== Elements == The '''chemical elements''' are the basic '''atoms''', from which all chemical compounds are made. All chemical elements are listed in the [http://en.wikipedia.org/wiki/Periodic_table Periodic Table of Elements]. Each has an atomic number, the number of protons in that atom. Hydrogen (H) has one proton in its nucleus, Helium (He) has 2, and so on. The '''atomic mass''' is roughly the number of protons + neutrons (plus a little more for the electrons and the fact that a neutron is slightly more massive than a proton). Most light atoms have the same number of neutrons as protons. So the atomic mass of He is (2 protons + 2 neutrons) roughly 4 (plus a little more). The '''exceptions''' are (1) Hydrogen, which is found most often as a proton with an electron and no neutron, and (2) the heaviest elements, which need more neutrons to glue the atom together keeping the protons from repelling each other. For example, copper has an atomic number of 29 (29 protons) but an atomic mass, not of 58 but of 63 meaning it has 34 neutrons. (Specifically one atomic mass unit equals 1/12th the mass of a carbon atom, but it is easiest just to look up the atomic mass on the Periodic Table.) Atoms are normally '''neutral''', that is there are the same number of protons (positive charges) in an atom, as there are electrons (negative charges). If an atom has too many or too few electrons, it is called an '''ion'''. If there are too many electrons it is a negative ion (since electrons have a negative charge.) If it has too few electrons it is a positive ion. Dissolve table salt in water and the NaCl molecule becomes Na+and Cl- in solution. In the Earth's atmosphere, N2  (nitrogen molecule) and O2 (oxygen molecule) may lose an electron when struck by a cosmic ray and become the ions N2+ and O2+. Sunlight and starlight can ionize elements and compounds. In interstellar gas, neutral H atoms may become H+, a bare proton with no electron. If positive ions and negative ions are adjacent, and the environment is right, they will naturally [http://www.youtube.com/watch?v=xTx_DWboEVs&NR=1 combine]. Another way elements can combine to form compounds is by [http://www.youtube.com/watch?v=1wpDicW_MQQ covalent bonding], sharing electrons. Chemical elements combine to make chemical compounds, such as water [http://en.wikipedia.org/wiki/Water_%28molecule%29 (H2O)] or olivine ( ( [http://en.wikipedia.org/wiki/Magnesium Mg] [http://en.wikipedia.org/wiki/Iron Fe] )2 [http://en.wikipedia.org/wiki/Silicon Si][http://en.wikipedia.org/wiki/Oxygen O]4) and organic compounds such as '''amino acids''' which make up proteins, and '''nucleotide bases''' (purines and pyrimidines) which make up [http://en.wikipedia.org/wiki/DNA DNA] and [http://en.wikipedia.org/wiki/RNA RNA] ... the building blocks of Life. [[File:atom2.jpg|300px]] An atom of helium, a chemical element Periodic Table of Chemical Elements [[File:periodic_table_text.jpg|600px]] Elements formed during the Big Bang, by fusion in stars, and by shockwaves in supernovae == Origins of Elements == '''The Big Bang''' At the time of the '''Big Bang''', '''pressure''' and '''temperatures''' were such that subatomic particles could form. As conditions changed so did the types of particles that formed. Electrons, quarks, protons and neutrons, all happened in a fraction of a second. Helium ions, 2 protons and 2 neutrons in one nucleus, were present after 3 minutes. Not until 300,000 years later was the universe cool enough to allow protons, helium and other nuclei to capture electrons to create atoms of hydrogen, and helium, and traces of lithium and beryllium. To this day the most abundant element in the universe is still hydrogen. It shows up as a magenta color in many star forming nebulae, such as the Horsehead Nebula where hydrogen is reacting with starlight. The dark absorbing cloud that forms the familiar shape and blocks our view of stars behind the nebula, is dust, mostly made of carbon. [[File:horsehead.jpg|600px]] Exaggerated magenta-colored ionized hydrogen in the Horsehead Nebula T.A.Rector (NOAO/AURA/NSF) and Hubble Heritage Team (STScI/AURA/NASA) '''Fusion in Stars''' As gravity pulled the hydrogen and helium together the earliest stars formed. Fusion inside stars would convert hydrogen (H) to more helium (He), then to carbon (C), and depending on the size of the star, the process might continue up to iron (Fe), but nothing heavier could fuse in a star and still release energy. [[File:stars_m103_kpno_big.jpg|600px]] Stars in M 103 fusing elements When small stars die they spew out these new heavier elements. These are caught up in later star-forming nebulae, so that solid planets may form around second and third generation stars. The carbon in the Horsehead Nebula came from inside stars. [[File:nebulae.jpg|600px]] Planetary nebulae from dying stars throwing off their outer layers '''Shock Waves in Supernovae''' When giant stars die, they not only send out elements up to iron, but in the [http://en.wikipedia.org/wiki/Shock_wave shockwaves] from their explosive supernova, create elements heavier than iron, such as silver (Ag), gold (Au), and platinum (Pt). [[File:elements_supernovae.jpg|600px]] Supernova remnants: Crab Nebula and remnants from a pair of Supernovae DEM L316 Credit: Gemini Observatory In the dense early Universe the first stars would have been huge. The larger the stars, the more gravitational pressure, and the faster they use up their fuel. These giant stars lasted only a few million years, then exploded in violent supernovae. Supernova remnants would fly out into space, to be caught up by later generations of stars. Copper (Cu), zinc (Zn), and iodine (I), were among the elements made in supernovae, elements which in trace amounts are necessary for Life. [[File:supernova_remnant_velaweb3.jpg|600px]] Vela supernova remnants [http://youtu.be/m5TwT69i1lU Every living thing] is made of bits of Big Bang (H), chemicals fused in stars (O) (C), and bits of Supernova remnants (Cu) ! Every living thing has stardust in it. == Origins of Chemical Compounds == '''''But where did water ( H2O ), olivine ( ( Mg, Fe )2SiO4 ), and amino acids (such as C3H5NO ) come from?''''' When dying stars explode and make beautiful planetary nebulae and supernova remnants, they spew out heavy elements that had been fused in their cores. [[File:elements_dumbbell_noao_big.jpg|600px]] Dumbbell Nebula (M27), a "planetary" nebula from a dying star [[File:elements_knots_dumbell_nebula_hs-2003-06-a-large_web.jpg|600px]] Detail of the Dumbbell Nebula showing knots of heavy elements flying out from the dying star In the intense heat inside a star, chemical compounds cannot form, but as dense clouds of gas and dust are kicked out into space they cool. When conditions and temperature are right, elements bond and create compounds. The denser the environment, the more likely elements are to collide and form compounds. This may happen either in gaseous knots, or in [http://apod.nasa.gov/apod/ap030127.html Bok globules] in giant star-forming nebulae where dust may be seen gathering under the influence of its own gravity (below), or in '''protoplanetary disks''' where dust is collecting to form stars and their planets. We can tell what compounds are present in the molecular clouds of star forming nebulae, because patterns show up in their spectra just they do for the atomic elements. [[File:starbirth_nebula_hs-2007-04-a-xlarge_web.jpg|600px]] Nebula in Large Magellanic Cloud where stars are forming [[File:bok_globule_opo0613a.jpg|600px]] Bok Globules before they become protoplanetary disks [[File:protoplanetary_diskm42proplyds.jpg|600px]] Protoplanetary disks, where future planets are forming around future stars, in the Orion Nebula '''Water''' [[File:water_ocean_compressed.jpg|600px]] Water (H2O) Everyone's favorite compound is water. H2O forms naturally in space, through chemical reactions on the surface of dust grains and in cold dense gas. Water on the cold dust remains ice as long as it is cold, eventually finding its way into the disk from which planets form. NASA has an [http://www.sofia.usra.edu/ airborn observatory] to study how this happens. The processes that determine water formation and destruction depend on temperature. You know that hydrogen "burns", and in the presence of oxygen it will self ignite at 550 C (1022 F) and form water. In the protoplanetary disk, from which the solar system formed, water was present in large quantities. It was ice in the cold outer regions, and gas was where it was warmer, closer to the early Sun. Above 3000 C water will dissociate into OH and H, so there is no water in the atmosphere of the Sun or close to it. However, even when it is cold, unprotected by a planetary atmosphere or by dust in the disk, water is dissociated by sunlight. Its oxygen and hydrogen atoms are ionized, and blown out by the solar wind. Small bodies like Mercury or the Moon had too little gravity to hold on to water, and no atmosphere to prevent its dissociation and loss. In the outer solar system, water and ice were retained by some of the satellites of Jupiter and Saturn. The Oort Cloud, a remant of the solar nebula, is where icy comets still reside. In thick protective atmospheres, water could have been held by early planets until they were cool enough to have rain. This, and comets, would continue to bring water to the busy early solar system, enough water to fill the oceans. The Earth still has its water and is warm enough for liquid oceans. Colder Mars also has its water, hidden as ice under the soil. '''Olivine and Pallasite Meteorites''' [[File:fukang-full-lg.jpg|600px]] A pallasite meteorite Olivine ((Mg,Fe)2SiO4) would also form in the protoplanetary nebula. If a planet or asteroid is large enough, it forms layers differentiating different minerals, with heaviest elements, usually iron, in the center. In a powerful enough collision, the iron, with a lower melting point than olivine, melts around the fragments of olivine. Together they fly out making beautiful pallasites. It is possible to get an idea of the energy in an impact of this sort by the heat that is generated, which would be above the melting point of iron, 1535 C, but not so hot as to melt olivine, 1760 C. [[File:imilac-meteorite6494-cp.jpg|600px]] Molten iron envelops pieces of olivine (which in its pure form is the gemstone peridot) in a pallasite meteorite '''Organic Compunds such as Amino Acids and Nucleotide Bases''' [[File:murchison_crop.jpg|600px]] The Murchison Meteorite [http://en.wikipedia.org/wiki/Carbonaceous_chondrite Carbonaceous chondrites] are a type of meteorite known to contain high concentrations of water and organic compounds. The [http://en.wikipedia.org/wiki/Murchison_meteorite Murchison Meteorite], which fell near Murchison, Australia, in 1969, has been found to contain over 100 [http://en.wikipedia.org/wiki/Amino_acid amino acids], some rarely seen on Earth, and also [http://en.wikipedia.org/wiki/Purine purines] and [http://en.wikipedia.org/wiki/Pyrimidine pyrimidines], nucleotide bases that are building blocks of DNA and RNA. This discovery shows that amino acids and components of the genetic code, were already present in the early solar system, available not only to Earth but to other planets and moons as well. In addition to organic chemicals coming via meteorites, seventeen of the twenty amino acids have been produced in the laboratory, in [http://news.bbc.co.uk/2/hi/science/nature/7675193.stm experiments simulating the early Earth], complete with water, heat, and an electric spark for lightning. Amino acids are made up simply of hydrogen (H), carbon (C), oxygen (O), and nitrogen (N), and occasionally sulfur (S). [[File:aminoacidsweb3.jpg|600px]] Amino acids are alike and different While amino acids are the building blocks of '''proteins''', purines and pyrimidines (also called nucleobases or nucleotide bases) are the building blocks of '''DNA''' and '''RNA'''. They, also, are simple compounds of hydrogen (H), carbon (C), oxygen (O), and nitrogen (N), all found in the interstellar gas from which stars and planets form. [[File:dna_purines_pyrimidines_fig2.jpg|600px]] Purines and pyrimidines are building blocks of DNA and RNA These [http://en.wikipedia.org/wiki/Nucleobases nucleotide bases] are abbreviated A,G,C, T, and U. A, G, C, T make DNA A, G, C, U make RNA When strung together they make the genetic code: all of which formed in the early solar nebula, and all of which could have landed on any planet or moon. Since these happened around our star, it is likely that organic molecules formed around other stars as well, making life a definite possibility elsewhere in the Universe.
Return to Periodic Table of the Elements.


