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Demographic information, psychological questionnaires, baseline expectation for pain, and thermal pain sensitivity measures were collected prior to random assignment of the studied intervention.

Quantitative sensory testing (QST) was performed using the Medoc Neurosensory Analyzer (TSA- 2001, Ramat Yishai, Israel) with hand- held peltier- element- based stimulator. Participants first underwent a practice session in order to familiarize themselves with the pain testing protocol. Participants then underwent the full QST following a previously established protocol to measure c- fiber mediated pain [ 43 , 44 ]. Briefly, c-fiber mediated pain was assessed on the plantar surface of the non- dominant foot using a train of ten consecutive heat pulses of less than one second duration at an inter- stimulus frequently of .33 Hz (temporal summation). The baseline temperature of each pulse was 35°C and temperature peaked at 51°C. Subjects were asked to rate their delayed (second) pain using a NRS. We used the same protocol to assess pain perception in the low back with the stimulator placed above the posterior superior iliac spine on the non- dominant side; however, in a previous pilot study, we found that subjects were unable to differentiate Aδ and c- fiber mediated pain in the low back [ 7 ]. Subsequently, while allowing inferences regarding pain perception following SMT, we are unable to attribute the findings in the low back specifically to c- fiber mediated pain. We chose to investigate both the lower extremity and the low back in this study due to prior studies having noted a region specific influence of non- specific effects. For example, a placebo provided with expectation of relieving experimental pain in the hand has been found to exert an effect localized to that hand, without change in pain perception in the other hand or either foot [ 45 ]. Our instructional set and the SMT used in this study were specific to the low back. We felt the region specific nature of the instructional set and the SMT technique might localize the influence of non- specific effects associated with SMT to the low back. Including both anatomical areas in our QST protocol allowed us to test the specificity of our instruction set in our data analysis.

Immediately following the practice session, participants were asked to quantify the amount of pain they expected to feel during the QST in both their back and lower extremity using separate numeric rating scales (NRS). These ratings served as the baseline expectation for pain. Following initial QST, participants were randomly assigned to receive a positive, a negative, or a neutral expectation instructional set.

Participants in the positive expectation group were told the SMT; "."

Participants in the negative expectation group were told the SMT; "."

Participants in the neutral expectation group were told the SMT; "."

\left . \textstyle\begin{array}{l} x''(t)+bx(t)+c \operatorname{sgn}x'(t)+d \sin x(t) = p(t), \quad \textit {for almost all } t \in[ 0, T], \\ x(0)=x_{0}, \qquad x(T)=x_{T}, \end{array}\displaystyle \right \}
(23)
\begin{aligned} \max_{t \in[0, T]} \bigl\vert x(t)\bigr\vert \leq \frac{ \mathcal{P}+T [\vert b\vert k_{2}+ |c|+|d| ]}{\sqrt{b} \vert \sin(\sqrt{b} T) \vert }+k_{2}, \\ \max_{t \in[0, T]} \bigl\vert x'(t)\bigr\vert \leq \frac{ \mathcal{P}+T [\vert b\vert k_{2}+ |c|+|d| ]}{\vert \sin(\sqrt{b} T)\vert } + \frac{|x_{T}-x_{0}|}{T}. \end{aligned}
\begin{aligned} \max_{t \in[0, T]} \bigl\vert x(t)\bigr\vert \leq \frac{e^{2 \sqrt{-b} T}}{2 \sqrt{-b}} \bigl[ \mathcal{P}+T \bigl(\vert b\vert k_{2}+|c| + |d| \bigr) \bigr]+k_{2}, \\ \max_{t \in[0, T]} \bigl\vert x'(t)\bigr\vert \leq e^{2 \sqrt{-b} T} \bigl[ \mathcal{P}+T \bigl(\vert b\vert k_{2}+|c| + |d| \bigr) \bigr] + \frac {|x_{T}-x_{0}|}{T} \end{aligned}
\begin{aligned} \max_{t \in[0, T]} \bigl\vert x(t)\bigr\vert \leq \frac{ T [\mathcal{P}+T( |c|+|d|) ]}{4}+k_{2}, \\ \max_{t \in[0, T]} \bigl\vert x'(t)\bigr\vert \leq \mathcal{P}+T\bigl( \vert c\vert +|d|\bigr) + \frac {|x_{T}-x_{0}|}{T}, \end{aligned}

