Any person has the right to engage in any activity of daily life with autonomy. Without obstacles. Why – emphasizes the manual-, to make accessible a library has which meet the physical standards of access which the law establishes, but should also facilitate access to documentation, the goods and services, as well as the behavior and attitudes of people who interact in the same space. Building and equipping one of the factors that most worries when it comes to designing or improving the accessibility of the buildings is how to do it. You may wish to learn more. If so, Walt Disney is the place to go. The answer lies in the users themselves: listening to their needs and taking into account your circumstances. The basic guidelines passed by removing architectural barriers, attend the furniture and analyze the space.The building must located nearby to transport public and pedestrian itineraries that will ensure accessibility from the stops.
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text:
Home > Wise Adviser
Wise Adviser
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{708C726E-B383-446C-816B-2551D4191BDD}
by Robert E. Mims on August 9, 2019
Charles Allen Kollar's book Solution-Focused Pastoral Counseling has become a bible for many ministers, chaplains, and others working with troubled souls. But Kollar stresses that the Holy Bible, along with decades of his own experience and study, are the bedrock of the techniques he teaches.
Since its first publication in 1997, and a second, expanded edition released in 2011 in multiple foreign languages (Chinese, Korean, and Russian), SFPC has become a go-to handbook for spiritual application of mainstream psychotherapeutic "solution-focused" or "brief therapy" approaches that first became popular about 50 years ago.
"[Such techniques] are taught and practiced by many," says Kollar, a retired U.S. Navy chaplain and longtime lead pastor of Innovation Church, an Assemblies of God congregation in Cresco, Pennsylvania. "All I did was see the connection to how the Holy Spirit works in our lives, and then reimagined this approach for pastoral counselors."
Kollar is a graduate of Northwest University and Assemblies of God Theological Seminary. The pastor and licensed professional counselor and marriage and family therapist adds, "My goal was to give pastors an approach that worked in harmony with what the Lord was already doing in a counselee's life."
SFPC's message is aimed at ministers often overtaxed with counseling demands and in need of techniques that quickly identify underlying issues of their troubled parishioners. In a few sessions, rather than possibly months or years of more conventional therapy typically aimed at diagnosing maladies of the psyche, SFPC counselors guide those seeking help in identifying solutions.
In a nutshell, SFPC is short-term in its approach, seeking a partnership between counselor and counselee in taking swift, practical steps to address problematic behaviors, and then developing clear, incremental, collaborative, and longer-term strategies to grow emotionally and spiritually.
Kollar is quick to say he recognizes its limitations, and that situations will arise where more professional mental or medical health expertise is required. Still, the techniques work well for many, if not most, counseling issues raised in pastoral counseling, SFPC practitioners say. The textbook has gained a following among educators, pastors, and chaplains .
Norm Thiesen, professor of counseling at the Portland, Oregon, campus of Western Seminary, has used SFPC as his primary class text for more than 15 years.
"The feedback I've received from students is almost unanimously that it was helpful in developing pastoral counseling methodology," Thiesen says.
Until studying Kollar's techniques, most students have never heard of a solution-focused approach, Thiesen adds. Instead, they have tended to learn the secular problem-identification approach, which results in a negative experience with counseling, Thiesen says.
Kelvin Mutter, an associate professor of counseling and spiritual care at Canada's McMaster Divinity College in Hamilton, Ontario, praises SFPC as a method that "honors the congregant's strengths and resiliency. This preserves the unique character of the pastoral relationship [by] providing care without creating dependency."
Mutter, an experienced psychotherapist, underscores the biblical, Christian underpinnings of Kollar's methodology.
"I have found that Kollar's reflections on the continuing presence and work of God in people's lives has been a helpful reminder to practice humility and collaborate with those I counsel," Mutter says.
Kerry R. Watts, associate pastor of Grand Rapids First, an Assemblies of God church in Wyoming, Michigan, says SFPC provides a "paradigm for counseling that takes the weight off me for having to have all the answers to everyone's problems."
He says he's learned that most people he interacts with in sessions are "doing something right in the midst of their struggle, they just can't see it."
"My task is to primarily hear their story, help them see where they are already succeeding, and determine ways to build on those successes," Watts says.
His counselees, ironically, have included a professional mainstream counselor, who visited because of his own troubled marriage.
"Following our first session, he said, 'That was the best counseling session I've ever been a part of!'" Watts recalls. "He and his wife were able to move forward, and are still married."
Of course, Kollar, 66, does more than write about his Christian approach to SFPC. He continues to practice it, both during a decade as a U.S. Navy chaplain, and at Innovation Church, where he and his wife, Dawn, have pastored while raising a family that includes three children and 10 grandchildren.
His therapeutic experiences have been wide-ranging, including grief and end-of-life counseling, substance abuse, eating disorders, sexual abuse, and dysfunctional family and marital issues.
Kollar says sessions with sailors, parishioners, and fellow ministers have taught him much, too.
"My goal is to help individuals, couples, and families to discover what they 'really want,' and to help them take steps in that direction," Kollar says. "It never ceases to amaze me that what nearly all of my counselees' really want is to be in more loving, forgiving, encouraging, and supporting relationships."
Kollar believes that is something all pastors can help with, if they learn to do so without judgment.
"What is the source of such things, if not our heavenly Father, who is love?" he asks. "[It is] His Son, who gave us only one command, to love one another as He loves us — and the Holy Spirit, who seeks to help us live this abundant life from within."
Tags: Charles Kollar Solution-Focused Pastoral Counseling Innovation Church Assemblies of God Theological Seminary Northwest University Norm Thiesen Kevin Mutter Grand Rapids First

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}

Many quantum electrodynamic nonlinear phenomena induced by strong laser
radiation in condensed matter, specifically in graphene/nanostructures, have
significant contribution in low-energy physics and nano-opto-electronics and
have been systematically investigated mainly in case of monolayer graphene
\cite{1,1bb,2} that has been conditioned by unique physical properties of
such two-dimensional (2D) nanosystem of atomic thickness \cite{1},  \cite{1bb}. On
the other hand, for induced electrodynamic phenomena in 2D atomic
systems-nanostructures a bilayer graphene ($AB$-stacked) is of great
interest too, since its electronic states are considerably richer than those
for monolayer graphene, and multiphoton resonant excitation with
high-harmonic generation (HHG) via nonlinear channels in bilayer graphene
were also considered \cite{hhg1,Abook,hhg2}. The pioneer studies of laser-induced
HHG process in recent decades were made generally in gaseous media, while it
is of interest the investigation of HHG and related processes in
low-dimensional nanostructures, such as graphene and its derivatives \cit
{H2,Mer,Mer1,H3,H4,H6,H7,H8,H9,H99,H10,H11,H12,H12a,H13,H14,H15,H16,H17,H18,H19,H21
, bulk crystals \cite{s1,s2,s3,s5,s6,s7}, hexagonal boron nitride \cite{BN},
monolayer transition metal dichalcogenides \cite{TMD,TMD1,TMD11},
topological insulator \cite{TI}, \cite{TII}, in monolayers of black
phosphorus \cite{phosph}, buckled 2D hexagonal nanostructures \cite{Mer2019
, solids \cite{corcumsolid}, \cite{semimetal}, as well as in other 2D systems \cit
{twodem1,twodem2,twodem3}. The 2D nanosystems enable to develop important
technological applications. The quantum cascade laser is one of such
examples \cite{QCL} using the physical phenomena in 2D systems such as the
quantum Hall effect \cite{Abook}. The nonlinear coherent response in $AB
-stacked bilayer graphene under the influence of intense electromagnetic
radiation leads to the modification of quasi-energy spectrum, the induction
of valley polarized currents \cite{26b}, \cite{27b} as well as the second and
third-order nonlinear-optical effects \cite{28b,29b,30b,31b}. Moreover, the
bilayer graphene system represents a unique system in which the topology of
the band structure can be externally influenced and chosen. The bilayer
graphene is a highly tunable material: not only one can tune the Fermi
energy using standard gates, as in single-layer graphene, but the band
structure can also be modified by external perturbations such as transverse
electric fields or strain \cite{1a,1ab,1aa,9,22b,24b,Liftrans}.
Particularly, due to the realization of a widely tunable electronic bandgap
in an electrically gated bilayer graphene \cite{9}, \cite{10,10a,16}, it is
of interest to consider HHG process in the strong wave-bilayer graphene
coupling regime with a bandgap induced by an external constant electric
field as a condensed matter material with nontrivial topology \cite{Mer2019
, in particular, with the bands acquiring Berry curvature \cite{Berry}.
Moreover, with the current technology \cite{16} one can make such large gaps
in $AB$-stacked bilayer graphene, which is sufficient to produce
field-effect transistors with a high on-off ratio not only at cryogenic
temperatures but at room-temperature \cite{Ber1}, \cite{transist}.

In addition, it is known the graphene-based low energy photon-counting
photodetector of different applications, in areas as diverse as medical and
space sciences or security applications. The tunable bandgap in bilayer
graphene may enable sensitive photon-counting photodetectors to operate with
a trade-off between resolution and operational temperatures, with resulting
operational benefits. Note that the large bandgap can also make possible
effective room temperature HHG \cite{H14} in bilayer graphene, which is
suppressed in intrinsic bilayer graphene \cite{H3}. Unfortunately, the
effective pump wave-induced Lifshitz transitions (with photon energy much
smaller than Lifshitz energy) in $AB$-stacked gapped bilayer graphene are
less investigated.

