text:
\section{Introduction}
Recent research of nanoscale radiative energy transfer has enabled advances and in-depth insight in several
fields of optical technologies related, e.g., to nanoplasmonics \cite{Sorger2011,Oulton2009,Huang2013,Sadi2013},
near-field microscopy \cite{Taubner2006,Hillenbrand2002}, thin-film light-emitting diodes \cite{Nakamura2013,Heikkila2013},
photonic crystals \cite{Russell2003,Akahane2003}, and metamaterials \cite{Tanaka2010,Mattiucci2013}.
The optical phenomena taking place in nanoscale also naturally lead to questions related to the quantum
nature of light, proper ways to quantize the fields, and maybe even more importantly on how to
interpret the results. The research related to quantum optics of nanoscale systems is strongly
influenced by the availability of simple and transparent theoretical tools and
models that allow in-depth understanding of the pertinent phenomena
in sufficiently simple form. Such insight has been used, for instance, in the recent
demonstrations and studies of
noiseless but nondeterministic optical amplifiers \cite{Zavatta2011,Ferreyrol2010,Partanen2012}
and optical properties of cavities \cite{Groblacher2009,Collette2013,Hayrynen2011c,Hayrynen2009b}.
Simple description of the quantum aspects of energy transfer is especially
interesting and challenging in lossy nanoscale systems often simulated by the
prototypical one-dimensional lossy structures.

The research of quantum optical processes in such lossy systems during the last few decades has
generated a wealth of information on the quantization of the electromagnetic (EM) field
in dielectrics and especially in layered structures.
In the context of the present work, the most relevant quantization approach
has focused on the input--output relation formalism (IORF) of the photon creation
and annihilation operators providing a detailed description of the spatial field
evolution. The formalism was originally developed for dispersionless and lossless
dielectrics by Kn\"oll \emph{et al.} \cite{Knoll1987} and soon extended for lossy and
dispersive media for the study of passive optical devices, such as dielectric plates,
interfaces, and optical cavities by several groups
\cite{Knoll1991,Allen1992,Huttner1992,Barnett1995,Matloob1995,Matloob1996}.
The complete quantization procedures studied, e.g., by Barnett \emph{et al.} \cite{Barnett1995}
fully accounting for the coupling between the EM field and the states of homogeneous lossy media clearly
highlighted that the noise and field operators in lossy systems became position
dependent. The vector potential and electric field operators in the above works
obeyed the well-known canonical commutation relation for an arbitrary choice of normal
mode functions as expected \cite{Barnett1995,Matloob1995}, but the commutation
relations of the ladder operators did not. The anomalous commutation relations
of the ladder operators were studied in several reports
\cite{Raymer2013b,Barnett1996,Ueda1994,Aiello2000,Stefano2000} but no clear resolution for the
anomalies was found apart from reaching a consensus that the anomalies were
irrelevant as long as the field commutation relations and classical field
quantities were well defined. Since then, the IORF has mainly been applied
in calculating the classical field quantities until the very recent suggestions that,
despite the early interpretations, the ladder operators and their commutation
relations might in fact relate to measurable physical properties
\cite{Collette2013}.

In this paper, we define position-dependent ladder operators associated with the vector potential
in a way that is consistent with the canonical commutation relations.
The introduced position-dependent annihilation and photon-number
operators give further insight on the local effective photon number, thermal balance, and the
formation of the local thermal equilibrium. We focus on thermal source fields, but in principle
the introduced operators also allow one to investigate fields with other kinds of quantum statistics.
We also discuss the possibility of dividing the photon number into left and right
propagating parts, and the origin of the anomalies reported in cavity operators based on this division.
The approach that is initially based on purely mathematical arguments is also shown
to result in a physically meaningful definition of the photon number that has a
very attractive and simple connection to the field temperature and thermal balance of the system.

The paper is organized as follows. In Sec.~\ref{sec:theory} the theoretical background
is briefly reviewed and the position-dependent ladder and photon-number operators
satisfying the canonical commutation relations are defined.
To enable comparison between the conventional field operators and
the position-dependent photon-number operator we also briefly review
the concepts for the energy density and Poynting vector in
lossy, dispersive media. In addition, we show how the introduced effective
photon-number operator is related to the thermal balance of the system.
In Sec.~\ref{sec:results}, the presented theoretical concepts are applied
to study the position dependence of the photon number, electric field fluctuation,
electrical contribution of the local density of EM states,
energy density, Poynting vector, and net emission rate in the geometries
of an interface separating a lossy medium from vacuum and a vacuum cavity between lossy media.

\section{\label{sec:theory}Field quantization}
\subsection{Overview of the noise operator formalism for EM field quantization}

Field quantization in lossy dielectrics is well established, but for the purposes of
the present discussion it is convenient to briefly review some of the key results and
theoretical background for the quantization of the EM field in one dimension.
In this section, we give an overview
of the results originally presented by Matloob \emph{et al.} \cite{Matloob1995}
to lay the ground for defining the position-dependent ladder and photon-number
operators and the related discussion in the following sections.

The electromagnetic waves are considered to propagate parallel to the $x$ axis with their
transverse electric and magnetic vector operators $\hat E(x,t)$ and $\hat B(x,t)$
parallel to the $y$ and $z$ axes, respectively. The field operators are related
to the vector potential operator $\hat A(x,t)$ by the relations \cite{Matloob1995}
\begin{align}
 \hat E^+(x,\omega) & = i\omega\hat A^+(x,\omega)\label{eq:EfromA},\\
 \hat B^+(x,\omega) & = \frac{\partial}{\partial x}\hat A^+(x,\omega)\label{eq:BfromA}
\end{align}
for positive frequencies. The negative frequency parts $\hat E^-(x,\omega)$,
$\hat B^-(x,\omega)$, and $\hat A^-(x,\omega)$ are Hermitian conjugates
of the positive frequency parts.

The field operators satisfy the frequency domain Maxwell's equations and,
when the relations in Eqs.~\eqref{eq:EfromA} and \eqref{eq:BfromA} are used,
the vector potential operator can be shown to satisfy the
one-dimensional nonhomogeneous Helmholtz equation \cite{Matloob1995}
\begin{equation}
\frac{\partial^2}{\partial x^2}\hat A^+(x,\omega)+\frac{\omega^2n(x,\omega)^2}{c^2}\hat A^+(x,\omega)=-\mu_0\hat J_\mathrm{em}(x,\omega),
\label{eq:Helmholtz}
\end{equation}
where $\mu_0$ is the permeability of vacuum,
$n(x,\omega)$ is the refractive index of the medium, and
$\hat J_\mathrm{em}(x,\omega)=j_0(x,\omega)\hat f(x,\omega)$ is a Langevin noise current operator
presented in terms of the scaling factor
$j_0(x,\omega)$ and the modified Langevin force operator $\hat f(x,\omega)$, which is a
bosonic field operator defined through the following commutation relations:
\begin{align}
 [\hat f(x,\omega),\hat f^\dag(x',\omega')] & = \delta(x-x')\delta(\omega-\omega')\label{eq:commutationf1},\\
 [\hat f(x,\omega),\hat f(x',\omega')] & =[\hat f^\dag(x,\omega),\hat f^\dag(x',\omega')]=0\label{eq:commutationf2}.
\end{align}
The scaling factor of the Langevin noise current operator is given by $j_0(x,\omega)=\sqrt{4\pi\hbar\omega^2\varepsilon_0\mathrm{Im}[n(x,\omega)^2]/S}$,
where $\hbar$ is the reduced Planck's constant, $\varepsilon_0$ is the permittivity
of vacuum, and $S$ is the area of quantization in the $y$-$z$ plane \cite{Matloob1995}.
The magnitude of the scaling factor has been determined by requiring that the vector potential
and electric field operators obey the canonical equal-time commutation relation
as detailed in Ref.~\cite{Matloob1995}.