CAC translated Mr. Ayers's radicalism into practice. Instead of funding schools directly, it required schools to affiliate with "external partners," which actually got the money. Proposals from groups focused on math/science achievement were turned down. Instead CAC disbursed money through various far-left community organizers, such as the Association of Community Organizations for Reform Now (or ACORN). SEE MY WEB LOG ON ACORN AND VOTER REGISTRATION FRAUD.


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Today is a big day for visualization. We are excited to welcome Ondra, Adam, Jaroslav and the entire Render Legion team to Chaos Group! Corona is fast, it's easy to use, and renders beautifully. From the beginning, our mission has been to help all artists and designers visualize anything they can imagine, and to push the boundaries of what rendering can do. Render Legion shares this same vision and together we believe that great visualization benefits us all.
The first thing you should know is both Corona and V-Ray are here to stay. Both products will continue to be developed independently by the same teams that you've come to trust, with the same level of innovation that you've come to expect. Now we can share ideas, research and technology to make both renderers as powerful as possible.
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text:
\section{Introduction}

The study of time-dependent quantum problems
has been of great interest in the literature since the work of  Lewis
and Riesenfeld \cite{lewis,LewRie69},  in the late $1960$s.
They developed a completely general  approach to the evolution
generated by a time-dependent Hamiltonian $H(t)$;
one re-obtains the results of the adiabatic
approximation in the case of slowly varying $H(t)$, and the results
of the ``sudden'' approximation in the case of  fast or even
discontinuously varying $H(t)$. In  Refs.\cite{lewis} and \cite{LewRie69},
the method was applied to a one-dimensional harmonic oscillator
with a $t$-dependent frequency and to a charged particle
in a $t$-dependent, axially symmetric electromagnetic field in
three dimensions. For zero electric field, the latter reduces
to a Landau problem with time-dependent magnetic field.
Several other applications of the method
have been worked out later; we just mention the application in
 \cite{GueLea77}
to the anisotropic three-dimensional harmonic oscillator, the ones
\cite{Lea78} to the damped harmonic oscillator and to a
\cite{LuaTan05} linear (in space) potential in one dimension.
In the present work, we apply the approach of Lewis and
Riesenfeld to a two-dimensional isotropic harmonic oscillator
with time-dependent mass $M$ and frequency $\Omega$
in a time-dependent (but space-independent
magnetic field) $B$ [formula (\ref{Mt})] [the term
$\Omega^2 x\!\cdot\! x$ in the Hamiltonian may contain,
in particular, an electric potential of the form
$\varphi(x)=\frac{e\eta(t)}{2M(t)c^2}x\!\cdot\! x$
\cite{Chee09}, \cite{footnote}]
for $\Omega\equiv 0$,
this reduces to a Landau problem with time-dependent mass $M,B$.
In the Coulomb gauge, the Hamiltonian can be rewritten as
the sum of the Hamiltonian of a harmonic oscillator
with suitable time-dependent mass $\mu$ and frequency $\omega$
and of the angular momentum $L$ multiplied by a suitable
time-dependent  coefficient $\nu$ [formula (\ref{hmt})].
In either case the model can be immediately embedded in a
three-dimensional one where $B$ is directed along the third direction, and
the motion in the direction of the latter is free; the latter
would describe, in particular, a charged particle in a suitable $t$-dependent
axially symmetric electromagnetic field (as in \cite{LewRie69}, but with a possibly
$t$-dependent mass).

The results can be applied also to a two dimensional
isotropic harmonic oscillator with time-dependent $M,\Omega,B$ on the
(canonical) {\it non-commutative} plane [formula (\ref{hMt})]. In fact,
the Hamiltonian can be again rewritten in the same form (\ref{hmt})
with new parameters $\mu,\omega,\nu$ involving also the deformation
parameter $\theta$ of the non-commutative plane in their definition.
Non-commutative space-time structure is an old subject dating back
over fifty years to Snyder \cite{sny}. The analysis of field theories
on non-commutative space-times has become a promising area
in theoretical physics \cite{doug}, and also  non-commutative quantum mechanics
has become subject for intense investigations. In the recent works \cite{laure}
the formulation, interpretation and applications of non-commutative quantum
mechanics have been investigated in configuration space, with the explicit
example of the (time-independent) two-dimensional harmonic oscillator
in \cite{laure}, or general Hamiltonians (including
the one of the Landau problem) in \cite{Fio10}, where an approach
to second quantization is also proposed.

In section $2$, we define the model and use the socalled Bopp-shift
to connect the noncommutative variables to the commutative ones.
In section $3$, we determine two commuting invariant observables $L,I$
($L$ is the angular momentum) in terms of
some solution of an auxiliary nonlinear ordinary differential
equation. In section $4$, we determine
an orthonormal basis of the Hilbert space consisting of joint eigenvectors of  $L,I$;
the presence of the parameter of noncommutativity $\theta$
does not modify much the results.
Then, we determine suitable time-dependent phase factors such that
their products with these joint eigenvectors make up
an orthonormal basis of the Hilbert space consisting of
solutions of the Schr\"odinger equation. Each phase factor
can be split as the product  of a  dynamical one and
geometric one (including the Berry phase) \cite{Berry84 - AhaAna87}.
The latter includes, in general, the effects of the socalled adiabatic
operator; the latter multiplied by the socalled dynamical operator
and the non-adiabatic one gives a decomposition of the evolution operator,
as explained e.g., in the introduction of \cite{Chee10}
(see also \cite{Messiah}).

\medskip
In the rest of this introduction,
we briefly recall the general Lewis-Riesenfeld approach to time-dependent
quantum mechanics \cite{LewRie69}. An operator
$I(t)$ is said to be an invariant if
\begin{eqnarray}\label{eq}
 \dot I(t) \equiv \frac{\partial}{\partial t} I(t) +
\frac{1}{i\hbar}\left[I(t), H(t)\right] = 0
\end{eqnarray}
(note that $H$ itself is not an invariant unless it is time-independent).
Here and in the sequel we use the Schr\"odinger ({\it not} the Heisenberg)
picture.  If $I(t)$  is  an invariant and
$\psi(t)$ solves the Schr\"odinger equation
\begin{equation}\label{Schr}
i\hbar\frac{\partial\psi}{\partial t} (t)=H(t)\psi(t),
\end{equation}
then also $I(t)\psi(t)$ does. If in addition $I(t)$ is hermitian,
then there exists a (in general time-dependent) orthonormal basis
$\{\varphi_{\lambda,\kappa}\}$ of
eigenvectors of $I$ with real eigenvalues $\lambda\in\Lambda$;
these eigenvectors are parameterized by  $\lambda\in\Lambda$
and if necessary  by some additional label $\kappa\in K$.
Deriving the relation $I\varphi_{\lambda,\kappa}=\lambda\varphi_{\lambda,\kappa}$
with respect to $t$ and using (\ref{eq}),
(\ref{Schr}) one finds that all eigenvalues $\lambda$ are
time-independent. Moreover, adjusting the phase, the $\varphi_{\lambda,\kappa}$
can be chosen so as to be a complete set of solutions of (\ref{Schr}),
provided $I$ does not contain the operator $\partial_t$
(for instance, operators of the form $I=\alpha\partial_t$ are not allowed).
If $H$ is time-independent and we choose
a time-independent $I$, then eq. (\ref{eq})
amounts to $[I,H]=0$, and
the above scheme amounts to finding a complete set of
solutions of  (\ref{Schr}) in the form of eigenvectors
of both $I$ and $H$, as usual.

\section{The model}

The Hamiltonian for the two dimensional isotropic harmonic oscillator
in a  magnetic field reads
\begin{eqnarray}\label{Mt}
 H_{hm}(t) &=& \frac{1}{2M(t)}\,[p\!-\!eA(t)]\cdot[p\!-\!eA(t)]
+\frac{M(t)\Omega^2(t)}{2}\, x\cdot x\\
 &=&\frac{1}{2M(t)}\left[\left(p_1\!+\!\frac e2
B(t)x_2\right)\!^2 + \left(p_2\!-\!\frac e2 B(t)x_1\right)\!^2\right]
+\frac{M(t)\Omega^2(t)}2\left( x^2_1 + x^2_2\right);\nonumber
\end{eqnarray}
we assume piecewise
continuously time-dependent mass $M$, frequency $\Omega$
and but magnetic field $B$ (assumed space-independent).
The second line holds after expressing the vector potential in
Coulomb gauge. As said, for $\Omega\equiv 0$
this reduces to a Landau problem with time-dependent mass $M,B$,
\begin{equation}
 H_L(t) = \frac{[p\!-\!eA(t)]\cdot[p\!-\!eA(t)]}{2M(t)}
=\frac{1}{2M(t)}\left[\left(p_1\!+\!\frac e2
B(t)x_2\right)^2 + \left(p_2\!-\!\frac e2 B(t)x_1\right)^2\right].
\end{equation}
We use units such that $\hbar = 1$ and $x_a,p_a,\omega$ are
dimensionless
(this can be achieved renormalizing as usual the latter variables
by dimensionful factors built out of
some constant mass $m_0$ and frequency $\omega_0$, and $\hbar$).
Using the canonical commutation relations
$[x_a,x_b]=0=[p_a,p_b]$, $[x_a,p_b]=i\delta_{ab}$
it is straightforwad to check that $H_{hm}(t)$ reduces to
\begin{eqnarray}\nonumber
 H(t) &=& \frac{1}{2\mu(t)}\,p\cdot p
+\frac{\omega^2(t)}{2}\, x\cdot x- \frac{\nu(t)}{2}L \\
&=&\frac{1}{2\mu(t)}\left(p_1^2 + p_2^2\right)
+\frac{\omega^2(t)}2\left( x^2_1 + x^2_2\right)- \nu(t)L,\label{hmt}
\end{eqnarray}
where $L = x_1p_2 -x_2p_1$ is the angular momentum, and
\begin{equation}
\mu(t):=M(t), \qquad \omega^2(t):=M(t)\Omega^2(t)\!+\!
\frac {[eB(t)]^2}{4M(t)}, \qquad \nu(t):=\frac {eB(t)}{2M(t)}.
\label{parameters1}
\end{equation}