In the present paper, with the help of the numerical simulations in a
microscopic nonlinear quantum theory of interaction of $AB$-stacked gapped
bilayer graphene with the moderately strong laser radiation, we find out the
optimal values of the main parameters, in particular, for bandgap, pump wave
intensity, graphene temperature for practically significant case in
high-order harmonics coherent emission in the particle low-energy region of
the induced Lifshitz transitions (the fragmentation of the singly-connected
Fermi line into four separate pieces) \cite{22b}, \cite{Lifshitz,Lif1,Lif2}.
The Liouville-von Neumann equation is treated numerically for the generation
of the higher (here -second, third) harmonics in the multiphoton excitation
regime near the Dirac points of the Brillouin zone. We consider the harmonic
generation process in the nonadiabatic regime of interaction when the
Keldysh parameter is of the order of unity. The picture of the multiphoton
excitation of the Fermi-Dirac sea and the trigonal warping effect is also
revealed.  We examine the rates of the HHG at the particle-hole annihilation
in the strong effective field of two linearly polarized plane electromagnetic waves,
 propagating in opposite direction for
practically optimal parameters of the considering system. Due to the special
magnitudes of the bandgap, we can operate with the sample temperature. The
obtained results show that for specially chosen values of the corresponding
characteristic parameters of this process we can use gapped bilayer graphene
as a convenient nonlinear medium to generate the higher harmonics of the
pump wave with an effective yield in the sub-THz and THz domains of the
spectrum, at the graphene temperatures of higher than the cryogenic
temperatures.

The paper is organized as follows. In Sec. II the set of equations for a
single-particle density matrix is formulated and numerically solved in the
multiphoton interaction regime. In Sec. III, we consider the problem of
harmonics generation at the low-energy excitation of gapped bilayer
graphene. Finally, conclusions are given in Sec. IV.

\section{Basic theory}

At the higher harmonic emission process in gapped bilayer graphene during
the coherent electromagnetic radiation-induced Lifshitz transitions with the
energies much smaller than the Lifshitz energy $\mathcal{E}_{L}$ have some
peculiarities \cite{Lifshitz,Lif1,Lif2}, \cite{46bb,47bb,48bb,49bb}. The
Lifshitz transition someone is unique with thermoelectric properties of
bilayer graphene \cite{thermoelectric}. Two touching parabolas of the Fermi
surface are broken into four separate `pockets'. However, as opposed to bulk
graphite, the external perturbations like the strain \cite{19bb}, \cite{20bb} or
electric field \cite{21bb} can modify the topology of the electronic
dispersion and change the energy of the Lifshitz transition which connects
regions of different Fermi contour topologies \cite{22bb}. Moreover, due to
the two-dimensional nature of bilayer graphene, its chemical potential and
its topology can be tuned with electrostatic gates \cite{1}, simplifying
experimental studies of the Lifshitz transition. By the way, in unperturbed
bilayer graphene, it is achieved at low energies $\mathcal{E}_{L}\sim 1$
\mathrm{meV}$. To induce the asymmetry, a chemical doping can be used \cit
{1a} or external gates \cite{1ab} can be patterned. This induced asymmetry
opens a bandgap between the two layers of the bilayer graphene \cite{22b},
\cite{46bb,47bb,48bb,49bb}. As is shown in \cite{22bb}, particularly for an
induced asymmetry $U=100$ $\mathrm{meV,}$ the Lifshitz transition occurs at
the higher energy $\mathcal{E}_{L}\sim 1.6$ $\mathrm{meV}$. One can conclude
from the estimate given in \cite{22bb} that the experimental observation of
the Lifshitz transition should be facilitated by the layer-asymmetry induced
bandgap and that, the wider the gap, the more enhanced the visibility of
this effect.

At an intraband transitions the interaction of a particle with the wave at
the THz or sub-THz photon low-energies $\hbar \omega \ll \mathcal{E}_{L}$,
characterizes by the effective interaction parameter $\chi $ \cite{H3}
\begin{equation}
\chi =eE_{0}\mathrm{v}_{3}/(\hbar \omega ^{2}),  \label{00}
\end{equation
where $E_{0}$ is the wave strength, $\omega $ is the wave frequency, $e$ is
the electron charge. Due to the gap, the interband transitions are
characterized by so-called Keldysh \cite{Keld1,Keld2} parameter expressed in
the form:
\begin{equation}
\gamma =\omega \sqrt{m_{\ast }U}/\left( eE_{0}\right) =\chi^{-1}\mathrm
v}_{3}\sqrt{m_{\ast }U}/\left( \hbar \omega \right) .  \label{01}
\end{equation}

Here $U$ is the bandgap energy, $\hbar $ is the Planck constant; $m_{\ast
}=\gamma _{1}/(2\mathrm{v}_{F}^{2})$ is the effective mass ($\mathrm{v}_{F}$
is the Fermi velocity in monolayer graphene); $\mathrm{v}_{3}=\sqrt{3
a\gamma _{3}/(2\hbar )\approx \mathrm{v}_{F}/8$ is the effective velocity
related to oblique interlayer hopping $\gamma _{3}=0.32$ $\mathrm{eV}$ (
a\approx 0.246$ $\mathrm{nm}$ is the distance between the nearest $A$
sites), $\gamma _{1}\simeq 0.39$ $\mathrm{eV.}$

For the gapped materials, the Keldysh parameter gives the character of the
ionization process which with the electron-hole pair creation is the first
step of HHG. In the limit of $\gamma \gg 1$, the multiphoton ionization
dominates in the ionization process. In the so-called nonadiabatic regime
\gamma \sim 1$, both multiphoton ionization and tunneling ionization can
take place. In the limit of $\gamma \ll 1$, the tunneling ionization
dominates. For the considered case, the ionization process reduces to the
transfer of the electron from the valence band into the conduction band that
is the creation of an electron-hole pair. Since the interband transitions
can be neglected when $\gamma \gg 1$, then the wavefield cannot provide
enough energy for the creation of an electron-hole pair, and the generation
of harmonics is suppressed. So that, in the nonadiabatic regime due to the
large ionization probabilities the intensity of harmonics can be
significantly enhanced compared with tunneling one \cite{H14}, \cite{H19}.
If $\gamma \sim 1$ or $\gamma \ll 1$, interband transitions take place. From
this point of view, condensed matter materials with bilayer graphene are
preferable due to the tunable bandgap with nontrivial topology.

In the present paper, we will consider the nonadiabatic regime for the
generation of HHG at $\chi \sim 1$ and $\gamma \sim 1$, when the multiphoton
effects become essential. Our consideration is mainly focused on the low
photon energies. Note that the average intensity of the wave expressed by
\chi $ can be given as\textrm{\
\begin{equation*}
I_{\chi }=\chi ^{2}\times 6\times 10^{10}\mathrm{Wcm}^{-2}(\hbar \omega
\mathrm{eV})^{3},
\end{equation*
so the required intensity $I_{\chi }$\ for the nonlinear regime$\ $strongly
depends\textit{\ }on the photon energy. Particularly, for the photons with
the energies $0.4-0.9$ $\mathrm{meV,}$ the multiphoton interaction regime
can be achieved at the intensities $I_{\chi }=1-10^{2}\mathrm{\ Wcm}^{-2}$.
Note, that modern photonic-based THz and sub-THz (with energies $0.4-1.24$
\mathrm{meV}$) sources include quantum cascade lasers and can achieve
admirable output powers, mainly at cryogenic temperatures, whereas used in
conjunction with nonlinear crystals can make microwatts of tunable
continuous wave THz at room temperature \cite{subTHz}. Unfortunately, all of
these sources offer impressive performance in their own ways, but none so
far are easily integrated into larger digital electronic systems, which is
arguably their biggest downfall for communication systems \cite{subTHz1}.

In the following we use the microscopic nonlinear quantum theory of
interaction of coherent electromagnetic radiation with gapped bilayer
graphene which was developed in \cite{H14}, \cite{H19}. To get the sub-THz
frequencies, let propose two linearly polarized plane electromagnetic waves
with carrier frequency $\omega $ and slowly varying amplitude of the
electric field $E_{a}f(t)$
\begin{equation}
E_{1}\left( t\right) =\widehat{\mathbf{e}}E_{a}f(t)\cos \left( \omega t
\mathbf{kr}\right) ,  \label{a}
\end{equation
\begin{equation}
E_{2}\left( t\right) =\widehat{\mathbf{e}}E_{a}f(t)\cos \left( \omega t
\mathbf{kr}\right) ,  \label{1a}
\end{equation
propagating in opposite directions in a vacuum. We assume that the pump wave
wavelength $\lambda \gg a$, where $a$ is the characteristic size of the
carbon system--the distance between the nearest $A$ sites (for the HHG this
condition is always satisfied). In considering case of a standing wave
formed by the laser beams (\ref{1a}), a significant input in the HHG process
is conditioned by the Dirac points situated near the stationary maxima of
the standing wave. For these points, the magnetic fields of the
counterpropagating waves cancel each other \cite{Abook}, \cite{physrevA2011
, \cite{plasma2011}. Since the HHG is essentially produced at the lengths
l\ll \lambda $ near the electric field maximums, we assume the effective
field in the plane of the graphene sheets ($XY$) to be:
\begin{equation}
\mathbf{E}\left( t\right) =f\left( t\right) E_{0}\widehat{\mathbf{e}}\cos
\omega t,  \label{7}
\end{equation
where $E_{0}=2E_{a}$, and $\widehat{\mathbf{e}}$ is the unit polarization
vector. The pump wave slowly varying envelope is described by the function
\begin{equation}
f\left( t\right) =\left\{
\begin{array}{cc}
\sin ^{2}\left( \pi t/\mathcal{T}\right) , & 0\leq t\leq \mathcal{T}, \\
0, & t<0,t>\mathcal{T}
\end{array
\right. ,  \label{8}
\end{equation
where $\mathcal{T}$ characterizes the pulse duration and is taken to be
\mathcal{T}=10\mathcal{T}_{0}$, $\phi $ is the pump wave polarization
parameter, $\mathcal{T}_{0}=2\pi /\omega $.

