that there would eventually be a marine patrol position here," says Hodgins. However, at the request (and cost) of the Town of Hilton Head Island the Unit was created six years ago and Hodgins is the marine patrol's sole officer. He purveys an aura of stout common sense and matter-of-fact seafaring wisdom.
In what are basically modified bass boats, Hodgins has two vessels at his disposal for patrolling the myriad breadth of Beaufort County's waterways, including Dafuskie Island. By working closely with South Carolina's Department of Natural Resources (DNR) and the Coast Guard, Hodgins feels his Unit and DNR are able to accomplish the goals of any tax funded patrol force. "It works out real well. The public doesn't feel harassed but we're getting to check boats and make sure people have what they need to stay safe."
And that's what Hodgins is most adamant about: safety. His advocacy comes across as colloquial, more of a universal take on the nature of oceans and tidal creeks than obsessive, obtuse zealotry.
If you've ever seen what people look like after they've come in contact with an oyster bed—or felt a jagged oyster's burning slice yourself—you're going to tell people to remain cautious and aware. If you've ever pulled a lifeless, bloated body out of the water because they weren't wearing a life jacket, you're going to make sure people have the necessary flotation devices onboard. If you've ever tried to find a victim radioing for help who can't operate their GPS to relay a fixed position, you're going to recommend people take a boater safety course with DNR or the Coast Guard. (And learn how to read longitude and latitude markings…)
Water can be fun, but it is merciless. And when things go wrong, they go wrong in a hurry. Hodgins can tell you by experience that if you are ill-equipped or unprepared you will get hurt, or worse, you will die. If that sounds overly dramatic, ask yourself, what you would do if your boat suddenly began taking on water. Do you have friends or family onboard? Can they swim? Do they know how to put on a life jacket?
The next time you're safe in your house when that sudden, nasty thunderstorm comes up, imagine what it would be like on a boat with no help around. Do you know where your flares are? What would you do if your boat caught fire? Has the charge on your fire extinguisher expired? How would you call for help? In a world without street signs, do you know where you are on the water?
If you can begin to understand that the ocean, the tide and oyster beds demand respect, you can begin to respect Sergeant Hodgins perspective. It's not that people are defiant (for the most part), they're just unaware. "I probably write more warnings or citations for either insufficient or improper life jackets as well as fire extinguishers." But, "I give them one of two choices. You can come to court and show me a fire extinguisher and a receipt so I know you didn't borrow it from your buddy, and I'll tear the ticket up. If you see me before your court date, and you've solved the problem, wave me down and I'll tear the ticket up. That's as fair as I can be."
While Hodgins responds to any call or mission in Beaufort County, as well as the Atlantic when his boat can handle the waves, his main patrol is in the waters around Hilton Head Island. At a Public Safety Committee Regular Meeting on August 1, 2005, Lieutenant Toby McSwain reported the marine unit's quarterly statistics (meaning Hodgins' quarterly stats) to the Town of Hilton Head. Hodgins made 278 boat stops— those instances when he comes into contact with another boater, boards the boat and performs an inspection. He had 9 boater assist stops, went to 8 back-up calls involving South Carolina Wildlife and wrote 77 uniform traffic tickets—being very strict on no wake zones. (Idle speeds cut down significantly on property damage.) Hodgins stays busy.
And loves what he does for a living.
"There's nothing like the first thing in the morning, when the sun is just coming up, and you're on patrol in these marshes. Same thing at the end of the day. The sun's setting. It's nice, and quiet, and calm. You see dolphins topping the water…" Hodgins smiles and sighs his appreciation.
Later, he picks absently at the stern of his boat. It is resting on the trailer, getting ready for a day's work. The Beaufort County Marine Patrol Unit can beat the other agency's average response time to calls by 45 minutes, but Tom's voice is quiet. "I turn down an average of 16 calls a year. That's the worst, when somebody's in trouble and I can't help them. When the boat can't handle the weather or they're too far out in the ocean…that bothers me." It's the first time all day Hodgins spirit seems to dent. Sometimes those minutes he can't get to people turn into lifetimes.
Surfing pioneer, Tom Blake, once etched into a rock decades ago, "Nature = God". You've got to be aware out there. Safety first. That's as fair as it's going to get.
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