Our two-dimensional non-commutative space is defined by
noncommuting coordinates   $\hat X_1, \hat X_2$
and associated momentum components $\hat P_1, \hat P_2$ satisfying
the following commutation relations:
\begin{eqnarray}
 \left[\hat X_1,\hat X_2 \right] = i\theta,\quad
\left[\hat X_1,\hat P_1 \right]  = i,\quad
\left[\hat X_2,\hat P_2 \right]  = i,\quad
\left[\hat P_1,\hat P_2 \right]  = 0.
\end{eqnarray}
All these operators are hermitian. On such a non-commutative space
we consider as a Hamiltonian that of a two dimensional  isotropic harmonic oscillator
in a  magnetic field with $t$-dependent $M,\Omega,B$,
\begin{equation}\label{hMt}
\hat H_{hm}(t) =\frac{1}{2M(t)}\left[\left(\hat P_1\!+\!\frac e2
B(t)\hat X_2\right)\!^2 + \left(\hat P_2\!-\!
\frac e2 B(t)\hat X_1\right)\!^2\right]
+\frac{M(t)\Omega^2(t)}2\left( \hat X^2_1 + \hat X^2_2\right).
\end{equation}
The aim is to find two independent invariants and then solve
the Schr\"odinger equation within each eigenspace of the latter.
We redefine the operators as follows
\begin{eqnarray}
x_1 = \hat X_1 +\frac{\theta}{2}\hat P_2,\qquad
x_2 = \hat X_2 -\frac{\theta}{2}\hat P_1,\qquad
p_1 = \hat P_1,\qquad
p_2 = \hat P_2;
\end{eqnarray}
the associated commutations relations are
\begin{eqnarray}
\left[x_1, x_2\right] = 0,\qquad
\left[x_1, p_1\right] = i,\qquad
\left[x_2, p_2\right] = i,\qquad
\left[p_1, p_2\right] = 0.
\end{eqnarray}
Such a redefinition is sometimes also called the Bopp shift. In
terms of these new operators $\hat H_{hm}(t) $
reduces again to (\ref{hmt}), where now
\begin{equation}
\mu^{-1}:=\frac {[4\!+\!eB\theta]^2}{16M}\!+\!M\Omega^2\frac {\theta^2}{4},
\qquad \omega^2:=M\Omega^2\!+\!
\frac {[eB]^2}{4M}, \qquad -\nu:=\frac {[4\!+\!eB\theta]eB}{8M}
\!+\!\frac {M\Omega^2\theta}2.
\end{equation}
(we have omitted the time dependence for brevity).
Note that in general $\mu,\omega$ are $t$-independent only if all of
$M,B,\Omega$ are.

Therefore for $B(t)\equiv 0$, we obtain the harmonic oscillator
with time-dependent frequency and mass, while
for $\Omega(t)\equiv 0$ we obtain the Landau problem with time-dependent
frequency and mass, both on the commutative and noncommutative plane.

An operator invariant of the model (\ref{hmt}) is an operator
that satisfies eq. (\ref{eq}).

\section{Derivation of the operator invariants}

As $x\!\cdot\! x,\, p\!\cdot\! p,\,x\!\cdot\! p,\,p\!\cdot\! x$,
and therefore $H$, are explicitly symmetric under rotations,
they commute  with the generator of rotations $L$,
\begin{equation}
[L,x\!\cdot\! x]=0,\quad [L,p\!\cdot\! p]=0,\quad
[L,x\!\cdot\! p]=0,\quad [L,p\!\cdot\! x]=0,\quad
[L,H]=0.                         \label{rotsym}
\end{equation}
Since $L$  is also time-independent, it fulfills
(\ref{eq}) and is a first operator
invariant. In order to find another one $I(t)$
commuting with $L$, we make the Ansatz
\begin{eqnarray}
\nonumber\label{eq11}
I(t) &=& \alpha(t)\,x\cdot x
+\beta(t)\,p\cdot p
+\gamma(t)\left(x\cdot p+p\cdot x \right)+\delta(t)L\\[8pt]
&=&\alpha(t)\left( x_1^2 +  x_2^2\right)
+\beta(t)\left( p_1^2 + p_2^2 \right)
+\gamma(t)\left(\{x_1,p_1\}
+ \{x_2,p_2\}\right)+\delta(t)L,
\end{eqnarray}
where $\{x_1,p_1\} = x_1 p_1 + p_1 x_1$, $\{x_2,p_2\} =
x_2 p_2 + p_2 x_2$.
As we need $I(t)$ to be hermitean, $I^\dagger = I$, the
coefficients $\alpha,\:\beta,\gamma,\delta$
 should be real. As said,
\begin{equation} \label{ILcom}
 [I, L] = 0,
\end{equation}
because $I$ is manifestly symmetric under
rotations. Using (\ref{rotsym}) and
$$
\begin{array}{llll}
\left[x_1^2, p_1^2 \right] = 2i\{ x_1, p_1 \},\qquad &
\left[x_1^2, \{ x_1, p_1 \} \right] = 4i x_1^2,\qquad &
\left[p_1^2, \{ x_1, p_1 \} \right] = -4i p_1^2, \\[8pt]
\left[x_2^2, p_2^2 \right] = 2i\{ x_2, p_2 \},\qquad  &
\left[x_2^2, \{ x_2, p_2 \} \right] = 4i x_2^2,\qquad &
\left[p_2^2, \{ x_2, p_2 \} \right] = -4i p_2^2,
\end{array}
$$
Eq. (\ref{eq}) reduces to
\begin{eqnarray}\label{eq1}
\dot \alpha - 2\omega^2\gamma  &=& 0,\\\label{eq2} \dot \beta +
\frac 2\mu \gamma &=& 0,\\\label{eq3} \dot \gamma + \frac 1\mu \alpha - \omega^2
\beta  &=& 0,\\\label{delta} \dot\delta &=& 0.
\end{eqnarray}
Eq. (\ref{delta})
implies that $\delta$ is a constant.
The solution of the system (\ref{eq1})-(\ref{delta})
with $\delta=1$ and all the other coefficients vanishing
is the already determined invariant $L$.
In the rest of the text, we choose $\delta = 0$ for the other invariant.
From (\ref{eq1})-(\ref{eq3}) it follows
\begin{equation}
 \frac{d}{dt}\left(\gamma^2 -\alpha\beta \right) = 0,
\end{equation}
whence
\begin{equation}\label{eq13}
 \gamma^2 - \alpha\beta = -\kappa^2,
\end{equation}
where $\kappa$ is either a real or an imaginary constant
(so that $\kappa^2$ is real).

\medskip
Since $I(t)$ and $L$ commute, they have joint eigenvectors.
One can find all of the latter using the same
operator technique as in Ref. \cite{lewis}, that is the Dirac method of
diagonalizing the Hamiltonian of a constant-frequency harmonic oscillator.
To this end, we choose a positive $\kappa$,
stick to positive-definite solutions $\beta(t)$ and
introduce an auxiliary real-valued function $\sigma(t)$ such that
\begin{equation}\label{eq5}
\beta (t) = \sigma^2(t);
\end{equation}
then by Eqs. (\ref{eq2}) and (\ref{eq13})
\begin{equation}\label{eq6}
 \gamma = -\mu\sigma\dot\sigma,
\qquad  \qquad
 \alpha = \dot\sigma^2 \mu^2 +\frac{\kappa^2}{\sigma^2}.
\end{equation}
Replacing (\ref{eq5}), (\ref{eq6}) in
(\ref{eq3}), we find that the system (\ref{eq1}-\ref{eq3})
is equivalent to the auxiliary equation
\begin{eqnarray}\label{neq1}
 \ddot{\sigma} +\frac{\dot \mu}{\mu}\dot\sigma
+ \frac{\omega^2}{\mu}\sigma =  \frac{\kappa^2}{\mu^2\sigma^3}.
\end{eqnarray}
In terms of a real solution $\sigma(t)$ of (\ref{neq1}) the  operator
invariant (\ref{eq11}) takes the form
\begin{eqnarray}\label{eq14}
I (t) = \left( \dot\sigma\mu x_1 -\sigma p_1\right)^2
+\frac{\kappa^2}{\sigma^2} x_1^2 + \left( \dot\sigma\mu
x_2 -\sigma p_2\right)^2 +\frac{\kappa^2}{\sigma^2} x_2^2.
\end{eqnarray}

\section{Eigenstates of $I(t)$ and the phases}

We can introduce ``raising'' and ``lowering '' operators
$a_1,\: a_2,\: a_1^\dagger,\: a_2^\dagger$ by
\begin{eqnarray}
 a_a(t) = \frac{1}{\sqrt{2\kappa}}
\left(\dot\sigma\mu x_a -\sigma p_a +
i\frac{\kappa}{\sigma} x_a\right), \qquad \quad a_a^\dagger(t) =
\frac{1}{\sqrt{2\kappa}}  \left(\dot\sigma\mu x_a -
\sigma p_a - i\frac{\kappa}{\sigma} x_a\right),\label{g1}
\end{eqnarray}
with $a=1,2$.
They fulfill the commutation relations
\begin{eqnarray}
 [a_1,\:a_1^\dagger] = 1,\quad [a_2,\:a_2^\dagger] = 1,\quad
[a_1,\: a_2] = 0,\quad [a_1,\:a_2^\dagger] = 0.
\end{eqnarray}
Then the operator invariants $I,L$ can be written as
\begin{equation}
 I_{-}(t) = 2\kappa\left(a_1^\dagger a_1  +
 a_2^\dagger a_2 + 1\right),
\qquad \qquad L = i(a_2^\dagger a_1 - a_1^\dagger a_2).
\end{equation}
Instead of working with the $a_a,a_a^\dagger$ it is convenient
to work with  the left and right circular annihilation operators
$A_{-}, A_{+}$, that are
respectively defined by
\begin{equation}
 A_{-}(t) = \frac{1}{\sqrt{2}}\left(a_1 -i a_2 \right),\qquad\qquad
A_{+}(t) = \frac{1}{\sqrt{2}}\left(a_1 + i a_2 \right),
\end{equation}
and the left and right creation operators, that are the
hermitean conjugates of the above:
\begin{equation}\label{fin0}
 A_-^\dagger(t) = \frac{1}{\sqrt{2}} \left(a_1^\dagger +i a_2^\dagger \right),\qquad
\qquad A_+^\dagger(t) = \frac{1}{\sqrt{2}} \left(a_1^\dagger -i
a_2^\dagger \right).
\end{equation}
The only non-zero commutators among $A_{-},\, A_{+},\;
A_+^\dagger,\; A_-^\dagger$
 are then given by
\begin{equation}
 [A_{-}, A_-^\dagger] = 1,\qquad \qquad [A_{+}, A_+^\dagger] = 1.
\end{equation}
Using the inverse relations
\begin{eqnarray}\nonumber
 a_1 &=& \frac{\sqrt{2}}{2}(A_{-} + A_{+}),\qquad\qquad
a_1^\dagger = \frac{\sqrt{2}}{2}(A_+^\dagger + A_-^\dagger),\\
\nonumber a_2 &=& \frac{i\sqrt{2}}{2}(A_{-} - A_{+}),\qquad\qquad a_2^\dagger
= \frac{i\sqrt{2}}{2}(A_+^\dagger - A_-^\dagger),
\end{eqnarray}
we find
\begin{equation}
\begin{array}{ll}
 [I_{-},A_{\pm}] = -2\kappa,\qquad \qquad &[I_{-},A_{\pm}^\dagger] = 2\kappa,\\[8pt]
[L,A_{\pm}] = \pm A_{\pm},\qquad \qquad &[L,A_{\pm}^\dagger] = \mp A_{\pm}^\dagger,
\end{array}              \label{bla}
\end{equation}
and
\begin{equation}
 I_{-}(t) = 2\kappa (A_+^\dagger A_{+} + A_-^\dagger A_{-} + 1),
\qquad \qquad L = (A_-^\dagger A_{-} - A_+^\dagger A_{+}).
\end{equation}
Let us assume $\Vert 0,0 \rangle$  is a normalized state
annihilated by $a_1, a_2$, or equivalently by $A_\pm$:
\begin{equation}
 A_{-}\Vert 0,0 \rangle = 0, \qquad \qquad A_{+}\Vert 0,0 \rangle = 0.
\end{equation}
For any  $r_{+},\; r_{-}\in\b{N}_0$ ($\b{N}_0$ stands for
the set of nonnegative integers) we find
\begin{equation}
\begin{array}{l}
 I_{-}(t)(A_-^\dagger)^{r_{+}}(A_+^\dagger)^{r_{-}}\Vert 0,0 \rangle =
2\kappa (r_{+} + r_{-} + 1) (A_-^\dagger)^{r_{+}}(A_+^\dagger)^{r_{-}}\Vert 0,0 \rangle ,\\[6pt]
L(t)(A_-^\dagger)^{r_{+}}(A_+^\dagger)^{r_{-}}\Vert 0,0 \rangle =
(r_{+} -r_{-}) (A_-^\dagger)^{r_{+}}(A_+^\dagger)^{r_{-}}\Vert 0,0 \rangle.
\end{array}              \label{eigen}
\end{equation}
The pairs $(r_{+}, r_{-})$ are in one-to-one correspondence with the
pairs $(n,m)$, with $n,m$ defined by
\begin{equation}
n = r_{+} + r_{-}\in\b{N}_0,\qquad\qquad
m = r_{+} -r_{-}\in \{-n,2\!-\!n,...,n\!-\!2,n\}.   \label{defn}
\end{equation}
The inverse of (\ref{defn}) are
\begin{equation}
r_{+} = \frac{n+m}2 \in\b{N}_0,\qquad\qquad r_{-} =
\frac{n-m}2 \in\b{N}_0.             \label{invdefn}
\end{equation}
An orthonormal basis of the Hilbert space of states
of the system consists of
\begin{equation}
 \Vert  n,m \rangle = \mathcal{N}
(A_-^\dagger)^{\frac{1}{2}(n+m) }
(A_+^\dagger)^{\frac{1}{2}(n-m)}\Vert 0,0 \rangle ,
\qquad\quad
\mathcal{N}= \frac{1}{\sqrt{ \frac{n\!+\!m}2!}}\frac{1}{\sqrt{ \frac{n\!-\!m}2!}}
\end{equation}
which by  (\ref{eigen}) are eigenvectors of $I_{-}(t)$  and  $L$:
\begin{equation}
I \Vert  n,m \rangle =2\kappa (n+1) \Vert  n,m \rangle,\qquad\qquad
L\Vert  n,m \rangle =m \Vert  n,m \rangle. \label{eigenvalues}
\end{equation}
The action of $A_\pm,A_\pm^\dagger$ on the basis reads:
\begin{eqnarray}
&& A_+\Vert  n,m \rangle = \sqrt{\frac{n\!+\!m}2}\:
\Vert  n\!-\!1,m\!-\!1 \rangle,\qquad\quad
A_+^\dagger\Vert  n,m \rangle=\sqrt{\frac{n\!+\!m}2\!+\!1}\:
\Vert  n\!+\!1,m\!+\!1 \rangle,\\
&& A_-\Vert  n,m \rangle = \sqrt{\frac{n\!-\!m}2}\:
\Vert  n\!-\!1,m\!+\!1 \rangle,\qquad\quad
A_-^\dagger\Vert  n,m \rangle=
\sqrt{\frac{n\!-\!m}2\!+\!1}\: \Vert  n\!+\!1,m\!-\!1 \rangle.
\end{eqnarray}