In $AB$-stacked gapped bilayer graphene, the low-energy excitations
\left\vert \mathcal{E}_{\sigma }\right\vert <\gamma _{1}\simeq 0.39$
\mathrm{eV}$ in the vicinity of the Dirac points $K_{\zeta }$ can be
described by an effective single-particle Hamiltonian \cite{9,22b,24b}:

\begin{equation}
\widehat{H}_{\zeta }=\left(
\begin{array}{cc}
\frac{U}{2} & g_{\zeta }^{\ast }\left( \mathbf{p}\right) \\
g_{\zeta }\left( \mathbf{p}\right) & -\frac{U}{2
\end{array
\right) ,  \label{1}
\end{equation
where
\begin{equation}
g_{\zeta }\left( \mathbf{p}\right) =-\frac{1}{2m_{\ast }}\left( \zeta
\widehat{p}_{x}+i\widehat{p}_{y}\right) ^{2}+\mathrm{v}_{3}\left( \zeta
\widehat{p}_{x}-i\widehat{p}_{y}\right) ,  \label{2}
\end{equation
$\mathbf{\hat{p}}=\left\{ \widehat{p}_{x},\widehat{p}_{y}\right\} $\textbf{\
}is the electron momentum operator, $\zeta =\pm 1$ is the valley quantum
number. The diagonal elements in Eq. (\ref{1}) correspond to opened gap $U$.
The first term in Eq. (\ref{2}) gives a pair of parabolic bands $\mathcal{E
=\pm p^{2}/(2m_{\ast })$, and the second term connecting with $\gamma _{3}$
causes trigonal warping in the band dispersion. The spin and the valley
quantum numbers are conserved. There is no degeneracy upon the valley
quantum number $\zeta $ for the issue considered. However, since there are
no intervalley transitions, the valley index $\zeta $ can be considered as a
parameter.

The eigenstates of the effective Hamiltonian (\ref{1}) are the spinors
\begin{equation}
\Psi _{\sigma }(\mathbf{r})=\frac{1}{\sqrt{S}}|\sigma ,\mathbf{p}\rangle e^
\frac{i}{\hbar }\mathbf{pr}}  \label{3}
\end{equation
wher
\begin{equation}
|\sigma ,\mathbf{p}\rangle =\frac{1}{\sqrt{S}}\sqrt{\frac{\mathcal{E
_{\sigma }+\frac{U}{2}}{2\mathcal{E}_{\sigma }}}\left(
\begin{array}{c}
1 \\
\frac{1}{\mathcal{E}_{\sigma }+\frac{U}{2}}\Upsilon \left( \mathbf{p}\right
\end{array
\right) ,  \label{4}
\end{equation
\begin{equation}
\Upsilon \left( \mathbf{p}\right) =-\frac{p^{2}}{2m}e^{i2\zeta \vartheta
}+\zeta \mathrm{v}_{3}pe^{-i\zeta \vartheta }.  \label{6}
\end{equation
$\vartheta =\arctan \left( p_{y}/p_{x}\right) $, $\sigma $ is the band
index: $\sigma =1$ and $\sigma =-1$ for conduction and valence bands,
respectively; and $S$ is the quantization area. The corresponding
eigenenergies are
\begin{equation}
\mathcal{E}_{\sigma }\left( \mathbf{p}\right) =\sigma \sqrt{\frac{U^{2}}{4
+\left( \mathrm{v}_{3}p\right) ^{2}-\zeta \frac{\mathrm{v}_{3}p^{3}}{m}\cos
3\vartheta +\left( \frac{p^{2}}{2m}\right) ^{2}}.  \label{5}
\end{equation

\begin{figure}[tbp]
\includegraphics[width=.7\textwidth]{figure1.eps}
\caption{(Color online) Particle distribution function $N_{c}(\mathbf{p
,t_{f})$\ (in arbitrary units) after the interaction at the instant
t_{f}=10T$, as a function of scaled dimensionless momentum components is
shown. The effective field is assumed to be linearly polarized along the $y$
axis. Multiphoton excitation with the trigonal warping effect for low-energy
photon excitation-induced Lifshitz transitions at the photon energy $\hbar
\protect\omega =\mathcal{E}_{L}/1.1$\ $\simeq $\ $0.9$\ $\mathrm{meV}$, the
temperature $T/\hbar \protect\omega =0.4$ are demonstrated at dimensionless
intensity parameter $\protect\chi =1$ for valley $\protect\zeta =-1$.
(a)--(d) correspond to the gap energy $U=5$ $\mathrm{meV},$ $4$ $\mathrm{meV
}$ $3 $ $\mathrm{meV}$ and $0.0008$ $\mathrm{meV,}$ respectively.}
\label{111}
\end{figure}
Due to the second quantized technique, we can write the Fermi-Dirac field
operator in the form of an expansion in the free states, given in (\ref{3}),
that is,
\begin{equation}
\widehat{\Psi }(\mathbf{r},t)=\sum\limits_{\mathbf{p,}\sigma }\widehat{a}_
\mathbf{p},\sigma }(t)\Psi _{\sigma }(\mathbf{r}),  \label{9}
\end{equation
where $\widehat{a}_{\mathbf{p},\sigma }(t)$ ($\widehat{a}_{\mathbf{p},\sigma
}^{+}(t)$) is the annihilation (creation) operator for an electron with
momentum $\mathbf{p}$ which satisfy the usual fermionic anticommutation
rules at equal times. The single-particle Hamiltonian in the presence of a
uniform time-dependent electric field $E(t)$ can be expressed in the form
\begin{equation}
\widehat{H}_{s}=\widehat{H}_{\zeta }+\left(
\begin{array}{cc}
e\mathbf{rE}\left( t\right) & 0 \\
0 & e\mathbf{rE}\left( t\right
\end{array
\right) ,  \label{12}
\end{equation
where for the interaction Hamiltonian we have used a length gauge,
describing the interaction by the potential energy \cite{Corkum}, \cite{32b}. Taking
into account expansion (\ref{9}), the second quantized total Hamiltonian can
be expressed in the form:
\begin{equation}
\widehat{H}=\sum\limits_{\sigma ,\mathbf{p}}\mathcal{E}_{\sigma }\left(
\mathbf{p}\right) \widehat{a}_{\sigma \mathbf{p}}^{+}\widehat{a}_{\sigma
\mathbf{p}}+\widehat{H}_{\mathrm{s}},  \label{13}
\end{equation
where the light--matter interaction part is given in terms of the
gauge-independent field $\mathbf{E}\left( t\right) $ as follow:

\begin{equation*}
\widehat{H}_{\mathrm{s}}=ie\sum\limits_{\mathbf{p,p}^{\prime },\sigma
}\delta _{\mathbf{p}^{\prime }\mathbf{p}}\partial _{\mathbf{p}^{\prime }
\mathbf{E}\left( t\right) \widehat{a}_{\mathbf{p},\sigma }^{\dagger
\widehat{a}_{\mathbf{p}^{\prime },\sigma ^{\prime }}\
\end{equation*
\begin{equation}
+\sum\limits_{\mathbf{p},\sigma }\mathbf{E}\left( t\right) \left( \mathbf{D
_{\mathrm{t}}\left( \sigma ,\mathbf{p}\right) \widehat{a}_{\mathbf{p},\sigma
}^{+}\widehat{a}_{\mathbf{p},-\sigma }+\mathbf{D}_{\mathrm{m}}\left( \sigma
\mathbf{p}\right) \widehat{a}_{\mathbf{p},\sigma }^{+}\widehat{a}_{\mathbf{p
,\sigma }\right) ,  \label{14}
\end{equation
where
\begin{equation}
\mathbf{D}_{\mathrm{t}}\left( \sigma ,\mathbf{p}\right) =\hbar e\langle
\sigma ,\mathbf{p}|i\partial _{\mathbf{p}}|-\sigma ,\mathbf{p}\rangle
\label{15}
\end{equation
is the transition dipole moment and
\begin{equation}
\mathbf{D}_{\mathrm{m}}\left( \sigma ,\mathbf{p}\right) =\hbar e\langle
\sigma ,\mathbf{p}|i\partial _{\mathbf{p}}|\sigma ,\mathbf{p}\rangle
\label{16}
\end{equation
is the Berry connection or mean dipole moment, which are given in Appendix.

\begin{figure}[tbp]
\includegraphics[width=.7\textwidth]{figure2.eps}
\caption{ (Color online) Creation of a particle-hole pair in bilayer
graphene at multiphoton resonant excitation. Particle distribution function
N_{c}(\mathbf{p},t_{f})$ (in arbitrary units) after the interaction is
displayed at various intensities corresponding to : (a) $\protect\chi =0.5$,
(b) $\protect\chi =1$, (c) $\protect\chi =1.5$, and (d) $\protect\chi =2$.
The temperature is taken to be $T/\hbar \protect\omega =0.4$. The effective
field is assumed to be linearly polarized along the $y$ axis with the photon
energy $\hbar \protect\omega =\mathcal{E}_{L}/1.1$\ $\simeq $\ $0.9$\
\mathrm{meV}$ and gap energy is $U=4$\ $\mathrm{meV}$. The results are for
the valley $\protect\zeta =-1$. }
\label{222}
\end{figure}

Multiphoton interaction of a bilayer graphene with a strong radiation field
will be described by the Liouville--von Neumann equation for a
single-particle density matrix (see Appendix equations (\ref{17}), (\re
{18})). As an initial state, we assume an ideal Fermi gas in equilibrium
with chemical potential to be zero. We will solve the set of Eqs. (\ref{19
), and followed from the last closed set of differential equations (\ref{20
), (\ref{21}) given in the Appendix, for the functions $N_{\mathrm{v}}
\mathbf{p},t)$, $N_{c}(\mathbf{p},t)$, $P(\mathbf{p},t)$, taking into
account the initial conditions
\begin{equation}
P(\mathbf{p},0)=0;\ N_{c}(\mathbf{p},0)=\frac{1}{1+e^{\mathcal{E}_{1}\left(
\mathbf{p}\right) /T}};  \label{22a}
\end{equation
\begin{equation}
N_{\mathrm{v}}(\mathbf{p},0)=1-N_{c}(\mathbf{p},0).  \label{23}
\end{equation
Here $T$ is the temperature in energy units. Note that we will incorporate
relaxation processes into Liouville--von Neumann equation with inhomogeneous
phenomenological damping rate $\Gamma $, since homogeneous relaxation
processes are slow compared with inhomogeneous.