The solution to Eq.~\eqref{eq:Helmholtz} can be written in terms of the Green's function
of the Helmholtz equation as
\begin{equation}
 \hat{A}^+(x,\omega) = \mu_0\int_{-\infty}^\infty j_0(x',\omega) G(x,\omega,x')\hat f(x',\omega)dx'.
 \label{eq:solutionA}
\end{equation}
The Green's function depends on the problem geometry via the refractive index of the medium.
For example, in a homogeneous space the Green's function can be written as
\begin{equation}
 G(x,\omega,x')=\frac{ie^{ik(\omega)|x-x'|}}{2k(\omega)},
\end{equation}
where $k(\omega)=\omega n(\omega)/c$ is the wave vector.
The Green's functions for the selected layered structures are given in the Appendix.

In order to write the field operators in compact forms, we define the scaled forms
of the Green's functions:
\begin{align}
 G_\mathrm{A}(x,\omega,x') =\; & \mu_0j_0(x',\omega)G(x,\omega,x')\label{eq:GA},\\[10pt]
 G_\mathrm{E}(x,\omega,x') =\; & i\mu_0\omega j_0(x',\omega)G(x,\omega,x')\label{eq:GE},\\[6pt]
 G_\mathrm{B}(x,\omega,x') =\; & \frac{i\mu_0\omega n(x,\omega)}{c}j_0(x',\omega)\nonumber\\
                               & \times[G_\mathrm{R}(x,\omega,x')-G_\mathrm{L}(x,\omega,x')]\label{eq:GB},
\end{align}
where $G_\mathrm{E}(x,\omega,x')$ and $G_\mathrm{B}(x,\omega,x')$ are obtained from $G_\mathrm{A}(x,\omega,x')$
by using Eqs.~\eqref{eq:EfromA} and \eqref{eq:BfromA}, and
$G_\mathrm{R}(x,\omega,x')$ and $G_\mathrm{L}(x,\omega,x')$ are the right and left
propagating parts of the Green's function identified from the factors
$e^{ikx}$ and $e^{-ikx}$,
respectively. In this paper, when treating lossless semi-infinite media,
an infinitesimal imaginary part of the refractive index is assumed in $j_0(x,\omega)$ and $G(x,\omega,x')$
and it is set to zero after calculating the integrals. Using the above definitions the
field operators are given by
\begin{align}
 \hat{A}^+(x,\omega) & = \int_{-\infty}^\infty G_\mathrm{A}(x,\omega,x')\hat f(x',\omega)dx'\label{eq:A},\\
 \hat{E}^+(x,\omega) & = \int_{-\infty}^\infty G_\mathrm{E}(x,\omega,x')\hat f(x',\omega)dx'\label{eq:E},\\
 \hat{B}^+(x,\omega) & = \int_{-\infty}^\infty G_\mathrm{B}(x,\omega,x')\hat f(x',\omega)dx'\label{eq:B}.
\end{align}
In time domain the fields are given by the inverse Fourier transforms of the frequency domain operators
as $\hat{A}(x,t)= \frac{1}{2\pi}\int_0^\infty\hat A^+(x,\omega)e^{-i\omega t}d\omega + \mathrm{H.c.}$,
where the Hermitian conjugate is the negative frequency part, and $\hat E(x,t)$ and $\hat B(x,t)$
are obtained from similar expressions.

The electric displacement field operator $\hat{D}(x,t)$ and the magnetic field strength operator $\hat{H}(x,t)$,
needed, e.g., in calculating the energy density and Poynting vector, are obtained from
the electric field and magnetic field density operators using the constitutive relations
$\hat{D}^+(x,\omega)=\varepsilon_0\varepsilon(x,\omega)\hat{E}^+(x,\omega)$
and $\hat{B}^+(x,\omega)=\mu_0\mu(x,\omega)\hat{H}^+(x,\omega)$,
where $\varepsilon(x,\omega)$ and $\mu(x,\omega)$ are the
position-dependent relative permittivity and permeability of the medium  \cite{Novotny2006}.

\subsection{\label{sec:operators}Ladder and photon-number operators}
In any quantum electrodynamics (QED) description, the canonical commutation relations are satisfied for
field quantities, i.e., $[\hat A(x,t),\hat E(x,t)]=-i\hbar/(\varepsilon_0S)\delta(x-x')$ \cite{Scheel1998},
but the same is not generally true for the canonical commutation relations of the ladder operators.
The dominant approach in evaluating the ladder operators has been to separate the
field operators obtained from QED either into the left and right
propagating normal modes or into the normal modes related to the left and right inputs
and the corresponding ladder operators so that the vector potential can be written as
$\hat A^+(x,\omega)=u_\mathrm{R}(x)\hat a_\mathrm{R}(\omega) + u_\mathrm{L}(x)\hat a_\mathrm{L}(\omega)$
\cite{Barnett1996,Gruner1996,Aiello2000}.
This is tempting in view of the analogy with classical EM, but in most cases results in
ladder operators that are not unambiguously determined due to the possibility to scale
the normal modes nearly arbitrarily. More recently, also divisions accounting for
the noise contribution and more physically transparent interpretations \cite{Stefano2000}
have been reported, but none of the previously reported definitions consistently give
the canonical commutation relations for the ladder operators.

We adopt a different starting point that ensures the preservation of the canonical
commutation relations by simply writing
\begin{equation}
 \hat A^+(x,\omega)=C(x,\omega)\hat a(x,\omega),
 \label{eq:initial}
\end{equation}
where $\hat a(x,\omega)$ is the position dependent photon annihilation operator and
$C(x,\omega)$ is a normalization factor that corresponds to the classical mode function
defined simultaneously for all the source points.
Solving Eq.~\eqref{eq:initial} for $\hat a(x,\omega)$ and using Eq.~\eqref{eq:A}
for $\hat A(x,\omega)$ gives
\begin{equation}
 \hat a(x,\omega)=\frac{\int G_\mathrm{A}(x,\omega,x')\hat f(x',\omega)dx'}{C(x,\omega)}.
 \label{eq:totalfielda}
\end{equation}
The canonical commutation relation for the ladder operators must fulfill
$[\hat a(x,\omega),\hat a^\dag(x,\omega')]=\delta(\omega-\omega')$.
Substituting the field annihilation operator in Eq.~\eqref{eq:totalfielda}
to the canonical commutation relation gives
\begin{equation}
 [\hat a(x,\omega),\hat a^\dag(x,\omega')]=\frac{\int |G_\mathrm{A}(x,\omega,x')|^2dx'}{|C(x,\omega)|^2}\delta(\omega-\omega'),
 \label{eq:acommutation}
\end{equation}
which can be used to determine $C(x,\omega)$ so that the canonical commutation
relation holds at any position. The phase factor does not play a role in our
calculations so, choosing $C(x,\omega)$ to be real and positive, we have
\begin{equation}
 C(x,\omega)=\sqrt{\int |G_\mathrm{A}(x,\omega,x')|^2dx'}.
\end{equation}
This can be expressed in terms of the imaginary part of the Green's function as \cite{Dung1998,Stefano2000}
\begin{equation}
 C(x,\omega)=\sqrt{\frac{4\pi\hbar}{\varepsilon_0c^2S}\mathrm{Im}[G(x,\omega,x)]}.
\end{equation}
Since the electric field operator is related to the vector potential
operator by Eq.~\eqref{eq:EfromA}, the electric field
operator is $\hat E^+(x,\omega)=i\omega C(x,\omega)\hat a(x,\omega)$.
The time domain electric field operator is naturally given by
taking the inverse Fourier transform of the frequency domain operator as
\begin{equation}
 \hat E(x,t) = \frac{i}{2\pi}\int_0^\infty\!\!\! \omega C(x,\omega)\Big[\hat a(x,\omega)e^{-i\omega t}-\hat a^\dag(x,\omega)e^{i\omega t}\Big]d\omega.
 \label{eq:Ea}
\end{equation}