Remark 3

Observe that, for b = 0 , the conclusion of Corollary Vans Unisex Authentic Lo Pro Chambray Casual Shoe Chambray Black/True Wht Byhjlpdt
reduces to the Dirichlet problem for a forced pendulum with a dry friction while, for d = 0 , the result concerns the Dirichlet problem for a forced ‘linear’ oscillator with a dry friction. Moreover, the non-resonance condition b \neq (\frac{k \pi}{T} )^{2} , k \in\mathbb{N} , distinguished in Corollary 1 in three cases ( b>0 , b<0 , b=0 ), is evidently optimal, when comparing it with all its analogies discussed above ( ( 20 ), Remark 1 and Remark Duckfeet Jylland Derby Shoe Brown Leather kF3wWhU
).

Finally, we can also consider a particular case with c=0 of the Dirichlet problem ( 9 ) in a vector form in \mathbb{R}^{n} , i.e. let a , b ( c=0 ) and T>0 remain real constants, but x_{0}, x_{T} \in\mathbb{R}^{n} , F_{1} \colon\mathbb{R}^{n} \multimap \mathbb{R}^{n} , F_{2} \colon\mathbb{R}^{n} \multimap\mathbb{R}^{n} be u.s.c. with convex and compact values and P \colon J \multimap \mathbb{R}^{n} be an Aumann (component-wise)-integrable mapping. In this way, dry friction terms can be involved, after their Filippov’s regularization, in some components of F_{2} .

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June 27th, 2018

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October 26th, 2017

– On October 23, 2017, friends, supporters, community partners, staff, and board members attended Berkshire Children and Families Annual Meeting at Zion Lutheran Church in Pittsfield. That evening, Berkshire Children and Families was pleased to elect five new members to their board of directors: retired educator and counselor Carole Siegel, community activist Shirley Edgerton, attorney Virginia Stanton Smith, retired President of the University of Baltimore and attorney Robert Bogomolny, and retired cardiologist William K. Levy, M.D.

The evening included testimonials from children and families who spoke of the impact of working with BCF. Dr. Jason McCandless, Superintendent of Pittsfield Public Schools, gave the keynote address sharing the importance of partnerships in solving the many issues facing our community.

The evening was themed on partnership and innovation. Colleen Holmes, President and CEO, stated, “We are grateful for our many partners and generous donors, and excited about what next we will accomplish together.”

Holmes continued, “Innovation is very familiar to BCF… Familiarity feels good, but it’s tricky; it can lull us right down the rabbit hole of taking things for granted. BCF will need to look beyond our 130 years of success and risk being on unfamiliar ground. That’s poetic justice given that we ask those we work with and serve to take a chance in order to reach their goals.”

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September 22nd, 2017

Berkshire Children and Families, Berkshire Museum, and Miss Hall’s School have teamed up to curate the exhibit a story-based portrait series featuring youth in the Pittsfield community from Herberg and Reid Middle Schools and based on the . Mikala L’Hote (a recent graduate from Miss Hall’s from Pittsfield and intern at the Berkshire Museum) and Gabriela Keator (also recent MHS graduate from Lenox and an intern at Berkshire Children and Families) worked with students at Herberg and Reid, asking them the question: “What do you want your message to the world to be?” Students then were photographed, with their message painted on their arms.

The exhibit will be displayed at the Lichtenstein Center for the Arts at 28 Renne Ave in Pittsfield with an opening reception on October 6, 5:00-8:00PM. For more information contact: Franco Sarto Womens Hespiria Slouch Boot Charcoal Grey NRWTArx6C

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