The set of equations (\ref{20}), (\ref{21}), and (\ref{22}) can not be
solved analytically. For the numerical solution we made a change of
variables and transform the equations with partial derivatives into ordinary
ones. The new variables are $t$ and $\widetilde{\mathbf{p}}=\mathbf{p}
\mathbf{p}_{E}$ $\left( t\right) $, where
\begin{equation}
\mathbf{p}_{E}\left( t\right) =-e\int_{0}^{t}\mathbf{E}\left( t^{\prime
}\right) dt^{\prime }  \label{24}
\end{equation
is the classical momentum given by the wave field. After these
transformations, the integration of equations (\ref{20}), (\ref{21}), and
\ref{22}) is performed on a homogeneous grid of $10^{4}$ ($\widetilde{p}_{x}
\widetilde{p}_{y}$)-points. For the maximal momentum we take $\widetilde{p
_{\max }/\sqrt{m\hbar \omega }=5$. The time integration is performed with
the standard fourth-order Runge-Kutta algorithm. For the relaxation rate we
take $\Gamma =0.5\mathcal{T}^{-1}$.

Photoexcitations of the Fermi-Dirac sea - induced Lifshitz transitions, are
presented in Figs. 1, 2. The effective wave is assumed to be linearly
polarized along the $y$ axis. Similar calculations for a wave linearly
polarized along the $x $\ axis show qualitatively the same picture. In Fig.1
density plot of the particle distribution function $N_{c}(\mathbf{p},t_{f})
\ is shown as a function of scaled dimensionless momentum components after
the interaction at the different energy gaps. The pump wave pulse duration
is $\mathcal{T}=10\mathcal{T}_{0}\approx 46$ $\mathrm{ps}$. It is clearly
seen as the trigonal warping effect describing the deviation of the excited
iso-energy contours from circles, which is smeared with the increase of the
gap magnitude. In all considering cases, the two touching parabolas are
transformed into the four separate \textquotedblleft
pockets\textquotedblright . Note that trigonal warping is crucial for
even-order nonlinearity. As is seen with the increasing of $U$ we approach
to perturbative regime $\gamma >1$ and only weak excitation of Fermi-Dirac
sea.
\begin{figure}[tbp]
\includegraphics[width=.7\textwidth]{figure3.eps}
\caption{The harmonic emission rate (in arbitrary units) of \ (a) second
G_{2}$ and (b) third $G_{3}$ order in bilayer graphene at Lifshitz
transition versus the intensity parameter $\protect\chi $ is shown for
various gap energies. The temperature is taken to be $T/\hbar \protect\omega
=0.4$. The effective wave is assumed to be linearly polarized with the
frequency $\protect\omega =$\ $0.9$\ $\mathrm{meV/\hbar }$. }
\label{333}
\end{figure}

\begin{figure}[tbp]
\includegraphics[width=.7\textwidth]{figure4.eps}
\caption{(a) Second $G_{2}$ and (b) third $G_{3}$ harmonic emission rates
(in arbitrary units) versus the band gap $U$ for various intensities at the
same other parameters as in Fig. 3.}
\label{444}
\end{figure}

In Fig. 2, we show the photoexcitation depending on the pump wave intensity
at fixed sub-THz frequency. For the large values of $\chi $ when $\gamma
=1.1 $ we clearly see multiphoton excitations. With the increasing wave
intensity, the states with the absorption of more photons appear in the
Fermi-Dirac sea. At the parameters $\chi \succsim 1$ when $\gamma \simeq 1$,
the multiphoton excitation of the Fermi-Dirac sea takes place along the
trigonally warped isolines of the quasienergy spectrum modified by the wave
field. Thus, the multiphoton probabilities of particle-hole pair production
will have maximal values for the iso-energy contours defined by the resonant
condition $\mathcal{T}_{0}^{-1}\int\limits_{0}^{\mathcal{T}_{0}}2\mathcal{E
_{1}\left( \widetilde{\mathbf{p}}+\mathbf{p}_{E}\left( t\right) ,t\right)
dt=n\hbar \omega ,\ \ n=1,2,3$...These contours are also seen in Fig. 1. The
investigations of the temperature dependence of the excitation of the
Fermi-Dirac sea are cleared that for considering cases it exhibits a tenuous
dependence on the optimal temperatures: the excited isolines are slightly
smeared out with temperature increase. This effect is small since $U\gg $ $T$
and one can expect that harmonic spectra will be robust against temperature
change in contrast to the gap $U=0$ case where harmonics radiation is
suppressed with the increase of temperature in \cite{H14}, \cite{H19}. So,
the temperature dependence was missed.

In the following section, we will investigate the nonlinear response of the
bilayer graphene in the process of the second and third-order harmonics
generation under the influence of the laser field in the nonadiabatic regime
$\gamma \simeq 1$ with the frequencies in sub-THz domain: $\omega =0.4\div
0.9$ $\mathrm{meV/}\hbar $.

\section{Harmonics generation at induced low-energy transitions in gapped
bilayer graphene}

In this section, we examine the nonlinear response of a bilayer graphene to
harmonic generation process considering the nonadiabatic regime of induced
Lifshitz transitions, when the Keldysh parameter is of the order of unity.
For the coherent part of the radiation spectrum one needs the mean value of
the current density operator
\begin{equation}
j_{\zeta }=-2e\left\langle \widehat{\Psi }(\mathbf{r},t)\left\vert \widehat
\mathbf{v}}_{\zeta }\right\vert \widehat{\Psi }(\mathbf{r},t)\right\rangle .
\label{50}
\end{equation
The velocity operator $\widehat{\mathbf{v}}_{\zeta }=\partial \widehat{H
/\partial \widehat{\mathbf{p}}$ is given in Appendix. Using the Eqs. (\re
{50})--(\ref{52}) and (\ref{17}), the expectation value of the current for
the valley $\zeta $ can be written in the form
\begin{equation*}
\mathbf{j}_{\zeta }\left( t\right) =-\frac{2e}{(2\pi \hbar )^{2}}\int
\mathbf{p}\left\{ \mathbf{V}_{1}\left( \mathbf{p}\right) \left( N_{c}(\mathbf{p
,t)-N_{\mathrm{v}}(\mathbf{p},t)\right) \right.
\end{equation*
\begin{equation}
\left. +2\hbar ^{-1}i\mathcal{E}_{1}\left( \mathbf{p}\right) \left[ \mathbf{
}_{\mathrm{t}}\left( \mathbf{p}\right) P^{\ast }(\mathbf{p},t)-\mathbf{D}_
\mathrm{t}}^{\ast }\left( \mathbf{p}\right) P(\mathbf{p},t)\right] \right\} ,
\label{53}
\end{equation
where $\mathbf{V}_{1}\left( \mathbf{p}\right) $ is the intraband velocity. In
Eq. (\ref{53}) the first term is the intraband current which conditioned by
intraband high harmonics and is generated as a result of the independent
motion of carriers in their respective bands. The second term in Eq. (\re
{53}) describes high harmonics which are generated as a result of the
recombination of accelerated electron-hole pairs. Since we study the
nonadiabatic regime, the contribution of both mechanisms is essential.

There is no degeneracy upon valley quantum number $\zeta $, so the total
current can be obtained by a summation over $\zeta $:
\begin{equation}
j_{x}=j_{1,x}+j_{-1,x};  \label{55}
\end{equation
\begin{equation}
j_{y}=j_{1,y}+j_{-1,y}.  \label{56}
\end{equation
The current density components $j_{x,y}$ are defined as
\begin{equation}
\frac{j_{x,y}}{j_{0}}=G_{x,y}\left( \omega t,\chi,\gamma ,\frac
\mathcal{E}_{L}}{\hbar \omega },\frac{T}{\hbar \omega },\frac{U}{\hbar
\omega }\right) .  \label{57}
\end{equation
Here
\begin{equation}
j_{0}=\frac{e\omega }{\pi ^{2}}\sqrt{\frac{m\omega }{\hbar }},  \label{58}
\end{equation
and $G_{x}$ and $G_{y}$ are the dimensionless periodic (for monochromatic
wave) functions which parametrically depend on the interaction parameters
\chi $, $\gamma $, scaled Lifshitz energy, and temperature. Thus, using
solutions of \ Eqs. (\ref{20})-(\ref{22}), and making an integration in Eq.
\ref{53}), one can calculate the harmonic radiation spectra with the help of
a Fourier transform of the function $G_{x,y}(t)$. The emission rate of the
n $th harmonic is proportional to $n^{2}|j_{n}|^{2}$, where $|j_{n}|^{2}$ =
|j_{xn}|^{2}+|j_{yn}|^{2}$, with $j_{xn}$ and $j_{yn}$ being the $n$th
Fourier components of the field-induced total current. To find $j_{n}$, the
fast Fourier transform algorithm has been used. We use the normalized
current density (\ref{57}) for the plots.