By the general theory \cite{LewRie69}, one can transform the basis $\{\Vert  n,m \rangle\}$
into an orthonormal basis $\{ \psi_{n,m}\}$ consisting of solutions of the
equation  (\ref{Schr}) applying  suitable phase transformations
\begin{equation}
 \psi_{n,m} =  e^{i\alpha_{m,n}(t)}\Vert  n,m \rangle
\end{equation}
By the orthonormality of the basis, the Schr\"odinger equation
$$
 i \frac{\partial}{\partial t}\left(e^{i\alpha_{m,n}} \Vert n,m \rangle   \right)
= H e^{i\alpha_{n,m}}\Vert n,m\rangle
$$
reduces \cite{LewRie69} to the following equations for the
time-dependent coefficients $\alpha_{m,n}$
\begin{equation}\label{pha}
 \frac{d\alpha_{m,n}}{dt} = \langle n,m \Vert
 \left(i\frac{\partial}{\partial t} -H\right) \Vert n,m\rangle.
\end{equation}
One can thus split $\alpha_{m,n}$ into the sum
$\alpha_{m,n}=\alpha_{m,n}^g\!+\!\alpha_{m,n}^d$
of a geometric phase (including the Berry phase phenomenon
for slowly varying parameters)
\cite{Berry84,Sim83,AhaAna87} (see also \cite{MooShaWil89})
and a dynamical phase $\alpha^d_{m,n}$ respectively fulfilling
\begin{equation}\label{phagd}
 \dot\alpha^g_{m,n} = i\langle n,m \Vert
 \left(\frac{\partial}{\partial t} \Vert n,m\rangle\right),\qquad \qquad
\dot\alpha^d_{m,n} = -\langle n,m \Vert H \Vert n,m\rangle.
\end{equation}
To compute the matrix elements
$\langle n,m \Vert H \Vert n,m \rangle $, we express
$H$ in terms of $A_{\pm}, A_{\pm}^\dagger$. As a first step,

\begin{equation}\label{bb1}
\begin{array}{ll}
x_1 = \frac{-i}{\sqrt{2\kappa}}\sigma(a_1 -a_1^\dagger),
\qquad \quad & p_1 =\frac{-i}{\sqrt{2\kappa}}\dot\sigma\mu (a_1
-a_1^\dagger) - \frac{\sqrt{2\kappa}}{2\sigma}(a_1 +
a_1^\dagger),\\[8pt]
x_2 = \frac{-i}{\sqrt{2\kappa}}\sigma(a_2
-a_2^\dagger), \qquad \quad &
p_2 =\frac{-i}{\sqrt{2\kappa}}\dot\sigma\mu (a_2
-a_2^\dagger) - \frac{\sqrt{2\kappa}}{2\sigma}(a_2 + a_2^\dagger);
\end{array}
\end{equation}
in terms of $A_{-}, A_+^\dagger, A_{+},
A_-^\dagger$ we find
\begin{equation}
\begin{array}{l}
 x_1 = \frac{-i\sigma}{2\sqrt{\kappa}} \left( A_{-} \!-\!A_+^\dagger
\!+\! A_{+} \!-\! A_-^\dagger\right),\\[8pt]
p_1 = \frac{-i\dot\sigma\mu}{2\sqrt{\kappa}}\left(A_{-}
\!-\!A_+^\dagger \!+\!A_{+} \!-\! A_-^\dagger\right)
-\frac{\sqrt{\kappa}}{2\sigma}
\left(A_{-} \!+\! A_+^\dagger \!+\! A_{+} \!+\! A_-^\dagger\right),\\[8pt]
x_2 = \frac{\sigma}{2\sqrt{\kappa}}
\left(A_{-} \!-\! A_+^\dagger \!-\! A_{+} \!+\! A_-^\dagger\right),\\[8pt]
p_2 = \frac{\dot\sigma\mu}{2\sqrt{\kappa}}\left(A_{-} \!-\!A_+^\dagger
\!-\!A_{+} \!+\! A_-^\dagger\right) -i\frac{\sqrt{\kappa}}{2\sigma}
\left(A_{-} \!+\! A_+^\dagger \!-\! A_{+} \!-\!A_-^\dagger\right).
\end{array}
\end{equation}
and
\begin{equation}
\begin{array}{ll}
 x_1\!+\!ix_2 = \frac{i\sigma}{\sqrt{\kappa}}
\left(A_-^\dagger \!-\! A_{+} \right),\qquad &
p_1\!-\!ip_2 = \frac{i\dot\sigma\mu}{\sqrt{\kappa}}
\left(A_+^\dagger\!-\!A_{-}
\right)\!-\!\frac{\sqrt{\kappa}}{\sigma}
\left(A_{-} \!+\! A_+^\dagger \right),\\[8pt]
x_1\!-\!ix_2 = \frac{i\sigma}{\sqrt{\kappa}}
\left(A_+^\dagger \!-\! A_-\right),
\qquad  &
p_1\!+\!ip_2 = \frac{i\dot\sigma\mu}{\sqrt{\kappa}}
\left(A_-^\dagger
\!-\!A_{+} \right) \!-\!\frac{\sqrt{\kappa}}{\sigma}
\left(A_{+} \!+\!A_-^\dagger\right).
\end{array}
\end{equation}

Replacing these formulae in (\ref{hmt}) we find
\begin{eqnarray}
 H &=& \frac{1}{2\kappa}\!
\left(\dot\sigma^2\mu +\frac{\kappa^2}{\mu\sigma^2}
 +\omega^2\sigma^2 \!\right)\!
 \left(\!A_-^\dagger A_{-} + A_+^\dagger A_{+} +1 \!\right)\!-
 \nu\!\left(\!A_-^\dagger A_{-} -
A_+^\dagger A_{+}  \!\right)\\
&+&\left[\left(\frac{i\sigma\mu}{\sqrt{2\kappa}} +
\frac{\sqrt{\kappa}}{\sqrt{2}\sigma}\right)^2
\!\!-\frac{\omega^2\sigma^2}{2\kappa} \right]A_{-}A_{+} +
\left[\left(\frac{-i\sigma\mu}{\sqrt{2\kappa}} +
\frac{\sqrt{\kappa}}{\sqrt{2}\sigma}\right)^2
\!\!-\frac{\omega^2\sigma^2}{2\kappa}
\right]A_+^\dagger  A_-^\dagger.\nonumber
\end{eqnarray}
Only the operators in the first line
contribute to the matrix elements $\langle n,m \Vert H \Vert n,m \rangle $,
the ones in the second line lead to vanishing terms. So we finally find
\begin{eqnarray}
 \langle n,m \Vert H \Vert n,m \rangle = \frac{n+1}{2\kappa}
\left(\dot\sigma^2\mu +\frac{\kappa^2}{\mu\sigma^2}
 +\omega^2\sigma^2 \right)- m\nu.         \label{dyn}
\end{eqnarray}

Now we wish to evaluate
\begin{equation}\label{mat}
 \langle n,m \Vert \frac{\partial}{\partial t} \Vert n,m \rangle
= \mathcal{N} \langle n,m \Vert \frac{\partial}{\partial t} \left[
(A_-^\dagger)^{\frac{1}{2}(n+m) }
(A_+^\dagger)^{\frac{1}{2}(n-m)}\Vert 0,0 \rangle\right].
\end{equation}
$\Vert  0,0 \rangle$ is determined up to a time-independent phase.