The photon number operator is given in
terms of the ladder operators as
$\hat n(x,\omega)=\int\hat a^\dag(x,\omega)\hat a(x,\omega')d\omega'$
and its expectation value is expressed in terms of the Green's function as
\begin{equation}
 \langle\hat n(x,\omega)\rangle=\frac{\int |G_\mathrm{A}(x,\omega,x')|^2\langle\hat\eta(x',\omega)\rangle dx'}{|C(x,\omega)|^2}.
 \label{eq:photonnumber}
\end{equation}
Here we have defined a source field photon-number operator as
$\hat \eta(x,\omega) =\linebreak \int\hat f^\dag(x,\omega)\hat f(x',\omega')\,dx'd\omega'$
and assumed that the noise operators at different positions and at different frequencies
are uncorrelated so that the source field photon-number expectation value at
position $x$ of a thermally excited medium is
\begin{equation}
 \langle\hat \eta(x,\omega)\rangle = \frac{1}{e^{\hbar\omega/(k_\mathrm{B}T(x))}-1},
 \label{eq:sourcefieldn}
\end{equation}
where $k_\mathrm{B}$ is the Boltzmann constant and
$T(x)$ is the position-dependent temperature of the medium.
In the case of thermal fields the photon-number operator in Eq.~\eqref{eq:photonnumber}
also allows one to calculate an effective local field temperature for the electric field as
$T(x,\omega)=\hbar\omega/\{k_\mathrm{B}\ln[1+1/\langle\hat n(x,\omega)\rangle]\}$.
As discussed later in Sec.~\ref{sec:results}, the local photon number and the associated
field temperature should be experimentally observable with a suitable measurement setup.

The above definition of the photon annihilation operator
may seem purely mathematical, but it will be shown to have
clear physical implications. In particular, as the ladder
operators are essentially defined to  be proportional to the
vector potential (and therefore also the electric field),
the photon-number operator can be considered as an effective
operator that partly reflects the physical properties of the
electric field. For instance, under certain nonequilibrium
conditions studied in Sec.~\ref{sec:results}, the photon number
can oscillate due to the interference seen in the electric
fields. It is also found that without the above exact form
for the position-dependent normalization coefficient
the resulting photon number expectation value
oscillates near material interfaces at thermal equilibrium. The properly
normalized annihilation operator defined in Eqs.~\eqref{eq:totalfielda} and
\eqref{eq:acommutation} always results in a photon-number
expectation value that is constant everywhere
at thermal equilibrium.

\subsection{Fields emitted by the left and right source domains}
For mathematical comparison of the proposed position-dependent photon annihilation
operator with previously used IORF approaches,
we separate the annihilation operator in Eq.~\eqref{eq:totalfielda} into
parts $\hat a_\mathrm{R}(x,\omega)$ and $\hat a_\mathrm{L}(x,\omega)$ arising from the emission
from the half spaces $]\!-\infty,x]$ and $[x,\infty[$, respectively. In the reflectionless
case these operators also correspond to the right and left propagating modes.
The left and right source domain operators are given by
\begin{align}
 \hat a_\mathrm{R}(x,\omega) & =\frac{\int_{-\infty}^x G_\mathrm{A}(x,\omega,x')\hat f(x',\omega)dx'}{C(x,\omega)}\label{eq:ar},\\
 \hat a_\mathrm{L}(x,\omega) & =\frac{\int_x^\infty G_\mathrm{A}(x,\omega,x')\hat f(x',\omega)dx'}{C(x,\omega)}\label{eq:al}.
\end{align}
These operators account for the normalized contribution of each source
point located to the left and right from the point of observation $x$ but generally
contain both right and left propagating terms. Alternatively to Eqs.~\eqref{eq:ar} and \eqref{eq:al}
one could also separate $\hat a(x,\omega)$ to the conventional left
and right propagating parts by separately accounting for the left and right propagating parts
of the Green's function $G_\mathrm{L}(x,\omega,x')$ and $G_\mathrm{R}(x,\omega,x')$,
introduced in Eq.~\eqref{eq:GB}.
However, this would not result in the canonical commutation
relations except for some special cases.
In the case of operators in Eqs.~\eqref{eq:ar} and \eqref{eq:al},
the commutation relations are generally given by
\begin{align}
 &[\hat a_\mathrm{R}(x,\omega),\hat a_\mathrm{R}^\dag(x',\omega')]\nonumber\\
 &\hspace{0.5cm} = \frac{\int_{-\infty}^{\min(x,x')} G_\mathrm{A}(x,\omega,y)G_\mathrm{A}^*(x',\omega',y)dy}{C(x,\omega)C(x',\omega')}\delta(\omega-\omega'),\\
 &[\hat a_\mathrm{L}(x,\omega),\hat a_\mathrm{L}^\dag(x',\omega')]\nonumber\\
 &\hspace{0.5cm} = \frac{\int_{\max(x,x')}^\infty G_\mathrm{A}(x,\omega,y)G_\mathrm{A}^*(x',\omega',y)dy}{C(x,\omega)C(x',\omega')}\delta(\omega-\omega'),\\
 &[\hat a_\mathrm{R}(x,\omega),\hat a_\mathrm{L}^\dag(x',\omega')]\nonumber\\
 &\hspace{0.5cm} = [\hat a_\mathrm{L}(x',\omega'),\hat a_\mathrm{R}^\dag(x,\omega)]^*\nonumber\\
 &\hspace{0.5cm} = \frac{\theta(x-x')\int_{x'}^x G_\mathrm{A}(x,\omega,y)G_\mathrm{A}^*(x',\omega',y)dy}{C(x,\omega)C(x',\omega')}\delta(\omega-\omega')\label{eq:lastcommutator},
\end{align}
where the integrals are taken over the source domain region that is common
for both operators. In regions where the field only propagates in one direction
[i.e., $G(x,\omega,x')$ only contains terms of the form
$e^{ikx}$ or $e^{-ikx}$], the canonical commutation relation
arises naturally and allows straightforwardly separating the photon annihilation
operator into the left and right propagating parts. If the
Green's function contains both $e^{ikx}$ and $e^{-ikx}$,
the photon annihilation operators $\hat a_\mathrm{R}(x,\omega)$
and $\hat a_\mathrm{L}(x,\omega)$ do not commute, and thus,
defining the left and right source domain operators in Eqs.~\eqref{eq:ar} and \eqref{eq:al}
while satisfying canonical commutation relations is not possible.
The same applies to defining the corresponding left and right
propagating operators. This is fundamentally the origin
of the anomalies found in the commutation relations of
the photon annihilation operator \cite{Barnett1996,Ueda1994,Aiello2000},
and also the origin of the photon-number oscillations observed in Sec. \ref{sec:results}.
Note, however, that the annihilation operators of the left and right source domains
commute at a common position since the integration domain in the commutation
relation in Eq.~\eqref{eq:lastcommutator} is of zero length when $x=x'$.
Therefore, the photon-number operator can always be separated into
parts corresponding to the left and right source domains.