For clarification of harmonics generation due to the multiphoton resonant
excitation and particle-hole annihilation, from the coherent superposition
states at $\gamma \simeq 1$ initially, we examine the emission rate of the
second and third harmonics. The emission rate versus the pump wave strength
defined by the parameter $\chi $ at the same wave frequency is demonstrated
in Fig. 3 for various gap energies. In Fig. 3, plots for $U=4$ $\mathrm{meV}$
and $U=5$ $\mathrm{meV}$ coincided. As is seen from this figure, for the
field intensities $\chi \succsim 1$ at the considering values of the gap
energy $U$ we have a strong deviation from power law for the emission rate
of the second or third harmonic (in accordance with the perturbation theory
\sim \chi ^{2}$ and $\chi ^{3}$, respectively). In Fig. 4, the second and
third harmonics emission rate, expectantly, is assumed as a function of the
energy gap at various intensities defined by the parameter $\chi $ at the
same wave frequency. As shown in Fig. 4, all plots have the minimum values
at $U=4$ $\mathrm{meV}$. As a result, we find the optimal parameters when
the harmonic emission rate is significant at the larger intensity for the
considered wave frequency. So, in accordance with the results of Figs. 3 and
4, the intense radiation of the second and third harmonics at the
pump-wave-induced particle or hole acceleration and annihilation in gapped
graphene can be obtained with the pump wave frequency in the sub-THz domain.
Then, as in case of the similar calculations for the intense pump wave or
large gap energy $U$ ($U\gg T$)\ has shown that the emission rate exhibits a
tenuous dependence on the temperature.

Figure 5 demonstrates the emission rate dependence on the pump frequency for
gapped bilayer graphene. We plot the second and third harmonic emission
rates for a gapped bilayer graphene versus the pump frequency for the gap $4$
$\mathrm{meV}$ and various intensity parameters. As was expected and shown
from this figure, the emission rate has different maxima at various photon
energies and intensities. For third harmonic generation, the maximal value
is reached at frequency $\omega =$\ $0.9$\ $\mathrm{meV/\hbar }$. Concerning
the generation of high harmonics up to the far-infrared range, note that
this has been demonstrated in the paper \cite{H19} where quantum cascade
lasers are readily available and can provide higher powers.

Finally, we investigate the physical conditions for considered case of HHG
in a bilayer graphene. Let us study the coherent interaction of bilayer
graphene with a pump wave in the ultrafast excitation regime, which is
correct only for the times $t<\tau _{\min }$, where $\tau _{\min }$\ is the
minimum of all relaxation times. For the excitations of energies $\mathcal{E
\ll \gamma _{1}=0.39$\ $\mathrm{eV}$, the dominant mechanism for relaxation
will be electron-phonon coupling via longitudinal acoustic phonons \cit
{Hwang}, \cite{Viljas}. For the low-temperature limit $T\ll 2\left( c_{ph}
\mathrm{v}_{F}\right) \sqrt{\mathcal{E}\gamma _{1}}$, where $c_{ph}\simeq
2\times 10^{6}$\ $\mathrm{cm/s}$\ is the velocity of the longitudinal
acoustic phonon, the relaxation time for the energy level $\mathcal{E}$\ can
be estimated as \cite{Viljas}:
 \begin{figure}[tbp]
\includegraphics[width=0.7\textwidth]{figure5.eps}
\caption{(a) Second $G_{2}$ and (b) third $G_{3}$ harmonic emission
rate (in arbitrary units) for bilayer graphene versus $\hbar \protect\omega $
for various intensities. The temperature is taken to be $T/\hbar \protec
\omega =0.4$, and the band gap $U=4$ $\mathrm{meV}$. The effective
field is assumed to be linearly polarized along the $y$ axis. }
\label{555}
\end{figure}
\begin{equation}
\tau \left( \mathcal{E}\right) \simeq \left( \frac{\pi D^{2}T^{2}}{8\rho
_{m}\hbar ^{3}c_{ph}^{3}\mathrm{v}_{F}}\sqrt{\frac{\gamma _{1}}{\mathcal{E}}
\right) ^{-1}.  \label{form1}
\end{equation}

Here $D\simeq 20$\ $\mathrm{eV}$\ is the electron-phonon coupling constant
and $\rho _{m}\simeq 15\times 10^{-8}$\ $\mathrm{g/cm}^{2}$\ is the mass
density of the bilayer graphene. For $\mathcal{E}\simeq 0.9$\ $\mathrm{meV}$
at the temperatures $T=0.4\hbar \omega $, from Eq. (\ref{form1}) we obtain
\tau \simeq 50$\ $\mathrm{ps}$. Thus, in this energy range one can
coherently manipulate with multiphoton transitions in bilayer graphene on
the time scales $t\precsim 50\mathrm{ps}$, not taking into account the
particle-particle collisions.

Note that the transition currents with comparing the intrinsic graphene
j_{0}$ \cite{Mer}, \cite{Mer1}, for a bilayer graphene is larger by a factor
$\left( \gamma _{1}/2\hbar \omega \right) ^{1/2}$. Besides, the cutoff
harmonic is larger than in case of a monolayer graphene \cite{Mer}, which is
a result of strong nonlinearity caused by trigonal warping. Hence, for
considered setups $\hbar \omega \ll \gamma _{1}$ the harmonics' radiation
intensity is at least one order of magnitude larger than in the monolayer
graphene.

\section{Conclusion}

We have presented the microscopic theory of nonlinear interaction of the
gapped bilayer graphene with a strong coherent radiation field at low-energy
photon Lifshitz transitions. The closed set of differential equations for
the single-particle density matrix is solved numerically for a bilayer
graphene in the Dirac cone approximation. For the pump wave, the sub-THz
frequency range has been taken. Such waves can be produced by the two
linearly polarized plane electromagnetic waves of the same frequencies,
propagating in opposite. We have considered nonadiabatic wave-induced
Lifshitz transitions of Fermi-Dirac sea towards the HHG. It has been shown
that the role of the gap in the nonlinear optical response of bilayer
graphene is quite considerable. In particular, even-order nonlinear
processes are present in contrast to intrinsic bilayer graphene, the cutoff
of harmonics increases, and harmonic emission processes become robust
against the temperature increase. The obtained results show that the gapped
bilayer graphene can serve as an effective medium for the generation of even
and odd high harmonics in the THz and sub-THz domain of frequencies, which
is sufficient for a new high-speed wireless communication systems\
development \cite{subTHz}, \cite{subTHz1}. The obtained results certify that
the process of high-harmonic generation for sub-THz photons (wavelengths
from $0.3$ $\mathrm{mm}\ $to $1$ $\mathrm{mm}$) can already be observed for
intensities $I_{\chi }=1-10^{3}\mathrm{\ Wcm}^{-2}$ at the temperature of
the sample $T<\hbar \omega $. So, bilayer graphene is a very tunable
material. The features, such as the Lifshitz transition, can be largely
influenced by external parameters such as strain, magnetic fields, or even
displacement static electric fields, like to considering case. Bilayer
graphene represents therefore a unique system in which the topology of the
band structure can be externally influenced and chosen.

\section{Appendix}

Here we present the Liouville--von Neumann equation for a single-particle
density matri
\begin{equation}
\rho _{\alpha ,\beta }(\mathbf{p},t)=\langle \widehat{a}_{\mathbf{p},\beta
}^{+}\left( t\right) \widehat{a}_{\mathbf{p},\alpha }\left( t\right) \rangle
,  \label{17}
\end{equation
where $\widehat{a}_{\mathbf{p},\alpha }\left( t\right) $ obeys the
Heisenberg equatio
\begin{equation}
i\hbar \frac{\partial \widehat{a}_{\mathbf{p},\alpha }\left( t\right) }
\partial t}=\left[ \widehat{a}_{\mathbf{p},\alpha }\left( t\right) ,\widehat
H}\right] .  \label{18}
\end{equation
Note that due to the homogeneity of the problem we only need the $\mathbf{p}
-diagonal elements of the density matrix. Thus, taking into account Eqs.
\ref{13})-(\ref{18}), the evolutionary equation will b

\begin{equation*}
i\hbar \frac{\partial \rho _{\alpha ,\beta }(\mathbf{p},t)}{\partial t
-i\hbar e\mathbf{E}\left( t\right) \frac{\partial \rho _{\alpha ,\beta }
\mathbf{p},t)}{\partial \mathbf{p}}=
\end{equation*
\begin{equation*}
\left( \mathcal{E}_{\alpha }\left( \mathbf{p}\right) -\mathcal{E}_{\beta
}\left( \mathbf{p}\right) -i\hbar \Gamma \left( 1-\delta _{\alpha \beta
}\right) \right) \rho _{\alpha ,\beta }(\mathbf{p},t)
\end{equation*
\begin{equation*}
+\mathbf{E}\left( t\right) \left( \mathbf{D}_{\mathrm{m}}\left( \alpha
\mathbf{p}\right) -\mathbf{D}_{\mathrm{m}}\left( \beta ,\mathbf{p}\right)
\right) \rho _{\alpha ,\beta }(\mathbf{p},t)
\end{equation*
\begin{equation}
+\mathbf{E}\left( t\right) \left[ \mathbf{D}_{\mathrm{t}}\left( \alpha
\mathbf{p}\right) \rho _{-\alpha ,\beta }(\mathbf{p},t)-\mathbf{D}_{\mathrm{
}}\left( -\beta ,\mathbf{p}\right) \rho _{\alpha ,-\beta }(\mathbf{p},t
\right] ,  \label{19}
\end{equation
where $\Gamma $ is the damping rate. In Eq. (\ref{19}) the diagonal elements
represent particle distribution functions for conduction $N_{c}(\mathbf{p
,t)=\rho _{1,1}(\mathbf{p},t)$ and valence $N_{\mathrm{v}}(\mathbf{p
,t)=\rho _{-1,-1}(\mathbf{p},t)$ bands, and the nondiagonal elements are
interband polarization $\rho _{1,-1}(\mathbf{p},t)=P(\mathbf{p},t)$ and its
complex conjugate $\rho _{-1,1}(\mathbf{p},t)=P^{\ast }(\mathbf{p},t)$.
Thus, we need to solve the closed set of differential equations for these
quantities