On one hand, deriving (\ref{eigenvalues}) with $n\!=\!m\!=\!0$
with respect to $t$, we find
\begin{equation}
\left(\frac{\partial I}{\partial t}\right) \Vert  0,0 \rangle =
(2\kappa -I) \left(\frac{\partial}{\partial t}\Vert 0,0  \rangle\right),\qquad\qquad
L\left(\frac{\partial}{\partial t}\Vert 0,0  \rangle\right) =0. \label{der}
\end{equation}
As the left hand-side of (\ref{der})$_1$ is different from zero,
$\frac{\partial}{\partial t}\Vert 0,0  \rangle$ cannot vanish,
but must be annihilated by $L$. We determine it by realizing
 $ a_a,\Vert 0,0  \rangle$ in configuration space:
\begin{equation}
a_a= \frac{1}{\sqrt{2\kappa}}\left[
\left(\dot\sigma\mu \!+\!i\frac{\kappa}{\sigma} \right)x_a
+i\sigma \partial_a\right],\qquad\quad
\psi_0(x,t)=\frac {\kappa}{\sigma\sqrt{\pi}}
\exp\!\left[-\!\left(\frac {\kappa}{\sigma^2}\!-\!
\frac {i\dot\sigma\mu}{\sigma}\right)\!\frac {x\!\cdot\! x}2\right];
\label{config}
\end{equation}
in fact $\psi_0$ is annihilated by both $a_1,a_2$, therefore also by
$A_-,A_+$, and is normalized w.r.t. the scalar
product $(\psi,\psi')=\int\!d^2\!x \,\overline{\psi(x)} \psi'(x)$.
Deriving (\ref{config})$_2$ we find
$$
\frac{\partial\psi_0}{\partial t}(x)=
\left[\left(\frac{i\ddot\sigma\mu}{\sigma}
+ \frac{i\dot \mu\dot\sigma}{\sigma} -
\frac{i\dot\sigma^2\mu}{\sigma^2}+\frac{2\kappa\dot\sigma}{\sigma^3}
\right)\frac {x\!\cdot\! x}2-\frac{\dot\sigma}{\sigma}\right]\psi_0(x)
$$
By the Stokes theorem and some straightforward computations we obtain
$$
\int\!d^2\!x \,\partial_a(|\psi_0(x)|^2 x^a)=0
\qquad\Rightarrow\qquad
\int\!\!d^2\!x \,|\psi_0(x)|^2x\!\cdot\! x=\frac {\sigma^2}{\kappa}
\int\!\!d^2\!x \,|\psi_0(x)|^2=\frac {\sigma^2}{\kappa}.
$$
From the two previous equations we conclude
\begin{eqnarray}
\langle 0,0 \Vert\left(\frac{\partial}{\partial t}\Vert 0,0
\rangle\!\right) &=&\int\!\!d^2\!x \:\overline{\psi_0}
\,\frac{\partial\psi_0}{\partial t} =\int\!\!d^2\!x
\:\overline{\psi_0} \,\psi_0
\left[\left(\frac{i\ddot\sigma\mu}{\sigma} +\frac{i\dot
\mu\dot\sigma}{\sigma} -
\frac{i\dot\sigma^2\mu}{\sigma^2}+\frac{2\kappa\dot\sigma}{\sigma^3}
\right)\frac {x\!\cdot\! x}{2}-\frac{\dot\sigma}{\sigma}\right]
\nonumber\\
&=& \frac {i\mu}{2\kappa}\left(\sigma\ddot\sigma+
\frac{\dot \mu\sigma\dot\sigma}{\mu} -
\dot\sigma^2\right).   \label{conclude}
\end{eqnarray}
On the other hand,
\begin{eqnarray}
 \frac{\partial}{\partial t}
 \left[(A_-^\dagger)^{\frac{1}{2}(n+m) }
(A_+^\dagger)^{\frac{1}{2}(n-m)} \right]&=&
\frac{n+m}{2}\frac{\partial A_-^\dagger}{\partial t}
(A_-^\dagger)^{\frac{1}{2}(n+m-3) }
(A_+^\dagger)^{\frac{1}{2}(n-m)}\nonumber\\
&+& \frac{n-m}{2} (A_-^\dagger)^{\frac{1}{2}(n+m)} \frac{\partial
A_+^\dagger}{\partial t} (A_+^\dagger)^{\frac{1}{2}(n-m -2)};
\end{eqnarray}
but from  (\ref{fin0}) it follows
$$
 \frac{\partial A_-^\dagger}{\partial t}
=\frac{1}{\sqrt{2}}\frac{\partial a_{1}^\dagger}{\partial t} +
\frac{i}{\sqrt{2}}\frac{\partial a_{2}^\dagger}{\partial t},\qquad\qquad
\frac{\partial A_+^\dagger}{\partial t}
=\frac{1}{\sqrt{2}}\frac{\partial a_{1}^\dagger}{\partial t} -
\frac{i}{\sqrt{2}}\frac{\partial a_{2}^\dagger}{\partial t},
$$
and by equations (\ref{g1}),
\begin{eqnarray}
 \frac{\partial A_-^\dagger}{\partial t} &=&
\frac{1}{2\sqrt{\kappa}}\left[\left(\ddot\sigma\mu + \dot
\mu\dot\sigma +
i\frac{\kappa\dot\sigma}{\sigma^2}\right)(x_1+ix_2)
-\dot\sigma (p_1+ip_2)\right]\nonumber\\
&=&\frac{i\mu}{2\kappa}\left[\left(\sigma\ddot\sigma + \frac{\dot
\mu\dot\sigma}{\mu} -\dot\sigma^2\right)A_-^\dagger
-\left(\sigma\ddot\sigma + \frac{\dot
\mu\dot\sigma}{\mu} -\dot\sigma^2+\frac{2i\kappa\dot\sigma}
{\mu\sigma}\right)A_+\right],\label{deriv1}\\
 \frac{\partial A_+^\dagger}{\partial t} &=&
\frac{1}{2\sqrt{\kappa}}\left[\left(\ddot\sigma \mu +\dot
\mu\dot\sigma +
i\frac{\kappa\dot\sigma}{\sigma^2}\right)(x_1-ix_2)
-\dot\sigma (p_1-ip_2)\right]\nonumber\\
&=&\frac{i\mu}{2\kappa}\left[\left(\sigma\ddot\sigma + \frac{\dot
\mu\dot\sigma}{\mu} -\dot\sigma^2\right)A_+^\dagger
-\left(\sigma\ddot\sigma + \frac{\dot \mu\dot\sigma}{\mu} -
\dot\sigma^2+\frac{2i\kappa\dot\sigma}{\mu\sigma}\right) A_-\right].
\label{deriv2}
\end{eqnarray}
Inserting (\ref{conclude})-(\ref{deriv2}) into (\ref{mat})
and using (\ref{neq1}) we finally find
\begin{equation}
 \langle n,m \Vert \frac{\partial}{\partial t} \Vert n,m \rangle
=i \frac{n\!+\!1}{2\kappa}\left( \sigma\ddot\sigma\mu +
\dot \mu\sigma\dot\sigma - \dot\sigma^2\mu\right)=
i \frac{n\!+\!1}{2\kappa}\left( \frac{\kappa^2}{\mu\sigma^2} -
\omega^2\sigma^2-\dot\sigma^2\mu \right), \label{conclude2}
\end{equation}
as the operators $A_+,A_-$ give vanishing contributions to
the scalar product.
Replacing (\ref{dyn}) and  (\ref{conclude2}) in
 (\ref{pha}), the latter takes the form
\begin{equation}
 \frac{d\alpha_{n,m}}{dt} = -(n+1)\frac{\kappa}{\mu\sigma^2} +
m\nu
\end{equation}
(there is a partial cancellation of the geometric and dynamical phase
derivatives), which is solved by
\begin{equation}\label{phs}
\alpha_{n,m} (t)= -(n+1)\int^t \!\! dt'\:\frac{\kappa}{\mu(t')\sigma^2(t')} +
m\int^t \!\! dt'\:\nu(t').
\end{equation}

\section{Conclusions}
We have derived a class of exact invariants for the time-dependent, isotropic
two dimensional harmonic oscillator in a magnetic field,
both on commutative and noncommutative plane.
This applies also to the time-dependent
Landau problem (which is obtained choosing zero
harmonic oscillator frequency
$\Omega(t)$). The angular momentum $L$ (absent in the one dimensional
case treated in Refs. \cite{lewis}) is trivially another invariant.
Using these two invariants, we
have constructed and an orthonormal basis of the associated Hilbert
space consisting of solutions of the  time-dependent Schr\"odinger
equation. The presence of the noncommutative parameter $\theta$
or of a time-dependent mass does
not change too much the results with respect to the commutative
space with constant mass, but induces a first order derivative term in the auxiliary
equation (\ref{neq1}), that is a general form of the Ermakov-Pinney
equation in Refs.\cite{PenYan07}. When we set $\theta=0$, then the equation
(\ref{phs}) are the same as the results in \cite{LewRie69}, but in two
dimensions. For some choices of $\Omega(t)$, exact solutions of
(\ref{neq1}) can be found and then the corresponding solutions of
the Schr\"odinger equation in close form. It would be also good to
calculate the transition amplitude connecting any initial state in
the remote past to any final state in the remote future with
constant $\omega$; we hope to report
on this point elsewhere.

{\it{Note added in proof}}. In the final stage of publication of the
present paper Prof. Dodonov has brought to our attention the very
interesting papers,\cite{Malkin}, \cite{dodonov}, where among
other things exact invariants in the form of generalized creation
and annihilation operators for a general N-dimensional harmonic
oscillator were constructed.\\

\noindent{\bf Acknowledgments}

\noindent The work of one of us (L. G.) is supported by the
Associate and Federation Schemes and the HECAP Section of ICTP.

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text:
Bill Wyman, właściwie William George Perks (ur. 24 października 1936 w Londynie) – brytyjski muzyk rockowy, basista. Od grudnia 1962 do grudnia 1992 był basistą w zespole rockowym The Rolling Stones.

Życiorys
W wieku 10 lat rozpoczął 3-letnią naukę gry na fortepianie, potem sam uczył się gry na gitarze basowej.
Przed przystąpieniem do zespołu Rolling Stones grał na gitarze basowej w kilku lokalnych zespołach.

Był trzykrotnie żonaty. 24 października 1959 poślubił Diane Cory, z którą miał syna Stephana Paula. Jednak w 1969 doszło do rozwodu. W 1984, kiedy Wyman miał 48 lat, związał się z wówczas 13-letnią Mandy Smith, którą poznał za kulisami jednej z gal rozdania nagród muzycznych. Przez dwa lata ich związek pozostał w ścisłej tajemnicy, ale kiedy informacja została podana do wiadomości publicznej, stała się największym skandalem show-biznesu dekady. Jej matka zaakceptowała ten związek. W 2010, w wywiadzie dla "Daily Mail", Smith wyznała, że rozpoczęła stosunki seksualne z Wymanem, mając zaledwie 14 lat. 2 czerwca 1989 52-letni Wyman poślubił wtedy 18-letnią Smith. Na ich ślubie pojawili się m.in. Mick Jagger, Jerry Hall i Keith Richards. W 1991 rozwiedli się. 21 kwietnia 1993 ożenił się z Suzanne Accostą, z którą ma trzy córki: Katherine Noelle (ur. 1994), Jessicę Rose (ur. 1995) i Matildę May (ur. 1998).

Po odejściu z zespołu zaczął nagrywać solowe płyty oraz występować i nagrywać z Bill Wyman's Rhythm Kings.

W 2012 wystąpił ponownie (po 20 latach) z The Rolling Stones na koncertach w The O2 Arena w Londynie w ramach trasy 50 & Counting z okazji pięćdziesięciolecia powstania zespołu.