\subsection{Poynting vector and energy density}
For additional physical insight, we will compare the position dependence of the photon-number
expectation value following from Eq.~\eqref{eq:photonnumber}
to the well-known fluctuations in the electric field, energy fluxes, and energy densities.
The one-dimensional quantum optical Poynting vector operator
is defined in terms of the positive and negative frequency parts of the electric
and magnetic field operators as $\hat{S}(x,t)=\hat{E}^-(x,t)\hat{H}^+(x,t)+\hat{H}^-(x,t)\hat{E}^+(x,t)$
\cite{Janowicz2003,Loudon2000}.
Substituting the positive and negative frequency parts of the given electric and magnetic field
operators and calculating the expectation value gives the spectral component of the
quantum optical Poynting vector as
\begin{equation}
 \Scale[0.95]{\displaystyle\langle\hat{S}(x,t)\rangle_\omega =\frac{1}{2\pi^2}\!\int\!\mathrm{Re}[G_\mathrm{E}^*(x,\omega,x')G_\mathrm{H}(x,\omega,x')]\langle\hat\eta(x',\omega)\rangle dx',}
 \label{eq:poynting}
\end{equation}
where $G_\mathrm{H}(x,\omega,x')=G_\mathrm{B}(x,\omega,x')/\boldsymbol{(}\mu_0\mu(x,\omega)\boldsymbol{)}$.
The brackets denote the expectation value over all states
resulting in the source field photon-number expectation value of Eq.~\eqref{eq:sourcefieldn},
and the subscript $\omega$ denotes the spectral component of the Poynting vector,
i.e., the integrand when the total Poynting vector is expressed as an integral
over positive frequencies.

Defining the electromagnetic energy density in a general, lossy, dispersive
medium has been challenging and common definitions have, e.g., led
to negative values for the energy density \cite{Ziolkowski2001}
or energy density expressions that are valid only for
Lorentz dielectrics \cite{Ruppin2002}.
We use a recently generalized definition of the average
total energy density introduced by Vorobyev \cite{Vorobyev2012,Vorobyev2013}.
However, as the definition was originally developed for time averages
assuming a classical sinusoidal electromagnetic field, we
use a prefactor $1/2$ instead of $1/4$ for general non-time-averaged
fields giving the energy density as
\begin{align}
 \langle\hat u(x,t)\rangle_\omega =\;&\frac{\varepsilon_0}{2}\Big(1+\Big|\frac{\partial(\chi_e(x,\omega)\omega)}{\partial\omega}\Big|\Big)\langle\hat{E}(x,t)^2\rangle_\omega\nonumber\\[4pt]
 &+\frac{\mu_0}{2}\Big(1+\Big|\frac{\partial(\chi_m(x,\omega)\omega)}{\partial\omega}\Big|\Big)\langle\hat{H}(x,t)^2\rangle_\omega.
 \label{eq:edensity}
\end{align}
Here $\chi_e(x,\omega)=\varepsilon(x,\omega)-1$ and $\chi_m(x,\omega)=\mu(x,\omega)-1$
are the position-dependent electric and magnetic susceptibilities.

The spectral components of the electric and magnetic field fluctuations in Eq.~\eqref{eq:edensity} can
be directly calculated by using the conventional Green's function expressions for
the field operators giving
\begin{equation}
 \langle\hat{E}(x,t)^2\rangle_\omega=\frac{1}{2\pi^2}\int|G_\mathrm{E}(x,\omega,x')|^2\Big(\langle\hat\eta(x',\omega)\rangle+\frac{1}{2}\Big)dx'\label{eq:efluct}
\end{equation}
for the electric field. The expression for the magnetic field strength fluctuation is obtained
with $G_\mathrm{E}(x,\omega,x')\rightarrow G_\mathrm{H}(x,\omega,x')$.
It is also possible to express the electric field fluctuation directly in terms
of the introduced position-dependent photon-number operator as
\begin{equation}
 \langle\hat E(x,t)^2\rangle_\omega=\frac{\hbar\omega}{\varepsilon_0}\rho(x,\omega)\Big(\langle\hat n(x,\omega)\rangle+\frac{1}{2}\Big),
\end{equation}
where we have used the conventional definition for the electrical contribution of the
local density of EM states (electric LDOS) as \cite{Joulain2003}
\begin{equation}
 \rho(x,\omega)=\frac{\varepsilon_0\omega}{2\pi^2\hbar}|C(x,\omega)|^2=\frac{2\omega}{\pi c^2S}\mathrm{Im}[G(x,\omega,x)].
 \label{eq:ldos}
\end{equation}

\subsection{\label{sec:balance}Thermal balance}
For a better understanding of the introduced photon-number concept it is essential to consider
its contribution to local energy balance at position $x$. The Poynting theorem
relates the local power dissipation and generation
to the current density and electric field at position $x$ and to
the divergence of the Poynting vector \cite{Jackson1999}. Therefore, in one dimension, the spectral
energy transfer rate $\langle Q(x,t)\rangle_\omega$, i.e., the spectral net emission between
the field and the local medium, is given by
\begin{equation}
 \langle Q(x,t)\rangle_\omega=\frac{\partial}{\partial x}\langle\hat S(x,t)\rangle_\omega=-\langle\hat J(x,t)\hat E(x,t)\rangle_\omega.
 \label{eq:conservation}
\end{equation}
The current density term $\hat J(x,t)=\hat J_\mathrm{abs}(x,t)-\hat J_\mathrm{em}(x,t)$
consists of parts corresponding to absorption and emission.
The photon emission is described by the Langevin noise current operator
$\hat J_\mathrm{em}(x,\omega)=j_0(x,\omega)\hat f(x,\omega)$
introduced as a field source in Eq.~\eqref{eq:Helmholtz}.
The photon absorption term is of the form
$\hat J_\mathrm{abs}(x,\omega)=\varepsilon_0\omega\,\mathrm{Im}[n(x,\omega)^2]\hat E^+(x,\omega)$
so that the absorption rate is proportional to the square of the electric field,
or equivalently the electric field fluctuation.
Substituting the time domain current terms (i.e., the Fourier
transforms of the frequency domain terms) to Eq.~\eqref{eq:conservation} and calculating
the expectation values over source field photon-number states gives the
local net emission rate in terms of the photon numbers of
the source and the total electromagnetic fields as
\begin{equation}
 \Scale[0.96]{\displaystyle\langle Q(x,t)\rangle_\omega=\hbar\omega^2\mathrm{Im}[n(x,\omega)^2]\rho(x,\omega)[\langle\hat\eta(x,\omega)\rangle-\langle\hat n(x,\omega)\rangle].}
 \label{eq:divP}
\end{equation}
Equation \eqref{eq:divP} directly shows that the local net emission rate is
zero only if the material is lossless $(\mathrm{Im}[n(x,\omega)^2]=0)$, the electric LDOS is zero $[\rho(x,\omega)=0]$,
or the field is in local thermal equilibrium $[\langle\hat n(x,\omega)\rangle=\langle\hat\eta(x,\omega)\rangle]$.
Equation \eqref{eq:divP} also nicely separates the effect of temperature and
wave features in the local net emission rate: The effect of temperature is described
by the photon-number operators and the effect of wave features is described by the
imaginary part of the Green's function.
In addition, Eq.~\eqref{eq:divP} is essentially the equivalent of the multiprobe
Landauer-B\"uttiker formula \cite{Buttiker1992,Saaskilahti2013} generalized for photons and continuous media.
In resonant systems where the energy exchange is dominated by a narrow frequency band,
condition $\langle\hat Q(x,\omega)\rangle_\omega=0$ can be used
to  approximately determine the steady-state temperature of a weakly interacting resonant
particle \cite{Bohren1998}. This leads to concluding that in order to reach a thermal
balance with the field, the particle must reach a temperature
that is equal to the effective field temperature so that the term
$\langle\hat\eta(x,\omega)\rangle-\langle\hat n(x,\omega)\rangle$ disappears.