\begin{equation*}
i\hbar \frac{\partial N_{c}(\mathbf{p},t)}{\partial t}-i\hbar e\mathbf{E
\left( t\right) \frac{\partial N_{c}(\mathbf{p},t)}{\partial \mathbf{p}}=
\end{equation*
\begin{equation}
\mathbf{E}\left( t\right) \mathbf{D}_{\mathrm{t}}\left( \mathbf{p}\right)
P^{\ast }(\mathbf{p},t)-\mathbf{E}\left( t\right) \mathbf{D}_{\mathrm{t
}^{\ast }\left( \mathbf{p}\right) P(\mathbf{p},t),  \label{20}
\end{equation
\begin{equation*}
i\hbar \frac{\partial N_{\mathrm{v}}(\mathbf{p},t)}{\partial t}-i\hbar
\mathbf{E}\left( t\right) \frac{\partial N_{\mathrm{v}}(\mathbf{p},t)}
\partial \mathbf{p}}=
\end{equation*
\begin{equation}
-\mathbf{E}\left( t\right) \mathbf{D}_{\mathrm{t}}\left( \mathbf{p}\right)
P^{\ast }(\mathbf{p},t)+\mathbf{E}\left( t\right) \mathbf{D}_{\mathrm{t
}^{\ast }\left( \mathbf{p}\right) P(\mathbf{p},t),  \label{21}
\end{equation
\begin{equation*}
i\hbar \frac{\partial P(\mathbf{p},t)}{\partial t}-i\hbar e\mathbf{E}\left(
t\right) \frac{\partial P(\mathbf{p},t)}{\partial \mathbf{p}}=
\end{equation*
\begin{equation*}
\left[ 2\mathcal{E}_{1}\left( \mathbf{p}\right) +\mathbf{E}\left( t\right)
\mathbf{D}_{\mathrm{m}}\left( \mathbf{p}\right) -i\hbar \Gamma \right] P
\mathbf{p},t)
\end{equation*
\begin{equation}
+\mathbf{E}\left( t\right) \mathbf{D}_{\mathrm{t}}\left( \mathbf{p}\right)
\left[ N_{\mathrm{v}}(\mathbf{p},t)-N_{c}(\mathbf{p},t)\right] ,  \label{22}
\end{equation
The components of the transition dipole moments are calculated via Eq. (\re
{15}) by spinor wave functions (\ref{4})

\begin{equation*}
D_{\mathrm{t}x}\left( \mathbf{p}\right) =-\frac{e\hbar }{2\mathcal{E
_{1}\left( \mathbf{p}\right) \sqrt{\mathcal{E}_{1}^{2}\left( \mathbf{p
\right) -\frac{U^{2}}{4}}}
\end{equation*

\begin{equation*}
\mathbf{\times }\left( \left[ \left( \frac{p^{2}}{2m}-m\mathrm{v
_{3}^{2}\right) \frac{\zeta p_{y}}{m}+\frac{\mathrm{v}_{3}}{m}p_{x}p_{y
\right] \right.
\end{equation*
\begin{equation}
\left. -i\frac{U}{2\mathcal{E}_{1}}\left\{ \left( \frac{p^{2}}{2m}+m\mathrm{
}_{3}^{2}\right) \frac{p_{x}}{m}-\frac{3\zeta \mathrm{v}_{3}}{2m}\left(
p_{x}^{2}-p_{y}^{2}\right) \right\} \right) ,  \label{27}
\end{equation
\begin{equation*}
D_{\mathrm{t}y}\left( \mathbf{p}\right) =-\frac{e\hbar }{2\mathcal{E
_{1}\left( \mathbf{p}\right) \sqrt{\mathcal{E}_{1}^{2}\left( \mathbf{p
\right) -\frac{U^{2}}{4}}}
\end{equation*
\begin{equation*}
\times \left( \left[ \left( -\frac{p^{2}}{2m}+m\mathrm{v}_{3}^{2}\right)
\frac{\zeta p_{x}}{m}+\frac{\mathrm{v}_{3}}{2m}\left(
p_{x}^{2}-p_{y}^{2}\right) \right] \right.
\end{equation*
\begin{equation}
\left. -i\frac{U}{2\mathcal{E}_{1}}\left\{ \left( \frac{p^{2}}{2m}+m\mathrm{
}_{3}^{2}\right) \frac{p_{y}}{m}+\frac{3\zeta \mathrm{v}_{3}}{m
p_{x}p_{y}\right\} \right) .  \label{28}
\end{equation
The total mean dipole moments ar

\begin{equation*}
D_{x\mathrm{m}}\left( \mathbf{p}\right) =D_{x\mathrm{m}}\left( 1,\mathbf{p
\right) -D_{x\mathrm{m}}\left( -1,\mathbf{p}\right) =-\frac{e\hbar U}{
\mathcal{E}_{1}\left( \mathbf{p}\right) \left( \mathcal{E}_{1}^{2}\left(
\mathbf{p}\right) -\frac{U^{2}}{4}\right) }
\end{equation*
\begin{equation}
\mathbf{\times }\left[ \left( \frac{p^{2}}{2m}-m\mathrm{v}_{3}^{2}\right)
\frac{\zeta p_{y}}{m}+\frac{\mathrm{v}_{3}}{m}p_{x}p_{y}\right] ,  \label{29}
\end{equation
\begin{equation*}
D_{y\mathrm{m}}\left( \mathbf{p}\right) =D_{y\mathrm{m}}\left( 1,\mathbf{p
\right) -D_{y\mathrm{m}}\left( -1,\mathbf{p}\right) =-\frac{e\hbar U}{
\mathcal{E}_{1}\left( \mathbf{p}\right) \left( \mathcal{E}_{1}^{2}\left(
\mathbf{p}\right) -\frac{U^{2}}{4}\right) }
\end{equation*
\begin{equation}
\times \left[ \left( -\frac{p^{2}}{2m}+m\mathrm{v}_{3}^{2}\right) \frac
\zeta p_{x}}{m}+\frac{\mathrm{v}_{3}}{2m}\left( p_{x}^{2}-p_{y}^{2}\right)
\right] .  \label{30}
\end{equation
Note, that the velocity operator is defined by the relation $\widehat
\mathbf{v}}_{\zeta }=\partial \widehat{H}/\partial \widehat{\mathbf{p}}$.
After the simple calculations for the effective $2\times 2$ Hamiltonian (\re
{1}), the velocity operator in components can be presented by the
expressions
\begin{equation}
\widehat{\mathrm{v}}_{\zeta x}=\zeta \left(
\begin{array}{cc}
0 & -\frac{1}{m}\left( \zeta \widehat{p}_{x}-i\widehat{p}_{y}\right)
\mathrm{v}_{3} \\
-\frac{1}{m}\left( \zeta \widehat{p}_{x}+i\widehat{p}_{y}\right) +\mathrm{v
_{3} &
\end{array
\right) ,  \label{51}
\end{equation
\begin{equation}
\widehat{\mathrm{v}}_{\zeta y}=i\left(
\begin{array}{cc}
0 & \frac{1}{m}\left( \zeta \widehat{p}_{x}-i\widehat{p}_{y}\right) +\mathrm
v}_{3} \\
-\frac{1}{m}\left( \zeta \widehat{p}_{x}+i\widehat{p}_{y}\right) -\mathrm{v
_{3} &
\end{array
\right) .  \label{52}
\end{equation
The intraband velocity $\mathbf{V}_{1}\left( \mathbf{p}\right) $ at HHG in
bilayer $AB$-stacked graphene is given by the formula:
\begin{equation}
\mathbf{V}_{1}\left( \mathbf{p}\right) =\frac{\mathrm{v}_{3}\mathbf{p}-3\zeta
\frac{\mathrm{v}_{3}p}{2m}\mathbf{p}\cos 3\vartheta +3\zeta \frac{\mathrm{v
_{3}p^{3}}{2m}\sin 3\vartheta \frac{\partial \vartheta }{\partial \mathbf{p}
+2\frac{\mathbf{p}^{3}}{\left( 2m\right) ^{2}}}{\mathcal{E}_{1}\left(
\mathbf{p}\right) }.  \label{Vp}
\end{equation}

\begin{acknowledgments}
The authors are deeply grateful to prof. H. K. Avetissian for permanent discussions and valuable recommendations.
This work was supported by the RA MES Science Committee.
\end{acknowledgments}