Dyskografia

albumy solowe
 Monkey Grip (czerwiec 1974)
 Stone Alone (marzec 1976)
 Bill Wyman (kwiecień 1982)
 Stuff (październik 1992 – Japonia i Argentyna, 2000 – Wielka Brytania)
 Back to Basics (22 czerwca 2015)

album wspólny
 Willie & The Poor Boys (maj 1985); Mickey Gee, Andy Fairweather-Low, Geraint Watkins i Charlie Watts

składanki
 A Stone Alone: The Solo Anthology 1974–2002 (2002)

Bill Wyman's Rhythm Kings
 Struttin' Our Stuff (październik 1997)
 Anyway the Wind Blows (październik 1998)
 Groovin''' (maj 2000)
 Double Bill (maj 2001)
 Just for a Thrill (maj 2004)

 gościnnie
 I Can Tell, John Hammond, Jr., 1967
 The London Howlin' Wolf Sessions, 1971
 Manassas, 1972
 Jamming with Edward!, 1972
 Drinkin' TNT And Smokin' Dynamite'', Junior Wells i Buddy Guy, 1977

single
 "In Another Land" (grudzień 1967)
 "Monkey Grip Glue" (czerwiec 1974)
 "White Lightnin'" (wrzesień 1974)
 "A Quarter to Three" (kwiecień 1976)
 "(Si, Si) Je suis un rock star" (lipiec 1981)
 "Visions" (1982)
 "Come Back Suzanne" (marzec 1982)
 "A New Fashion" (marzec 1982)
 "Baby Please Don't Go" (czerwiec 1985)
 "What & How & If & When & Why" (czerwiec 2015)

Wybrana filmografia

Przypisy

Linki zewnętrzne
 Oficjalna strona internetowa Billa Wymana

Członkowie The Rolling Stones
Brytyjscy basiści rockowi
Brytyjscy kompozytorzy
Brytyjscy producenci muzyczni
Ludzie urodzeni w Londynie
Urodzeni w 1936

redpajama_set_name: RedPajamaWikipedia


Tamilnadu Telecommunications Ltd.. is a company engaged in the manufacture of telecom cables of all sorts including jelly filled, optic fibre and copper cables.During the current year though sales have registered a sharp increase, expenditure has risen commensurately in view of higher raw material cost.The optical cables factory was operational only from 1-12-99.
HFCL is a company that is engaged in the manufacture of equipment related to telecommunication. It has done extremely well for the current year with net profits zooming up by 138%.
ITI Ltd. is a government owned organisation that is engaged in the manufacture and sale of telecommunication equipment such as handset,EPABX equipment,cables,switching equipment,relays and related equipment.
Krone Communications Ltd. was incorporated in 1988 and is engaged in the manufacture of communication equipment such as main distribution frames, tag block accessories,modules,over voltage protection magazines, backmount frames, tools and test cords.
Himachal Futuristic Communications Limited (HFCL) is to launch set top boxes for direct to home (DTH) services. The move is aimed at tapping demand in Southeast Asia and India.
ITI Limited has posted a 24% decline in profits during the quarter ended 31st December 1999. The decline in profits and net margins has mainly been brought about by the 14.6% rise in interest expenditure. The company has however posted a sharp rise in operating profits.
Government owned telecom company ITI Limited has registered a net loss of Rs 54 m in second quarter ended September 30, 1999. The company had registered a net profit of Rs 45 m in 2QFY99.


 What every wire-spoked wheel rider should know before hitting the trail.
For any kind of moderate to gnarly off-road riding, wire-spoke wheels are a must on adventure bikes. They offer a combination of strength and flex that you just can't get with cast wheels. But, unlike cast, a spoke wheel has a lot more "moving" parts and requires some attention and periodic maintenance. We reached out to Woody's Wheel Works, one of the most widely respected wheel builders in the country, to get some tips on how to keep things rolling smoothly.
"I recommend checking when you bring the bike home. I cannot tell you how many wheels we get in from brand new motorcycles and are out of true according to Woody's specs (+/- 0.010-0.015″). However, after the first ride in general it is good to check the spoke tension again as well," says Rachelle McMullin of Woody's Wheel Works.
By tapping on the spoke, you'll be able to hear a ping or thud and know if you need to snug the spoke up, loosen it, or leave it be.
She also suggests using a screwdriver or spoke wrench to tap each individual spoke. If there is any thud or ring at a different pitch than the rest, they should be adjusted. If the pitch is noticeably higher, loosen the spoke and if it thuds or is lower tighten it up. They also do not go off of torque values for truing wheels. Truing a wheel with a torque wrench will pull the wheel all out of whack. The torque wrench is there to double check the wheel once you've gotten it trued (the wheel spins straight).
"If you've had your bike for a while, check the spokes at least every tire change. From our experience, not every shop out there checks a wheel for true, so it is good to get into the habit of this on your end," Rachelle recommends.
What if a you break a spoke out on a ride? We asked if there are any measures to take to sure up the wheel.
Dented Rim: Fix or Replace?
No one likes to shell out cash when it isn't necessary, but Rachelle warns about trying to stretch the life of a dented stock rim.
The hope of any tubeless rider is that all he or she has to do in the case of a flat is plug a hole. Done. But that isn't always the case. You might get a gash in the sidewall or get a puncture that is just too big for a plug to work. If you dent your rim bad enough, it may not allow the tire bead to seal and hold air. You can try to bang it back into shape with rock or hammer but that rarely works and often takes longer than just putting a tube in it.
And, if you take this advice, don't forget to carry tire tools as well. A tube alone won't do any good if you don't have a wrench to take off your wheel, tire spoons/levers and something to use for a bead breaker. To make spooning that tire back on the rim easier, bring individual packs of dish soap or shampoo to use as tire lube.


I hate to suggest that WordPress isn't a good choice for someone, because I love WordPress. I love the community, love what it stands for—love it all.
But, no: downloading WordPress, finding a host and installing your own site is not a good idea for everyone. Evermore takes so much of the complexity out of it, but what if you have no money? What if DIY is your only option?
Since the self-hosted, open-source WordPress is free to download, it's easy to get anchored at that cost. Nothing beats free, right?
Unfortunately, it's not always that cut-and-dry.
This is the unfortunate experience that's all too common, causing good people to end up pulling their hair out and exhausting themselves. Does this sound fun to you?
If you don't want (or have time) to learn about WordPress, and you aren't a tinkerer, and you don't want to pay much of anything, you may need to go with a "closed" platform that is drag-and-drop. It's a hard truth, but it's an easier pill to swallow than learning it the hard way.
Ask yourself these questions to help determine if self-hosted WordPress would actually end up difficult for you.
If zero dollars was a budget, would that be your budget for a website?
Are you interested in WordPress because it is free?
Will your site essentially be an online business card or brochure?
Do you prefer to use a manual calendar rather than one on your phone?
Does everything to do with technology, no matter how simple, seem to somehow end in frustration for you?
Does the idea of resizing a photograph give you anxiety?
If the internet didn't exist, do you think the world would be a better place?
If you answered "yes" to many of these questions, going the "free" route with WordPress may cause you pain. Yes, pain—I don't use that word lightly. On top of the story I told earlier, read what happened to another friend of mine when their family blog got hacked.
It's alright if you have a tough time with technology, but it's important to recognize that in yourself.
Maybe you find yourself frustrated with FaceTime on your iPhone, even though you know you only have to press one button.
Or perhaps you finally learned how to use Microsoft Word at work on whatever version existed seven years ago, and, due to the recent upgrade, your entire next month is ruined, because you have to relearn everything.
These issues are not age-specific either! Some people just aren't great at "techy" stuff, no matter how basic.
My advice for you, if you're one of those folks: embrace it. Yes, step into it, own it, and move on.
You're likely great at sales, art, business strategy, writing, or whatever else! Don't fight an uphill battle. Focus on what you are good at, because the world needs your best. It has enough "average", doesn't it?
Let me save you a lot of time and headache. If you aren't willing to spend the money (Evermore doesn't do "freemium"), and if the thought of spending the time learning all this puts you in a bad mood, do yourself a favor and go with an easy drag-and-drop site builder. It won't be the most gorgeous site, but it will get the job done until you can afford to outsource everything.
For the most part, these are affordable and truly drag-and-drop. If you aren't good at that sort of thing, this is a good route, because you can start with some good designs. If you get stuck, even your teenage nephew could be a legitimate resource to help you get moving. With WordPress, your nephew likely isn't going to cut it.
If you do go with one of these companies and you need certain functionality, make sure you do your research. Many of them start free, and then charge extra for things later. That can still work for you, though, because you don't have to pay a lot upfront, and you can ease into it.
To get a design perfectly matched to your brand without any work, your only other option is to pay someone upfront. There is no magic bullet. You can go looking for a talented, yet reliable, contractor, or you can sign up for our Branded plan, where your website comes to you in a matter of days, fully completed, matched to your brand with a beautiful design, ready to go live.
I wrote this to help you have a better resource than many of the articles out there when you're trying to decide how to move forward. So many of them are focused on people who love to spend their weekends tinkering, learning about web development acronyms, and breaking things until they work. If you're not like that, what's left that's helpful to you? Hopefully, this is, and can help you get going and avoid the time and energy drains I mentioned earlier.
Still confused? Send me an email. I'd be glad to help you along, so you can get back to doing what you already do best.


Two asylum seekers from Syria are to be deported to Bulgaria, despite international condemnation of asylum seeker treatment in Bulgaria.
Stundin reports that Ahmad Aldzasem and Wajden S. Rmmo, two Syrians who sought asylum in Iceland, are to be deported this Tuesday to Bulgaria. The Directorate of Immigration made their decision based on the two having been granted asylum in that country, although they attest this "granting" of asylum was done under pressure of torture.
Unfortunately, the Bulgarian asylum is the excuse used by the Directorate of Immigration to deport him and Wajden. This is despite condemnation from Amnesty International about the horrible conditions asylum seekers are forced to endure there.


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Jackson County News Public notices, events, road closures and announcements from your Jackson County government.
Animal Shelter Receive reminders about Animal Shelter events.
Board of Supervisors Receive reminders about upcoming Board meetings.
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If you are a therapist, healer or holistic practitioner of some sort, you will know how hard it can be to get clients because: 1. It's hard to succinctly explain what you do. 2. What you provide is not something physical which can be picked up, held or 'tried on' beforehand. 3. Your skills can help so many people with so many limiting issues and problems making it hard to know how to get your message out there. 4. As more people become interested in alternative therapy, it's getting harder to standout. 5. You want to help as many people as possible but sales and marketing techniques can feel unethical. 6. Making a profit and a very comfortable living from the work you do can also feel uncomfortable or unethical. Make A Bigger Difference helps you overcome all of these barriers and more. Each chapter progressively layers in more knowledge and structure so you can promote your line of work easily, effectively and ethically without spending a small fortune. By the end of the book you will have a clear and concise step-by-step method to promote what you do so you can help more people and make a bigger difference. The Author is not a marketeer or sales professional. As a fellow practitioner himself, this book is delivered with compassion and a genuine desire to help you. Through years of trial and error with his own practice, the author wants to share what he knows will work ethically and effectively for you too.