\section{\label{sec:results}Results}

\begin{figure*}
\includegraphics[width=\textwidth]{fig1}
\caption{\label{fig:semi}(Color online) (a) The effective photon number, (b) electric field fluctuation, (c) electric LDOS, (d) energy density,
(e) Poynting vector, and (f) net emission rate in the vicinity of an interface separating a lossy medium with refractive index
$n_1=2.5+0.5i$ and temperature 300 K from vacuum at 0 K.
The solid lines correspond to the photon energy $\hbar\omega=0.10$ eV ($\lambda=12.4$ $\mu$m)
and the dashed lines correspond to the photon energy $\hbar\omega=0.14$ eV ($\lambda=8.86$ $\mu$m).
The electric field fluctuation is given in the
units of $\hbar\omega/(2\pi\varepsilon_0cS)$,
the electric LDOS in the units of $2/(\pi cS)$,
the energy density in the units of $\hbar\omega/(2\pi cS)$,
the Poynting vector in the units of $\hbar\omega/(1000\pi S)$,
and the net emission rate in the units of $\hbar\omega^2/(1000\pi cS)$.}
\end{figure*}

To investigate the physical implications of the concepts presented in Sec.~\ref{sec:theory}
we compare the position-dependent photon number to the corresponding electric field fluctuation, electric
LDOS, energy density, Poynting vector, and net emission rate in two geometries: a single interface
separating a lossy medium from vacuum and a vacuum cavity formed between two
lossy media. The definitions
for the electric field fluctuation, energy density, electric LDOS, and Poynting vector coincide
with the conventional Green's function based definitions. Instead, the position-dependent
photon-number operator predicts different results.

\subsection{Dielectric-vacuum interface}

The single interface structure consists of a semi-infinite lossy
medium with refractive index $n=2.5+0.5i$ at temperature $T_1=300$ K. The field
incident from vacuum is a vacuum field with $T_2=0$ K.
Figure \ref{fig:semi} shows the effective photon number, electric field fluctuation, electric LDOS,
energy density, Poynting vector, and net emission rate as a function of position for the single
interface geometry for photon energies $\hbar\omega=0.10$ eV and
$\hbar\omega=0.14$ eV, corresponding to wavelengths $\lambda=12.4$ $\mu$m and $\lambda=8.86$ $\mu$m.
The expectation value of the photon number operator in Eq.~\eqref{eq:photonnumber}
is plotted in Fig.~\ref{fig:semi}(a). The effective photon number has a strong position dependence
and it oscillates both in the vacuum and inside the lossy medium. In the lossy medium
the oscillations are damped and the photon number saturates to a constant
value far from the interface. The damping takes place over a distance of
10 $\mu$m that approximately corresponds to the penetration depth of radiation.
The oscillations in the vacuum can be explained by separately considering
the interference of the field component terms generated by the lossy half-space
and the incident field from the vacuum, i.e., the left and right source domain contributions
$x'\in]\!-\infty,0]$ and $x'\in[0,\infty[$ in Eq.~\eqref{eq:photonnumber}.
On the vacuum side, the term $|G(x,\omega,x')|^2$ in Eq.~\eqref{eq:photonnumber}
is constant for the right source domain contribution as it describes
a simple propagating wave in that region. The contribution from the left
source domain involves a Green's function with standing wave features
and therefore $|G(x,\omega,x')|^2$ for the left source domain oscillates.
To preserve the canonical commutation relations,
however, the oscillations are compensated by changes in the contribution
of the fields generated by the lossy medium. This is a direct
mathematical consequence imposed by the preservation of the canonical
commutation relations and results in variations of the contributions
of the vacuum field at $T_2=0$ K and the lossy layer at $T_1=300$ K
as a function of position even in the vacuum. In lossy media, similar
oscillations occur but they are quickly damped by the losses.
The oscillations are expected to be related to defining the ladder operators so
that they are proportional to the vector potential and the electric field. This implies
that the resulting photon number is in fact a quantity that mainly reflects the features
related to electric field and field--matter interactions involving electrical dipoles.

The corresponding position-dependent magnitude of the electric field
fluctuation in Eq.~\eqref{eq:efluct} is plotted in Fig.~\ref{fig:semi}(b). The magnitude
in the vacuum is larger than inside the lossy medium. This is not
always the case, since it depends on the refractive index of the medium and
the source field temperature. The field fluctuations also exhibit
similar oscillations as the photon numbers in Fig.~\ref{fig:semi}(a)
but the minima of the electric field fluctuations coincide with
the maxima of the photon-number oscillations. In the lossy layer the
fluctuations are quickly damped to a constant value. Overall,
oscillations in the photon number are accompanied by the oscillations
in the electric field fluctuations, but there is no direct correspondence
between the two.

The electric LDOS in Eq.~\eqref{eq:ldos} is plotted in Fig. \ref{fig:semi}(c).
The electric LDOS graphs clearly resemble the electric field fluctuations in Fig. \ref{fig:semi}(b)
oscillating in the vacuum and saturating to constant values inside the lossy medium.
In contrast to the field fluctutations, the electric LDOS is temperature independent and not directly
proportional to the fluctuations. However, since the zero-point-field contribution dominates at
chosen temperatures and frequencies, the oscillating photon number has only a small effect
on the electric field fluctuations. The oscillations in the electric LDOS describe the modified
emission rate due to interference better known as
the Purcell effect in cavities.

The energy density in Eq.~\eqref{eq:edensity} is shown in Fig.~\ref{fig:semi}(d).
Inside the lossy medium, the energy density exhibits damped oscillations and
in the vacuum it is perfectly constant since the electric and magnetic field
contributions in the energy density are equal and out of phase so that the total
energy density becomes constant. In the lossy medium the electric field contribution
dominates in the energy density. This leads to oscillations that
resemble the forms seen in the electric field fluctuation graphs in
Fig.~\ref{fig:semi}(b).

The Poynting vector in Eq.~\eqref{eq:poynting} is shown in Fig.~\ref{fig:semi}(e).
No net power propagates deep inside the lossy material since the
absorption and emission of thermal photons is in balance, and therefore,
the Poynting vector equals zero. The field generated in the material near
the interface can propagate into the vacuum so that the Poynting vector
grows exponentially and preserves its constant value through the vacuum
indicating a constant radiative heat flow out of the lossy half-space.