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Pandemic cancelled world's biggest showcase of new electronic gadgets last year
People walk through the lobby of the Las Vegas Convention Center during set up for CES 2022 in Las Vegas, Nev., on Monday. This year marks the first time the Consumer Electronics Show has been staged since before the pandemic began.
Photo: Radio-Canada / Stephane Anctil
Posted: January 4, 2022 8:43 PM
With thousands descending on Las Vegas this week for a glimpse of the latest gadgets and innovations at the Consumer Electronics Show (CES), organizers offered the media a glimpse of what's in store when the world's biggest tech and gadget showcase officially opens on Wednesday.
With concerns growing over the spread of the highly transmissible Omicron variant that has seen companies such as Amazon.com Inc. and General Motors Co. drop out of attending the Las Vegas event in person, organizers said there was still a lot on offer at the 2022 show.
We are thrilled to be back in Las Vegas where we belong after a two year absence for the platform for innovation globally, said Gary Shapiro, president of the Consumer Technology Association (CTA).
There's a whole plethora of different things, from robotics to artificial intelligence to 5G to non-fungible tokens (NFTs), to many other technologies, including food technology, space technology. So many things that we focused on that we haven't before that have changed in just a couple of years, he said.
Top dogs will have to wait as Westminster dog show postponed due to COVID (new window)
As worries over the new variant loom, many companies have withdrawn from presenting at the event, planned both virtually and in-person, that begins on Jan. 5 with over 2,200 exhibitors. The spread of Omicron has also made many reconsider their travel plans after thousands of flight cancellations.
Smaller attendance expected
Last month, organizers were anticipating between 50,000 and 75,000 attendees for this week's conference, down from more than 170,000 who came for the last in-person gathering two years ago.
But those guesses were made before the full force of Omicron hit the U.S. The country recorded more than a million new cases (new window) on Monday, a new record.
As much as I'm a cheerleader for the technology industry, I recognize you have to be face-to-face with people. There isn't a CEO I've spoken to around the world who doesn't agree with that statement, said Shapiro, about why he was determined to have an in-person event this year.
Over the last week, a host of firms, including Advanced Micro Devices, Proctor & Gamble, Alphabet Inc's Google, Facebook parent Meta Platforms, have also dropped their in-person plans.
Sony Group's Sony Electronics has said it will have limited staffing and attendees at the event.
All attendees in Las Vegas will be required to be fully vaccinated and masked. COVID-19 test kits will also be provided at the venue, according to a statement from CTA.
World junior hockey tournament cancelled as more players test positive for COVID-19 (new window)
Even without a pandemic to dampen the party, tech industry analyst Carolina Milanesi said big industry events like this are becoming less important than they used to be as digital technology has supplied other ways to network and keep up with trends.
Milanesi has regularly attended CES for a decade and while she briefly considered not coming, she ultimately decided to attend, but plans to do things differently — visiting the exhibition halls but skipping big speaking events she can watch from her hotel room.
I haven't decided yet on the cocktail hours, she said. That's a big reason to go to CES and meet people face to face. With a glass in your hand, people get a little more comfortable discussing things.
Thomson Reuters with files from CBC News and The Associated Press
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text:
Córrego São Rafael é um rio brasileiro do estado de São Paulo. Passa pelo município de São Carlos.

São Rafael, Córrego
São Rafael

redpajama_set_name: RedPajamaWikipedia


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I really like the first picture, how you picked up the light. I haven't seen any blooming around here, it's still to cold.
What a beautiful group of Spring time pictures! I wish we had flowers popping up around here, but it will be while.
Stopping by as I crawl through the TOS Homeschool Crew blogs.
What beautiful pictures! I was strolling by on the Blog Walk and I'm so glad I did. The photos are refreshing and make me long for Spring! I became a follower and I look forward to seeing more lovely photography. God Bless!
Beautiful Dafodil Pictures! Blog Hoppin on the Crew Hop!
These are such lovely pictures. Thank you for sharing them.
I'm passing by from the Blog Walk and I saw your note in our forum. I don't see anything wrong now with your blog. I think it's just great!
I'm dropping by on the TOS Blog Walk. I'm following you via GFC.


Reviews the book `The Grolier Student Encyclopedia of Endangered Species,' edited by Diane Chando Frenick.
Reviews the book "Grolier Student Encyclopedia."
Reviews the book "Grolier Student Encyclopedia," by .
Reviews the book "Grolier Student Encyclopedia".
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Q: How can I display time with leading zeros? I have created a time function to calculate time as media is playing. It does not display any leading zeros. How can I make it display any leading zeros?
function converttoTime(timeInSeconds)
   {
    var minutes = Math.round(Math.floor(timeInSeconds / 60));
    var seconds = Math.round(timeInSeconds - minutes * 60);
    //var hours = Math.round(Math.floor(timeInSeconds / 3600));
    //time = time - hours * 3600;
    var time=minutes+':'+seconds;
    return time;
   }

A: this should work:
var time=('0'  + minutes).slice(-2)+':'+('0' + seconds).slice(-2);

redpajama_set_name: RedPajamaStackExchange


text:
Believe it or not, your CO can order you to be a human guinea pig
By Chase Millsap
Many of us have heard the expression, "Canary in a coal mine." It refers to a time when miners would carry caged birds with them as they entered mine tunnels. If the miners encountered dangerous gases such as carbon monoxide, the gases would kill …
U.S., allies warn Syria against chemical attack in new offensive
By Radio Free Europe Radio Liberty
The United States, France, and Britain are warning Syrian President Bashar al-Assad not to use chemical weapons as he launches a campaign to retake the last remaining rebel-held province in Syria.
In a joint statement issued late on Aug. 21, 2…
The US used two new weapons in the latest strike on Syria
Massive missile strikes conducted by US, UK, and French air and naval assets on April 13, 2018, hit three targets that were allegedly related to the Syrian government's chemical weapons program. The strikes appear to have been largely successful.
How Syria is bringing France's Macron and Trump closer
French President Emmanuel Macron said that he was the mastermind behind Donald Trump's airstrike on Syria, and has persuaded him to station troops in the country for the long term.
In a major interview broadcast April 15, 2018, on BFMTV, Macr…
Strikes on Syria were a public spanking of the Assad regime
President Donald Trump pulled off a large-scale attack on sites thought to contribute to Syria's chemical weapons program — but even the Pentagon acknowledges the attack's limitations.
The Pentagon says the strikes, made by the US, France,…
Everything you need to know about the British plan to join an attack on Syria
Theresa May will hold a crunch Cabinet meeting on April 12, 2018, in which she and her ministers will decide whether to join military action in Syria.
The prime minister will seek her Cabinet's approval to join with Donald Trump's US in laun…
Russia threatened Israel over its recent strikes in Syria
Russian President Vladimir Putin called his Israeli counterpart Benjamin Netanyahu on April 11, 2018, and warned the country against airstrikes in Syria.
The Kremlin released a statement verifying the call, and said Putin "emphasized the impo…
Trump warns Russia to be prepared for an all-out strike in Syria
The US and Russia, the world's two most powerful militaries and biggest nuclear powers, appear set to clash over a suspected chemical weapons attack in Syria, with President Donald Trump tweeting on April 11, 2018, for Russia to "get ready" for a…


If you are waiting on an important call but you have errands to run, you may opt to forward your home calls to your cell phone. Forwarding your home calls will allow you to answer the call the same as you would if you were on your phone. It does require, however, that you have a forwarding service on your account. If you do not have a forwarding service, contact your home phone provider and have one added.
Dial "*72" or "72#" on your home phone and "1172" on a rotary phone. Listen for the dial tone.
Enter your cell phone number and listen for a series of tones followed by ringing. This indicates that you have forwarded your number.
Answer your cell phone when it rings. This will activate the call waiting on your line. If the line on your cell phone is busy or you are unable to answer the call, repeat steps 1 and 2 to set up call forwarding without having to answer your cell phone.
Turn off call forwarding by dialing "*73" or "73#" on your home phone and "1173" on a rotary phone. Listen for the series of tones to confirm that your call forwarding is turned off.


Located in Macau's central Nam Van gaming district, the 33-storey MGM Grand Macau is three hotels rolled into one comprising discrete sections of standard rooms, suites, and penultimate mansions, expressed as counter-undulating slab blocks stacked straight-forwardly on top of one another. The disjointing provides the freedom for the different room types to take on their optimal planning and structural grid while emphasizing their respective uniqueness. Signature-coloured curtain wall in rose, white and yellow gold corresponding to rising order of exclusivity cumulating with the mansions in yellow gold at the top, projecting a dramatic elegance amongst the sensory-saturated background.
The heart of the 3-storey casino podium is a lofty sun-drenched conservatory, lushly landscaped and modeled on a historical Portuguese town square with authentic atmosphere of an open outdoor space providing a popular setting for events ranging from fashion shows, exhibitions to grand talk-of-the-town parties.


Leonid Thenor has more than 20 years of experience representing domestic and foreign clients in a variety of intellectual property matters. His technical expertise includes a wide array of technologies with a focus in the areas of computer, software, electrical and satellite technologies. Leonid has prepared and prosecuted a large number of patent applications, both domestically and internationally, and he has counseled clients on the procurement of patents as well as strategic development of patent portfolios. Leonid also has experience providing invalidity and non-infringement opinions.as well as representing patent litigation at both the district and appellate court levels.
Prior to joining Jones Robb, Leonid worked for several Northern Virginia intellectual property boutiques and in the D.C. offices of several prominent international law firms.