The man later told South Korean investigators that he believed his trip to North Korea would resolve tensions between Washington and Pyongyang over the death of Otto Warmbier, an American university student who died last year days after being released from the North in a coma.
In September 2014 North Korea sentenced Miller — then a 24-year-old from Bakersfield, California — to six years of hard labor on charges he illegally entered the country to commit espionage.
"As North Korea clearly could have held this American citizen to gain leverage in up and down nuclear negotiations, that Pyongyang released this person is a good a sign.
Byron's reported initials match that of a US citizen deported from South Korea last year, caught in a civilian-restricted area near the North Korea border.
On Thursday, Vice President Mike Pence announced that President Donald Trump would meet with his North Korean counterpart for a second time despite the fact that Pyongyang had not revealed how many nuclear weapons the country had.
The detained man had told South Korean officials that he knew "lots of people in the Trump administration so that he wants to work as a bridge between the United States and North Korea to help improve their ties…" Earlier today, North Korean state media also declared leader Kim Jong-un to have taken part in his first publicized weapons test since the country's test-launch of an ICBM last November.
Authorities at the time identified him as a man from Michigan in his late 50s who claimed that he was there to resolve the standoff between North Korea and the international community over the former's nuclear weapons program.
But North Korea has chosen to use American hostages as a fig leaf in its ongoing negotiations with the U.S. Before Trump's summit with North Korean leader Kim Jong Un in Singapore in June, the country released three American hostages who had been held for months in a labor camp.
North Korea has decided to deport detained American citizen "Bruce Byron Lowrance" to the United States amid announcing the test of an "ultramodern tactical weapon," the Korean Central News Agency says.
Lowrance was arrested in South Korea on the same day a North Korean soldier made a dramatic escape to the South, rushing across the border under a barrage of bullets fired by his former comrades.
While the majority of Americans detained by North Korea have been released in relatively good condition, Warmbier, a 22-year-old University of Virginia student, died in June last year shortly after he was flown home comatose after 17 months in captivity.
The North has firmly defended its military program as a deterrent against hostile US policies along with its regional allies, South Korea and Japan.
Observers believe the simultaneous weapons test and detainee release may signal that North Korea is frustrated with the pace of US peace talks while seeking to keep channels open for future negotiations.
Americans captured or imprisoned in North Korea had previously vanished into the country's brutal prison system, where they were forced into hard labor.
The Korean Central News Agency said U.S. national Bruce Byron Lowrance told investigators that he was under the "manipulation" of the CIA.
A look at some of the Americans who have entered North Korea in past decades: The North's official Korean Central News Agency said Lowrance was detained last month after he entered illegally from the border with China.


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HOME > News > Regarding the rules for the use of electric scooters in other countries or regions
Regarding the rules for the use of electric scooters in other countries or regions
pxid 2021-09-10 93 times
What are the rules for electric scooters in other countries/regions?
Some countries treat electric scooters like bicycles, while in others they are treated as vehicles. Therefore, in some places, electric scooters must meet the same requirements as vehicles traveling on the road.
If the speed of the scooter does not exceed 25 mph, the electric scooter in the United States can be driven on roads without bicycle lanes. Unless you turn left or pass, you must bring the electric scooter close to the curb on the right.
Different states in the United States also have certain regulations on electric scooters. In California, as long as the user wears a helmet and is over 16 years old, riders can use their electric scooters on roads, bicycle lanes and sidewalks.
Until April 2020, the use of electric scooters is prohibited in New York. Before legislation was passed earlier this year, riding an electric scooter in New York could cost riders US$500 (approximately £385).
In France, the speed limit for driving an electric scooter is 15.5 mph. Those who ride electric scooters at higher speeds will be fined 1,500 euros (approximately £1,359). The minimum age to drive an electric scooter in France is 12 years old.
It is forbidden to use electric scooters with multiple passengers, and those who fail to comply with the regulations will be fined 35 euros (about 32 pounds). Electric scooters in France are also prohibited from driving on the sidewalk.
In Germany, the speed of electric scooters must not exceed 12.4 miles per hour, and the minimum age is 14 years old. Vehicles can be used on roads and bicycle lanes, but not on sidewalks. They must also be equipped with equipment similar to bicycles, such as lights, brakes, mirrors and bells.
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Q: How do i add column header, in the second row in a pandas dataframe? I have a data frame frame from pandas and now I want to add columns names, but only for the second row. Here is an example of my previous output:

Desired output:

My code:
data_line=open("file1.txt", mode="r")

lines=[]
for line in data_line:
    lines.append(line)
for i, line in enumerate(lines):
    # print('{}={}'.format(i+1, line.strip()))
    file1_header=lines[0]
num_line=1
Dictionary_File1={}
Value_File1= data_type[0:6]
Value_File1_short=[]
i=1
for element in Value_File1:
    type=element.split(',')
    Value_File1_short.append(type[0] + ", " + type[1] + ", " + type[4])
    i += 1
Dictionary_File1[ file1_header]=Value_File1_short
pd_file1=pd.DataFrame.from_dict(Dictionary_File1)

A: You should have a look at DataFrame.read_csv. The header keyword parameter allows you to indicate a line in the file to use for header names.
You could probably do it with something like:
pd.read_csv("file1.txt", header=1)

From my python shell I tested it out with:
>>> from io import StringIO # I use python3
>>> import pandas as pd
>>> >>> data = """Type    Type2   Type3
... A           B   C
... 1           2   3
... red     blue    green"""
>>> # StringIO below allows us to use "data" as input to read_csv
>>> # "sep" keyword is used to indicate how columns are separated in data
>>> df = pd.read_csv(StringIO(data), header=1, sep='\s+')
>>> df
     A     B      C
0    1     2      3
1  red  blue  green

A: So if I understand properly, you have a file "file.txt" containing your data, and a list containing the types of your data.
You want to add the list of types, to the pandas.DataFrame of your data. Correct?
If so, you can read the data from the txt file into a pandas.df using pandas.read_csv(), and then define the columns headers using df.columns.
So it would look something like:

df = pd.read_csv("file1.txt", header=None)
df.columns = data_type[0:6]

I hope this helps!
Cheers

A: You can write a row using the csv module before writing your dataframe to the same file. Notice this won't help when reading back to Pandas, which doesn't work with "duplicate headers". You can create MultiIndex columns, but this isn't necessary for your desired output.
import pandas as pd
import csv
from io import StringIO

# input file
x = """A,B,C
1,2,3
red,blue,green"""

# replace StringIO(x) with 'file.txt'
df = pd.read_csv(StringIO(x))

with open('file.txt', 'w', newline='') as fout:
    writer = csv.writer(fout)
    writer.writerow(['Type', 'Type2', 'Type3'])
    df.to_csv(fout, index=False)

# read file to check output is correct
df = pd.read_csv('file.txt')

print(df)

#   Type Type2  Type3
# 0    A     B      C
# 1    1     2      3
# 2  red  blue  green

redpajama_set_name: RedPajamaStackExchange


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Collective Soul and Switchfoot to perform at Kemba Live in Columbus – The Columbus Dispatch
Two bands that got their start in the '90s will be performing together for the first time this summer.
Collective Soul, based in Atlanta, and Switchfoot, based in San Diego, will be co-headlining on July 20 at Kemba Live, 405 Neil Ave.
"We're fans of their music, and we think the energy is going to be great. The sum will be greater than its parts. I think a lot of our fans will enjoy Switchfoot, and vice versa. It can't get any better than that, really," said Will Turpin, who has been playing bass for Collective Soul since its beginnings in 1992.
He has been working closely on making music since then with lead vocalist and songwriter Ed Roland and his brother, rhythm guitarist Dean Roland.
Summer concert:Buckeye Country Superfest 2022 at Ohio Stadium in Columbus: What you need to know
The band — best-known for early hits including "Shine," "The World I Know" and "December" — released the album "Blood" in 2019 to celebrate its 25th anniversary, and will release a new album, "Vibrating," in August.
The distance between the two albums is actually not as great as it seems: Both were recorded at the same time. At first, the band contemplated releasing a double album. Then, they planned to release a second album in 2020.
COVID put a stop to that, and they waited until they were touring consistently again to release the new material.
"We think of it as phase one and phase two," Turpin said. "Last year, we didn't have a lot of dates, and we just kept working on mixes, and taking our time. We're super-proud of it. It's a strong record."
Though Ed Roland generally writes the melodies and lyrics for the group's songs before they get together to record, the other musicians also play a significant role in the final product.
"I take a big role with the foundation of the music, with the rhythm section," Turpin said. "And how to run transitions smoothly from one section to another. Ed is more in charge of the ornamental stuff that goes on. But we're all involved in all of it."
Besides working on fine-tuning the new album, and working on his own music, during the past two years Turpin has also taken over the record studio that his father ran for 40 years outside Atlanta, Real 2 Reel.
July concerts:Outdoor music venues in Ohio boast big acts in July: Keith Urban, Rod Stewart, Bonnie Raitt
"I have a passion for working with younger artists, seeing where they can go with their craft," he said.
Right now, he's working on putting out albums for a young female pop singer, an eight-piece band with a horn section, and a prog-rock band.
"So I'm all over the place with my styles, and I enjoy all of them."
But for the next couple months, he will be concentrating on touring.
"After touring for so many years, the way we approach the live shows is as a celebration of life, rather than us worrying about technical things. Live music boils down to emotion. That's what people are attracted to. The emotions it makes them feel, the memories it brings back. When we play live, we're not that band that sticks exactly to the CD, but we're also not that band that jams too much. We just try to make sure that the emotion is clear and present," he said.
"We're going to get in that big room with everybody and celebrate the memories, celebrate the songs, celebrate life and enjoy being able to be together in the same room."
margaretquamme@hotmail.com
Collective Soul and Switchfoot will perform at 6 p.m. July 20 at Kemba Live, 405 Neil Ave. Tickets: $44.50 (614-461-5483, promowestlive.com)
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text:
Faces of OLu
Why do OLu alumni send their kids to their alma mater?
Growing up in the 80s seemed a lot less stressful than today, with more pressures being placed upon the kids of today than in 1985. How blessed we are to live in the land of the free where we can decide where our children can go to high school.
However, making a decision on that next step to high school can be a hard one for any parent.
OLu Alumni Relations Coordinator Sharon Nelson '85 - mother to one current Lancer - sat down with friend and fellow alum Bill Boezinger - father to two current Lancers - to discuss what goes behind picking a high school for their young adults.
Q: Why do OLu Alumni send their kids to their alma mater?
Boezinger: I had such a positive experience when I attended, what we called back then "Lutheran High" or "Lu High," that I wanted my own children to have a similar positive experience for high school.
Q: How has Orange Lutheran grown from when you attended? What differences do you see?
Boezinger: The enrollment has grown, almost tripled, but what hasn't changed is the small school, close knit community that I experienced here as a student 30 years ago. With a larger student body, there are more opportunities and more resources. A very intentional effort has been made to create an environment where students can excel in academics, sports and the arts, surrounded by a caring Christian atmosphere. Super engaged compassionate teachers and faculty is still a key component, and that hasn't changed a bit.
I would also say there is certainly better overall awareness of the school. OLu has a great reputation for its excellence in the classroom, on the playing field, and in the Arts. The campus has much better facilities like the Nechita Center, the new student union & cafe, and the state-of-the art weight room. During my time at OLu, the Nechita Center was the quad and there wasn't even one gym. There has been a constant effort and drive from alumni, parents and other donors to create a generous legacy, which has enhanced our school and brought us to where we are today.
Q: Why did you and your teen choose your alma mater for your his/her high school education? What were the deciding factors?
Boezinger: After high school graduation, I stayed connected in some way or another with my alma mater. I tried to keep up on what was happening at my high school, which helped in the decision on where to send my kids. I attended homecoming football games, stayed connected with classmates, and helped plan and attended regular reunions.
The decision to invest in my kids high school education at OLu really wasn't that hard. OLu is just the right size school. It's not too small where they would feel limited, and also not too big where they might feel lost. It is big enough to offer a lot of opportunities: college prep academics, excellence in athletics and lots of unique offers in the arts. It was a good balance for my kids' personalities to allow them to be active and involved in high school, like I was. Most importantly, it is a Christian environment where my kids feel safe and secure with their shared faith with teachers, staff, students and families. It's important to me to have a setting where everyone has a shared set of core common values.
Q: What does a Christian education mean to you and to your family? Why is it important? How did it pave the way for you as you went into college and adulthood?
Boezinger: Honestly, the high school decision was an easy one. We sent our children to Lutheran elementary and middle school. We choose to continue the Christian education, to further strengthen their foundation in faith, so that upon graduation they would be prepared to enter college and the secular world. Our faith is very important to our family. My parents set the stage for this tradition with me and my siblings. Their decision to send me to OLu over 30 years ago, set the foundation that helped me prepare to go on to a large college like UCLA. It kept me grounded and prepared me for a healthy college experience and beyond. I really do believe in the mission statement at OLu: To help students internalize the gospel message of salvation in Christ Jesus.
Bill Boezinger was the ASB President while at OLu and graduated from UCLA in 1990 with a BA in Political Science and a minor in Business Administration. He has worked for the Walt Disney Company since 1999. A member of St. John's Lutheran Church, he is a longtime Life Group Bible Study leader and currently serves on the St. John's School Board. He has also been active in the Floral Park community as well as the YMCA Indian Princess/Guides program, serving 4 terms as "chief." Bill, aka "Boe," and his lovely wife, Cathe, have been married for over 20 years.