The net emission rate given by Eq.~\eqref{eq:divP} is plotted
in Fig.~\ref{fig:semi}(f). The net emission is naturally zero in the vacuum.
The positive net emission in the lossy medium
near the interface denotes that the rate of photon emission
outweighs the rate of photon absorption. Inside the lossy medium
the net emission rate decays to zero since the photon emission
and absorption become balanced. However, no oscillations appear
in the net emission rate. This is due to the infinitely large uniform
half spaces and thermal field statistics. In the presence
of a nonuniform temperature profile in the lossy medium
(not shown) the oscillations seen in
the electric LDOS in Fig.~\ref{fig:semi}(c) are also present in the
net emission rate in the lossy medium.

\begin{figure*}
\includegraphics[width=\textwidth]{fig2}
\caption{\label{fig:slab}(Color online) (a) The effective photon number, (b) electric field fluctuation,
(c) electric LDOS, (d) energy density, (e) Poynting vector, and (f) net emission rate
in the vicinity of a vacuum gap separating lossy media with refractive indices
$n_1=1.5+0.3i$ and $n_2=2.5+0.5i$ at temperatures 400 and 300 K. The width of the cavity is 10 $\mu$m.
The solid lines correspond to the second resonant photon energy $\hbar\omega=0.118$ eV ($\lambda=10.5$ $\mu$m)
and the dashed lines correspond to the off-resonant energy $\hbar\omega=0.140$ eV ($\lambda=8.86$ $\mu$m).
The electric field fluctuation is given in the units of
$\hbar\omega/(2\pi\varepsilon_0cS)$, the electric LDOS in the units of $2/(\pi cS)$,
the energy density in the units of $\hbar\omega/(2\pi cS)$,
the Poynting vector in the units of $\hbar\omega/(1000\pi S)$,
and the net emission rate in the units of $\hbar\omega^2/(1000\pi cS)$.}
\end{figure*}

\subsection{Vacuum gap between lossy media}

As a slightly more complex example we also investigate a cavity structure which consists of two semi-infinite media
with refractive indices $n_1=1.5+0.3i$ and $n_2=2.5+0.5i$ at temperatures
$T_1=400$ K and $T_2=300$ K, separated by a vacuum gap of thickness $10$ $\mu$m.
Figure \ref{fig:slab} shows the effective photon number, electric field fluctuation, electric LDOS,
energy density, Poynting vector, and net emission rate as a function of position
for the cavity geometry for photon energies $\hbar\omega=0.118$ eV ($\lambda=10.5$ $\mu$m)
corresponding to the second resonance of the cavity and $\hbar\omega=0.140$ eV ($\lambda=8.86$ $\mu$m)
that is off-resonant. As in the case of results for the single interface geometry
presented above, there are periodic oscillations in the effective photon number as presented
in Fig.~\ref{fig:slab}(a). For the second resonant energy the photon number has two
peaks in the cavity as expected. At resonant energies observing oscillations in the
photon number, however, requires an asymmetric cavity: If the refractive indices
of the left and right lossy media were equal (not shown), the photon-number
oscillations inside the cavity would completely disappear for
resonant frequencies. On the left and right of the cavity in Fig.~\ref{fig:slab}(a),
the photon number again saturates to constant values depending
on the source field temperature.

The corresponding electric field fluctuations are presented in Fig.~\ref{fig:slab}(b).
As in the case of the single interface geometry, the magnitudes of the
electric field fluctuations are larger in the vacuum than in the lossy medium.
The extrema of the electric field fluctuations are located at the same
positions as the extrema of the photon number in Fig.~\ref{fig:slab}(a).
Inside the lossy media, the oscillations are again damped and eventually
reach constant values, which are different
on the left and right due to the different source field temperatures.

The electric LDOS is plotted in Fig. \ref{fig:slab}(c).
Again, the electric LDOS oscillates in the vacuum and saturates to
constant values in the lossy media resembling the electric field fluctuation
in Fig.~\ref{fig:slab}(b). However, there are some differences.
For example, the difference in the oscillation magnitudes
of the resonant and off-resonant energies in the electric LDOS in the vacuum
is larger than the corresponding difference in the electric field fluctuation
in Fig.~\ref{fig:slab}(b). This is due to the effect of the oscillating photon
number in the electric field fluctuation. The effect is hardly visible
in the electric field fluctuation in Fig.~\ref{fig:slab}(b), but becomes larger
when the temperature of the left medium is increased (not shown).

The energy density shown in Fig.~\ref{fig:slab}(d) exhibits damped
oscillations inside the lossy medium and in the vacuum it is perfectly
constant as in the case of the single interface geometry.
In the lossy media the energy density due to the
electric field contribution is again larger than in the vacuum
and leads to oscillations that
resemble the form seen in the electric field fluctuation graph in
Fig.~\ref{fig:slab}(b). Note that the energy density is
smaller in the left medium than in the right medium even though the left
medium has a higher temperature. This is due to the
effect of electric susceptibility which is larger
at the right medium. However, if the temperature is increased on
the left the energy density on the left at some point naturally
exceeds the energy density on the right.

The Poynting vector is plotted in Fig.~\ref{fig:slab}(e). In the vacuum gap,
the Poynting vector is again constant since there is no dissipation.
The positivity of the Poynting vector denotes
net energy transfer towards the medium at lower temperature.
Inside the lossy media, the Poynting vector
asymptotically reaches zero far from the interfaces.
The damping of the Poynting vector is faster in the right medium than in the left medium due
to the larger imaginary part of the refractive index.

The net emission rate is shown in Fig.~\ref{fig:slab}(f).
Again the net emission rate is zero in the vacuum and it
decays to zero inside the lossy media. Positive (negative)
values denote that the rate of photon emission (absorption)
outweighs the rate of photon absorption (emission).
The higher absolute value of the net emission rate in
the lossy medium with higher imaginary part of the refractive
index is related to larger loss and the faster damping of the Poynting vector
in Fig.~\ref{fig:slab}(e). In the presence of small losses inside
the cavity (not shown) the net emission rate exhibits
oscillations similar to the oscillations of the electric
LDOS in Fig.~\ref{fig:slab}(c). This directly reflects the Purcell effect
and position-dependent emission rate of particles placed in the cavity.

The proposed position-dependent ladder and photon-number operators predict
that the effective photon numbers oscillate with respect to the positions as shown in
Figs.~\ref{fig:semi}(a) and \ref{fig:slab}(a).
In contrast to the field quantities, the effective photon number provides
a simple metric for finding the thermal balance formed due to interactions
taking place through the electric field and electric dipoles as detailed in
Eq.~\eqref{eq:divP}. Since the photon number
as defined in this work is also expected to be directly related both
to local temperature and rate of energy exchange taking place between the
electric field and the dipoles constituting the lossy materials, we
expect that the predicted photon-number oscillations can also be measured.
A good candidate for such a measurement would be a setup consisting of a
high-quality-factor cavity where
the magnitude of oscillations as well as the incoming radiation
on the left and right can be better controlled than in the single interface case.
Photon-number measurements have already been performed in cavities \cite{Maitre1997},
but not in nonequilibrium conditions which is necessary for the oscillations of the effective
photon number with respect to the position. If the cavity is asymmetric,
the photon-number oscillations are more easily observable
than in a symmetric cavity where the photon-number oscillations
can disappear at resonant frequencies. If one
had a thermometer that resonantly couples to one of the cavity resonances and
is anisotropic so that it is capable of detecting only the single perpendicular mode
studied in this work, then the predicted photon-number oscillations could be easily
detected experimentally. In reality the measurement configuration is naturally
more complex as controlling the directivity of a nanoscale
thermometer may not be that straightforward, but similar
effects are nevertheless also expected to be observable in fully three-dimensional
configurations. As the taken approach is very general, generalizing the model
to three dimensions is expected to be straightforward.
In this paper we have investigated only thermal source fields in detail, but
the introduced operators are expected to enable also a much more general description
of the quantized fields obeying other kinds of quantum statistics.
For example, replacing the noise operators with operators describing partly
saturated emitters \cite{Hayrynen2010b} could result in a simple but realistic
quantum description of the generation of laser fields, and furthermore,
the use of nonlinear source field operators \cite{Hayrynen2012b,Hayrynen2010c}
could even allow modeling single photon sources and detectors.