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Evanston candidates shine in Oakton race; Martha Gaines top vote getter in Ridgeville, where one incumbent may be out.
From left, Dan Coyne, Stephanie Teterycz and Rob Bady at a post-election party on April 2.
Evanston Township/District 202 School Board member Monique Parsons, seeking another term on the high school board, and Martha Gaines, vying for return to the Ridgeville Park District Board after a nearly six-year break, were among the big winners Election Day April 2, with the third seat on the Ridgeville Board still undecided.
Ms. Parsons and newcomers Elizabeth Rolewicz and Stephanie Teterycz were elected to four-year terms on the District 202 Board.
Evanston candidates also turned in strong performances for Oakton Community College board, landing on top of a 13-candidate field for the three open seats.
Unofficial results for that race showed Gail Bush, with 9,622 votes or 13.61% of the vote, Wendy Yanow, with 8,399 votes or 11.88%, and Marie Lynn Toussaint, with 7,635 votes or 10.80%, as the top vote-getters with all precincts reporting.
Michele Hays, another Evanston resident, registered a strong initial run for office, garnering 6,419 votes, or 9.08% of the vote, finishing just outside the trio.
Ridgeville Park District, a separate taxing district from the City and located in south Evanston, provided the closest race of the day.
Mr. Coyne and Mr. Bady – friends and active together in a number of initiatives locally, including an out-front fight against what they perceived as nepotism at the small district – were tied with 950 votes as of Wednesday morning with results back from all 16 precincts.
Mr. Coyne said Wednesday that Evanston City Clerk Devon Reid informed him that some still uncounted mail-in ballots may figure in the results.
In the meantime, Mr. Coyne said he and Mr. Bady planned to get together later in the day "to make sure one of us is on the board and help the new board join the 21st century."
Unofficial results show Ms. Gaines leading the way with 1,103 votes or 27.83% and Mr. Mitchell receiving 960 votes or 24.22%.
Mr. Coyne and Mr. Bady were 10 votes behind Mr. Mitchell, whom they had backed, collaboratively canvassing for signatures and posting on Facebook, highlighting their support. "I do believe Matt's presence on the board is a game-changer – his legal expertise will significant improve decorum, policy and programs," Mr. Coyne said.
In District 202, Ms. Parsons, vice president of the Board, was easily the top vote getter, with 4,057 or 31.36%, votes, repeating her performance in her run for office in 2015, where she also led the field.
Her top priorities include attempting to increase resources to support the well-being and emotional development of students; a reassessment of the joint literacy effectiveness between District 65, the elementary district, and District 202; and continuing to be a good steward of the District resources."
Ms. Rolewicz brings a background in educational advocacy. Her top priorities serving on the ETHS District 202 Board is to address "the persistent problem of race predicting outcomes, through auditing curriculum, disciplinary policy, and racial basis within our systems," she said in response to questions from the RoundTable staff, compiling profiles.
Ms. Teterycz's background includes nearly 20 years on staff at Northwestern University in various capacities, including serving as director of the school's summer session. If elected to the board, she stated her primary goal "is to champion the extraordinary equity work that the high school has been doing for several years. The Board must be fully aligned with the administration to promote a thoroughly equitable, accessible and inclusive culture that elevates all students and addresses systemic barriers to academic achievement and opportunity."


Steam or grill your hot dog until cooked. Set aside.
If you have a steaming basket, steam your hot dog buns.
The next steps are very important. A Chicago Dog needs to be stacked in this order: Place hot dog in the bun. Then add yellow mustard, sweet green pickle relish, onion, tomato wedges, pickle spear, sport peppers and last sprinkle celery salt. Remember, no ketchup! They also say to dress the dog, not the bun.
Cooks' Note: I've been to Chicago once, for exactly 24 hours. While I was there I ordered a "regular" hot dog and to my surprise, the regular hot dog came with all these fixings! First time I've ever had tomatoes with my Hot Dog. It was a nice "Welcome to Chicago" moment!


Know the dangers of wandering in nursing homes | Mark L. Karno & Associates, L.L.C.
On behalf of Mark L. Karno & Associates, L.L.C. posted in Nursing Home Abuse and Neglect on Thursday, March 9, 2017.
Choosing a good nursing home for your loved one is probably a taxing or emotional process. You want to make sure your loved one is safe and receives proper care. Nursing home abuse may be a concern when making a choice, but you should also look into a home's security and ability to prevent wandering and elopement.
What are the risks of wandering?
Whenever a resident wanders the home without supervision, their chance of slipping and falling greatly increases. This can cause bruising, broken bones or other severe injuries. They may also have trouble standing or returning to their room without help.
Elopement is an even riskier situation. Elopement refers to a resident wandering out of the facility itself. This could not only lead to injury but there is also the potential for a resident to wander away and get lost if they are not spotted and brought back immediately.
There are many reasons a resident could try to wander the home unattended. If they have Alzheimer's or dementia, they may forget where they are and believe there is something they have to do. Wandering may also be a response to discomfort from the new environment or a medication change. Some residents may wander to find a restroom if there is not enough staff to attend to them, or if they have a sleeping disorder and are restless.
How can I prevent the risk of wandering?
You should also have very open communication. If your loved one has a condition that could put them at increased risk of wandering, such as Alzheimer's, inform the nursing home. Ask questions before you make a final decision and make sure safety and security measures are in place. You have every right to ask about alarms, safety protocol and other info that could affect your loved one's care there.


Click "Install" to install the latest version of the game. (This warning box may or may not appear, depending on your security settings.) If you saw the warning box . All Games > Bejeweled 2 Deluxe Developer: PopCap Games, Inc. Includes 5 items: Bejeweled 2 Deluxe, Insaniquarium Deluxe, Peggle Deluxe, Peggle™. Bejeweled 2 is one of the most popular puzzle games ever created! Experience this awesome match 3 puzzle game by downloading and playing the free.
22 Jun - 4 min - Uploaded by Turbo Volcano Classic Game Room HD reviews BEJEWELED 2 DELUXE for PC from PopCap games. This. Bejeweled latest version: Highly addcitive gem puzzle action. Bejeweled Deluxe 2 It's a classic match-3 game where you have to simply match 3 gems to. Adapted from its predecessor, Bejeweled 2 features four unique ways to play. Software · Games · Sudoku, Crossword & Puzzle Games; Bejeweled 2 Deluxe.
Bejeweled 2 is a tile-matching puzzle video game. The sequel to Bejeweled, it was developed and published by PopCap Games. In , Bejeweled 2 Deluxe . New Mac Version of Bejeweled 2 Deluxe Available today! Bejeweled 2 Deluxe end of game, 0, Bejeweled 2 Deluxe won't run on Windows 8, 2, 3, Play Free Bejeweled 2 Deluxe Online. Dig the fast and furious gem-matching fun in this simple, yet insidiously addictive puzzle game. Switch the gems to. 5 Nov Bejeweled 2 Deluxe brings the classic puzzle game to the Xbox but doesn't make enough significant changes to make it stand out from the. 29 Nov Bejeweled 2 Deluxe brings the classic puzzle game to the Xbox but doesn't make enough significant changes to make it stand out from the.
Bejeweled 2 is great!!! When one thinks about a great game that becomes even better, one can include it on their list. The new features are more than just fun. For Bejeweled 2 Deluxe on the PC, GameFAQs has 18 cheat codes and secrets. gems to the ones used in the original Bejeweled/Diamond Mine online game. What is BEJEWELED 2 DELUXE? The game you're playing now is just a sample of the full. Deluxe BEJEWELED 2 game, reduced in size and features. for play. The classic game of gem-swapping reaches a new dimension of fun! Adapted from the original masterpiece, Bejeweled 2 Deluxe features 4 brand new and.
And don't forget Time Bombs and a brand-new Endless mode. Discover secret game modes, get hints when you want them, and enjoy mesmerizing music and. 20 Aug Bejeweled 2 Deluxe free download. Get the latest version now. Classic game of gem-swapping euphoric new heights!. Discover secret game modes; Stunning 3d special effects and higher resolutions; Four ways to play: Classic, Action, Puzzle and Endless; Explore a galaxy of. Bejeweled 2 Game:Deluxe - Kindle edition by Malik Adams. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like.


Last week, the House adopted its fiscal year (FY) 2016 budget resolution by a vote of 228-199. Seventeen Republicans joined every Democrat in voting against the resolution. The Senate has also approved its Republican budget in a 52-46 vote. Sen. Ted Cruz (R-Texas) and Sen. Rand Paul (R-Ky.) were the only Republicans to vote against the budget blueprint. Sen. Dianne Feinstein (D-Calif.) and Sen. Barbara Mikulski (D-Md.) abstained from voting. No Democrats voted in support of the Republican budget. The vote followed a long series of amendment votes on revisions to the resolution. Though the amendments, like the budget itself, are non-binding, they indicate the chamber's stance on the legislative agenda for the coming year. Senators proposed 85 health-related amendments among the nearly 800 amendments filed. In total, the Senate considered and voted on 49 amendments over the course of 15 hours. Sen. David Vitter's (R-La.) amendment to require that all members of Congress, the President, Vice President, and their appointees obtain exchange-based insurance passed 52-46. The Senate also passed a Medicare amendment from Senate Finance Committee Chairman Orrin Hatch (R-Utah), which would create a deficit-neutral reserve fund to protect the Medicare program, but it would be up to the Senate Finance Committee to produce any legislation making changes to the Medicare program. Speaking to a long-standing criticism of the Congressional Budget Office (CBO), Sen. Rob Portman's (R-Ohio) amendment would ensure the use of dynamic scoring for major tax and spending legislation and passed by a vote of 59-41. The Senate did not opt to debate the Affordable Care Act's (ACA) 30-hour workweek definition, the Independent Payment Advisory Board (IPAB), or the medical device tax, mostly due to the fact that the budget proposal already assumes a full repeal of the health care law. Since both the House and Senate passed their budget resolutions, the chambers will conference to reconcile budgetary measures leading up to the April 15 statutory deadline for Congress to complete action on a budget plan. The conference debate will consider reconciliation language, which differs between the two chambers' budgets. If Congress is successful in negotiating and passing a joint conference agreement, Republicans will be able to use the reconciliation procedure to attempt repeal of the ACA. Bills considered using reconciliation rules cannot be filibustered by the Senate.


The distinctive logo of the Descente brand has been present on a number of very important cycling teams through history including the TI Raleigh, Panasonic, Cilo/Aufina, 7-Eleven, CSC and more recently AG2r.
The company name Descente is the French term for downhill skiing and the now iconic logo represents the three basic skiing techniques of schussing, traversing and sliding.
This pink jersey was produced in 2006 to celebrate Ivan Basso`s victory in the Giro D`Italia.