The dense synthetic brush allows you to collect just the right amount of product to create a smooth surface.
The brush size helps you to apply Get Brush Tan more quickly to large areas of the body.
Thanks to the big top and long shafts, you can now apply quickly and without hassle.


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Isochaetes is a genus of Limacodid moths.

Selected species
Isochaetes beutenmuelleri (H. Edwards, 1889)
Isochaetes dwagsi Corrales & Epstein, 2004
Isochaetes heevansi Epstein, 2004
Isochaetes kenjii Corrales & Epstein, 2004
Isochaetes tapantiensis Corrales & Epstein, 2004

External links

Isochaetes at funet

Limacodidae genera
Limacodidae


A fault in the Apennine Mountains wreaked damage on structures including the Colosseum.
The geological fault responsible for a series of Italian earthquakes in 2016 might also have caused a quake mentioned in ancient accounts of fifth-century Rome.
Until 2016, scientists had considered the 30-kilometre-long Mount Vettore fault in the central Apennine Mountains to be dormant. But between August and October that year, it generated three big earthquakes; the first killed nearly 300 people.
To explore the fault's history, a team led by Paolo Galli at the Department of Civil Protection in Rome dug trenches across it to look for soil disturbances caused by past earthquakes. The researchers found evidence of 6 big quakes in the past 9,000 years.
One of those probably occurred in the middle of the fifth century ad. It could be the same earthquake that, according to medieval historians, damaged the Colosseum and other buildings in Rome in ad 443.
On average, the Mount Vettore fault has generated quakes greater than magnitude 6.5 every 1,800 years. In retrospect, the authors write, the 2016 earthquakes shouldn't have been so surprising.
The dominant US crop plant has a voracious appetite for fertilizer, which leads to air pollution and health problems.
Green maize fields stretching to the horizon are part of the iconography of the United States. But a nationwide analysis suggests that air pollution caused by the cultivation of maize (corn) takes a high toll on human life.
With favourable weather, US farmers can raise more than 385 million tonnes of maize a year. To quantify the health consequences of the crop's production, Jason Hill at the University of Minnesota, Saint Paul, and his colleagues tallied up maize yields, air-quality impacts and deaths related to air pollution across the United States.
The researchers found that the air pollution released by maize production causes 4,300 deaths annually. More than 70% of those deaths stem from farms' use of nitrogen-based fertilizers, which emit ammonia that is converted to a deadly type of pollutant called fine particulate matter.
Maize farming's health costs could fall if fertilizer levels were precisely tailored to a field's needs, the authors say.
Artefacts found in Lake Titicaca include bones of a six-month-old llama killed in an ancient rite.
Divers scouring the bed of a lake high in the Andes Mountains have found prehistoric deposits of gold, gems and a sacrificed baby llama — evidence of rituals that may have helped leaders to strengthen their hold over an expanding empire.
The Tiwanaku civilization took root some 1,500 years ago next to Lake Titicaca, which sits on the border of modern Bolivia and Peru, and eventually came to dominate a large swathe of the region. Christophe Delaere at the Université Libre de Bruxelles, José Capriles at Pennsylvania State University in University Park and Charles Stanish at the University of South Florida in Tampa studied items placed in the lake between roughly AD 800 and 950, when Tiwanaku power and influence were spreading.
The objects include a turquoise pendant, seashells imported from the distant Pacific Ocean and a gold medallion depicting a Tiwanaku deity. Such sumptuous offerings would have advertised Tiwanaku leaders' authority and wealth. The ceremonies also promoted religion, which can bind together far-flung peoples and encourage cooperation.
Seismic shivers documented in the Golden State after record-breaking snows in 2016 and 2017.
Water from melting snow sets off swarms of small earthquakes in California's Sierra Nevada mountains.
Emily Montgomery-Brown at the US Geological Survey in Menlo Park, California, and her colleagues analysed records of earthquakes near Long Valley Caldera, in the eastern part of the state. The scientists compared the seismic patterns with streamflow in the area.
Since 1984, small earthquakes have rattled the ground 37 times more often when streamflow has been very high than when it has been very low. Water percolating into the ground as snow melts in spring seemingly changes the pressure in the ground, triggering the quakes.
After a record snowfall in the Sierra Nevada area between late 2016 and early 2017, for example, the region experienced a swarm of minor quakes, including more than 3,000 such events between 28 May and 1 August 2017.
The work represents one of only a few examples of a documented link between precipitation and earthquakes.


mLease solution consists of three integrated business layers: trade, operational and booking. The concept of using layered structure enables an easy integration capabilities with third party financial, operational or booking systems. Such approach also makes data conversion from older legacy system simpler, less time consuming and allows to proceed with phased implementation in contrast to rip and replace project. In heterogeneous IT environment, very common nowadays, layered structure of mLease helps to quickly integrate and adapt it to existing solutions and quickly gain operational readiness.
All modules of mLease are integrated, however they can work independently as self-reliant components as well. From the user experience perspective, navigating between various functions of the modules is transparent. All of modules have been implemented using the same, proven Oracle technology and the same architectural concepts what makes the whole system coherent.
Core mLease calculation module, based on our payment and reconciliation engine consists of three integrated software layers, each focused on specyfic business activity: trade, operational and booking. Such approach provides integration capabilities with 3rd party systems and ease of data migration.


A sleek and stylish bracelet watch set in stainless steel, the perfect gift for your loved one. The round black dial features silver tone detailing and a stunning stone set border. Fastening securely with a push button deployment clasp.


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Q: SharePoint 2013/16 Doc Library web part - change view but no new page I have a requirement to change the view in the Document Libarary web part, and I already have the change view links enabled. They do not want the view to open in a new page, but to change the view within the web part itself? Any idea on how to do this?
Thank you
Doug

A: To switch view that are already created for a document library web part, you don't need to open a new page.
Just edit the page, edit the web part, then switch view from the web part:


I am frustrated. What by? By having to describe myself as the opposite of something that I am not, rather than what I actually am.
Atheists of the UK unite: in the census due here on 27 March, describe yourself not as "atheist" but as "scientific realist", to demonstrate what you do believe in, deeply and objectively.
If Jedi knights could get wide recognition in the previous census in 2001, I am sure that scientific realists can now.


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Cisco Network Security Flaw Leaks Sensitive DataPrevious article
News Wrap: Twitter Hack, Apple Under Fire and Global Privacy Finger WagsNext article
Malicious 'Blur' Photo App Campaign Discovered on Google Play
Twenty-nine bad mobile apps with a combined 3.5 million downloads bombard users with out-of-context ads.
A new campaign of malicious photo apps on Google Play floods Android devices with random ads instead of functioning as advertised. They also elude detection by making its icon disappear from the device home screen soon after it's downloaded.
Researchers at the White Ops Satori Threat Intelligence and Research Team discovered the Android apps — 29 in total — which they said "manifested suspiciously high volumes of ad traffic" during threat-hunting investigations, according to a recent report.
The team — comprised of researchers Gabi Cirlig, Michael Gethers, Marion Habiby, Christopher Soo and Dina Haines — called the campaign "ChartreuseBlur," in part because the majority of apps include the word "blur" in their package name. Many also claim to be photo editors that allow users to blur sections of an image, they said.
There are several key characteristics that can alert users if they've fallen victim to downloading one of the bad apps (the apps combined have more than 3.5 million downloads, researchers said).
One of the hallmarks of the app is that once it's downloaded, it plays "hide and seek" with the device, with the icon disappearing from the home screen, forcing users to go into the Settings menu to find the app if they want to see if it's been installed or open it. This makes it "very difficult for an average user to remove the app," they said. Square Photo Blur has since been moved from the Google Play store, researchers added.
Researchers conducted analysis on one of the apps in particular, called Square Photo Blur, finding that its behavior was consistent with all of the malicious apps. They found that once the app is downloaded, it begins bombarding the device with ads, "just appearing out of nowhere," a phenomenon known as delivering out-of-context (OOC) ads, researchers said.
Another hallmark of the apps in the campaign is that all of the developers listed for the apps have random, English-sounding names that are clearly fake, according to the report. The developer listed for Square Photo Blur on Google Play, for example, was called "Thomas Mary."
The apps in the campaign generally have a a three-stage payload evolution, researchers observed. In the first two stages, the code appears innocent, but the third phase is where they detected nefarious activity.
In the first stage, the app is installed using a Qihoo packer, which in and of itself is not suspicious. It also uses a stub app, or stubs, which typically are used by developers as a placeholder for not-yet-developed code while testing of other parts of the code.
This sets the app up for stage two, in which it's used as a wrapper around another Blur app, com.appwallet.easyblur, which is visible after Square Photo Blur is unpacked. This app also does not do anything malicious; threat actors probably used it "to trick users into believing they have downloaded a legitimate app with Square Photo Blur," researchers observed.
Stage three of the app's installation is where the app begins to get malicious, according to the report. It's in this phase that the malicious code generates the OOC ads, and it appears in the form of packages com.bbb.*, such as com.bbb.NewIn. Code present in the app can deliver OOC ads every time a user unlocks the screen, starts charging the phone, or switches from cellular data to WiFi and vice versa, researchers said.
Indeed, the Satori team discovered the code snippet responsible for the OOC ads on VirusTotal (VT), adding that VT samples appear to be slight variations of the same base code with incremental changes. This is likely so the app can avoid detection by antivirus companies, researchers said.
Once fully installed, researchers clicked on the Square Photo Blur app's launcher icon on a test device and found it's basically a "hollow shell of an app, just enough to just pass the Play Store checks," they said.
They pointed out that reviews can be helpful in avoiding malicious apps like these: "Looking at the comments in the Reviews section for this app reveals negative sentiment against this developer. The reviews suggest the app is barely functional with many reports of OOC ads."
The Satori team included a list of the malicious apps in the report and recommended that anyone using them remove them immediately. Researchers plan to continue to monitor the situation, they said.
The apps have been removed from the Google Play store, but users will need to remove any that have already been installed. The Satori team included a list of the malicious apps in their report and recommended that anyone using them remove them immediately. Researchers plan to continue to monitor the situation, they said.
Ryuk Rakes in $150M in Ransom Payments
An examination of the malware gang's payments reveals insights into its economic operations.