\section{\label{sec:conclusions}Conclusions}
We have defined and studied position-dependent ladder operators for the electromagnetic
field in a way that is consistent with the canonical commutation relations
and also enables a physically meaningful definition of an effective position-dependent
photon-number operator that has a very attractive and simple connection to the
electric field, the temperature, and thermal balance of the system.
The introduced operators predict oscillations in the expectation value of the effective
photon number even in simple one-dimensional
layered geometries. Since the effective photon number is expected to be directly related to
experimentally observable local temperatures in measurements in which the field-matter
interaction is dominated by the coupling to the electric field, this suggests that the
oscillations could be experimentally observable by measuring similar
oscillations in the temperature. This essentially differentiates our definition of the
effective photon number from the conventional position-independent definitions that
do not take the physical properties of the electric field similarly into account.

The introduced ladder and photon-number operators provide an additional means
to quantify the electric field and give further insight into the local
photon-number balance associated with the electric field and the formation
of the local thermal equilibrium.
The additional insight provided by the approach also allows improved understanding
of the challenges and physical implications of separating the photon annihilation operator
into parts emitted by the left and right source domains or left and right propagating parts as done in
many seminal quantization schemes. If the requirement of canonical commutation
relations and ease of physical interpretation are not relaxed,
the separation is not generally possible. This is in agreement with the
anomalies found in the commutation relations of
the photon annihilation operator. However, possibly the greatest opportunities enabled by the
new formulation and the consistent definitions of the ladder and photon-number
operators are in extending the description to quantum systems
that are not limited to thermal fields. This could, e.g., enable a more versatile description
of the noise and measurement backaction in complex and realistic quantum systems.

\begin{acknowledgments}
This work has in part been funded by the Academy of Finland and the Aalto Energy Efficiency Research Programme.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


Institution of Incorporated Engineers, Sri Lanka (IIESL) established in 1977 as "All Ceylon Engineering Diplomates Association", was transformed to a professional body under the name of " Institute of Engineering Diplomates, Sri Lanka", by an Act of Parliament(Act No. 64 of 1992). It was renamed with the present status as "Institution of Incorporated Engineers, Sri Lanka" by an Act of Parliament (Act No.11 of 2000). IIESL has a wide opening for personnel of all level in the field of Engineering Technology. Incorporated Engineers are the internationally recognised category of Engineers in the field of Engineering Technology, who effectively manage the construction, operation, maintenance and project management functions, by implementing appropriate technology.
ELIGIBILITY CRITERIA TO BECOME A MEMBER OF IIESL?
HOW TO PARTICIPATE IN CPD & SHORT TERM PROGRAMS?
DOES IIESL HAVE FOREIGN BRANCHES?
Yes. IIESL has two overseas branches. One in Dubai, UAE and the other in Doha, Qatar.
WHAT ARE THE AVAILABLE FACILITIES AT IIESL HEAD OFFICE?
The Head office Building constructed at Udumulla, Battaramulla consists of IIESL Secretariat and Council Meeting Room. This Council meeting Room is available for hire where it has facilities to conduct training programmes. At present IIESL Toastmasters Meetings for IIESL Members are conducted there. There are plans to construct seven storied building in the same premises to accommodate an auditorium. Seminar rooms, Library in future. Once the construction is completed the Inco office will be housed in the same building.
WHAT IS SDEF (SAARC DIPLOMA ENGINEERS FORUM)?
SAARC Diploma Engineers Forum (SDEF) was established in 1998 and its' first International Convention was held in Dhaka, Bangladesh in October 1998.SAARC Diploma Engineers Form consists of following Member Organisations.
To establish a common recognition, a dignified position for the Diploma Engineers in the SAARC countries.
WHO IS AN INCORPORATED ENGINEER?
Incorporated Engineers are specialists in the development and application of today's technology, managing and maintaining applications of current and developing technology at the highest efficiency. With their detailed knowledge and understanding of current engineering applications, they possess the skills and know-how to make things to happen and often have key operational management roles. They have detailed understanding of a recognized field of technology and exercise independent judgement and management within that field. They add substantial value, independently and as leaders, to any organization where technology is a core activity or supports the business.
HOW TO GET A STALL AT INCO EXHIBITION?


text:
Colleen Murphy
Born in Rouyn-Noranda, Quebec Colleen Murphy is a playwright and filmmaker. Her distinct, award-winning films have played at festivals around the world and include Putty Worm ('93), The Feeler ('95), Shoemaker ('96), Desire ('00), War Holes ('02) and Girl with Dog ('06). Murphy's play The December Man (L'homme de décembre), about the Montreal Massacre, won the 2007 Governor General's Literary Award for English Language Drama and the 2008 Canadian Author's Association/Carol Bolt Award for Drama. She is currently Playwright-in-Residence at Tapestry New Opera Works in Toronto.
Director's Artistic Statement
Writers often talk to the dead through their work, but sometimes it is better to let the dead talk. It was this notion that drew me to Cheryl Jack's script. What makes Cheryl's small drama so compelling is her absolute refusal to vilify, redeem, or judge. Instead, the author imagines how it might feel to be inside the situation of men who have been left to die on an icy field. Never sentimental, always emotionally truthful, Cheryl's script is wholly original.
While doing a one-year Playwriting Residency at the University of Regina, I was privileged to direct this film; to work with talented students and local professionals, to work on 16mm film, to work in minus 20 degree temperatures and to work on a story that was meaningful to the actual ground I was standing on. Out In The Cold is a metaphor for the blinding disregard Canadians continue to demonstrate towards the First Nations people in this country.
Films by Colleen Murphy

redpajama_set_name: RedPajamaCommonCrawl


Are You Leveraging the Right Tools for Marketing Your E-Commerce Site?
No matter what type of marketing campaign you're working on, I can't overstate the importance of analytics. Top online marketers are able to achieve conversion rates over three times higher than their competition just by virtue of investing in analytics, testing, and optimizing.
Try to leave room for changes in the design of your campaigns. And, as data comes in, start thinking of ways to change them to accommodate your customers. That way, you can make immediate use of what you're learning about what works and what doesn't. Make a habit of conducting A/B testing for all of your marketing efforts. Let the data you receive determine which option you should go with over the long term.
That said, in this post, I'll briefly run through several forms of marketing and touch on some fundamental ways to implement them. Some of this advice may seem simplistic, but you'd be surprised how far you'll get just by making sure you're doing these things. A lot of that has to do with the fact that many of your competitors are doing them!
Developer Tools, the "batbelt" of developers everywhere, generally stirs up conversations telling you about what you should and shouldn't use. However, I've always had a different take on it, I change my toolset based on the work that I'm doing. When I was a .NET developer I worked on Windows and in Visual Studio. With WordPress and PHP development, I'm not going to use those tools as I don't have to.
So having said all that, I'm going to tell you what works for me and in general I try to use the bare minimum to get stuff done here at WooThemes. With so much code to write, I don't want a million apps and settings to go by – I just want to login, write code, and deploy.


Jamaicans traveling to PyeongChang, South Korea, for the 2018 Winter Olympics have nothing to fear, says the country's Charge d'Affaires Young-Gyu Lee.
His assurance comes as the 92 teams begin arriving in the Asian nation for the start of the Games, which are scheduled for February 9 to 25. The two Koreas are technically still at war, following the July 27, 1953 armistice.
Now that tensions have been eased, Lee said he wants to assure Jamaicans of their safety and well-being while in PyeongChang.
He said that it was vital that Jamaicans who plan on making the trip to witness the Games be made to feel comfortable and safe, while in South Korea.
Jamaica will be represented by Carrie Russell and Jazmine Fenlator-Victorian.
"There is nothing to worry about while in Korea; I know that there may be lingering cause for some people to worry, but I am assuring the whole Jamaica - and, by extension, everyone coming - that it will be totally safe and exciting," Lee said.
"Jamaicans are lovely people and anywhere they go they are warmly welcomed. We are looking forward to them bringing their unique style and lively colours to PyeongChang," he added.
Hostile rhetoric between the North's leader Kim Jung-un and US President Donald Trump only served to bring the nations ever so close to renewed hostilities.
Subsequent attempts aimed at de-escalating tensions have resulted in an agreement that will see the North sending high-ranking officials, athletes, cheering and performing arts squads, taekwondo demonstration teams and journalists to PyeongChang. It means that a unified Korean team will participate under one Korean flag.
North Korea will be sending 22 athletes to compete in five disciplines including women's hockey, figure skating, short track speed skating, cross-country skiing and alpine skiing.
"It is expected that the Olympics and Paralympics Winter Games will be another great opportunity for Korea and Jamaica to deepen friendship and I must say that people in my country is looking forward to welcoming talented Jamaican athletes.
I remember the success of Jamaica's Cool Runnings team in Canada and we are hoping for a similar achievement and better in Korea for our Jamaican friends," Lee told The Gleaner.


text:
PS1 And PS2 Games Will Be Playable On PlayStation 4 Very Soon
By Oliver Haslam | January 29th, 2014
Backward compatibility is a big deal in the gaming world, and when Sony announced its PS4 console, much of the talk was about the lack of any ability to play those back catalogues of games that everyone had spent the last few years accumulating. Sony has since sought to rectify that by announcing PlayStation Now, the game streaming service that will see PS3 games streamed over the Internet, but there is no local support being added to consoles.
While this is all well and good for PS3 titles, what about those classic PS2 and PlayStation games that enthusiasts love so much? If the original Tomb Raider is your bag, then being able to play Lara's first outing on your PS4 is something you'd enjoy, and it seems Sony is getting ready to accommodate just that.
A source inside Sony's streaming service team has said that while PS3 games will only be streamable via PlayStation Now, older PlayStation and PS2 games will actually be able to run locally using hardware emulation, something Sony hasn't done since the early PS3 days. Software emulation via PSN has since been the order of the day for Sony's PlayStation brand, but the idea of hardware support returning to the brand will please hardcore gamers.
Part of that hardware emulation is Sony's aim to try and get enhanced HD visuals into the mix. Many of the past generations' biggest hits have had HD remixes over the years, and improved HD support across the board for PlayStation and PS2 titles would most definitely be a welcome addition.
While hardware support is great news though, we can't help but be much more interested in PlayStation Now. From a purely technical standpoint, streaming HD games over the Internet without having the video and input lag that plagued startups like Onlive is no mean feat, though with Sony's clout and tactical business purchases of late, we wouldn't put it past them. Early indications have been roundly positive, so we may not need hardware support after all!
But it would've been great that such things were cleared up at the announcement of the PS4 itself. After all, adding bits and pieces after the launch somewhat lays most of the excitement to rest.
(via: Eurogamer)


text:
Story Uuid: c3d1723d-5fd0-40a6-aae0-806f316ee7e1
Story Link: /#story/c3d1723d-5fd0-40a6-aae0-806f316ee7e1
Ad Zone: weather/blog
Story Slug: 2015-weather
2015 Weather
by Elizabeth McGiffin
KTVL
It's hard to talk about the weather over the past year without focusing on how hot it was!
This helped to extend the goring year, or the time period where temperatures stay above freezing to the 5th longest for the Medford Area. 2015 brought a stretch of 218 days between the last spring freeze and the first fall night to hit 32 degrees. This is still well behind last year's all time record of 241 days.
2015 has been securing its spot in the record books as the 2nd hottest year recorded in the Medford area. The average temperature (both daily highs and lows) for the year was around 59 degrees. This puts us just behind last year's record of 59.2 degrees, and pushes well past the 1992 average temperature of 57.8.
The past 3 years, the summer months have been setting new levels of record heat. The average temperature for the months of June, July and August came to 76.4 degrees. This is a degree and a half warmer than last summer and almost 2.5 degrees warmer than 2013.
The summer of 2015 was not only the hottest summer on record for the Medford area, but this year the Medford area recorded 21 days over 100 degrees. Including a new all-time record high temperature on June 31 of 109 degrees.
Despite all the heat we saw this year, we have been making up for it with plenty of snow to start the winter. The month of December has been setting record snowfall totals in places like Crater Lake where the snowiest December to date was set in 1948 when they picked up 196 inches. However, this year we've been able to set a new record of 196.7 inches.


Bradford go into the game on the back of two wins, against Port Vale and MK Dons but prior to that, the Bantams had only won 2 of 22 games.
"They're a club that've turned their own fortunes round, they couldn't win a game for love nor money and then all of a sudden out of the blue they've nicked a couple of wins and In fairness to them they've played very well in those performances.
"We know what they're about; they don't make any secret of how they play. They're a very direct side, they are back-to-front, they've got two wide players who want to cross early balls, they've got a big centre forward who wants to hold it up, they bang the ball at him and get out of midfield and they're effective at what they do. They're an organised and strong side.
Sign into Boro Player to watch the full interview with Graham Westley where he speaks about Tuesday's game with Crewe, the teams lack of goals and more on Bradford.
Jimmy Smith also had plenty to say before facing Bradford, read our interview with him here.


Dr. Jegan Jabez, MD is an internal medicine doctor who practices in Benton Harbor, MI. He is 64 years old and has been practicing for 26 years.
Summary: Jabez, Jegan MD: License # 4301064652: NATURE OF COMPLAINT: The physician engaged in Negligence – incompetence. ACTION TAKEN: The Michigan Department of Licensing and Regulatory Affairs, Bureau of Health Care Services has imposed a FINE and placed the physician's license on SUSPENSION.
Summary: Jabez, Jegan MD: License # 036084226: NATURE OF COMPLAINT: The physician has a sister-state discipline in the State of Michigan. ACTION TAKEN: The Illinois Department of Financial and Professional Regulation has placed the physician's license in REFUSE TO RENEW status.
Check the quality of care at hospitals where Dr. Jabez treats patients.


Have you ever found yourself wondering where in the world did God go? Why did I find myself in this intense visitation only to now find myself groping in the darkness, trying to find an ounce of light to cling to? What in the world happened? Did I do something wrong? Why isn't God speaking now when He was just showing me so much? These are all valid questions that go through every believers mind at some time or another, even those who are closest to God experience these uncertain seasons. This is the very place that takes the believer from an ordinary life, to an intense walk of faith.
From my own personal experience, while i'm in a season of encounter with God, the plans of heaven cause my spirit to cry out with tremendous joy and utter satisfaction and life just couldn't get any better than this; being in the safe place of Gods Presence, hearing the wonderful thoughts He has in His heart for me and the incredible future He speaks to my heart. What bliss, just to know that God has something planned for me that is for my benefit and for His Glory. It's quite undeniable when ones been visited with this type of transforming season. The Presence of God quenches every thirst and you feel as if nothing could bring you down, there's nothings bigger than your God in these moments and nothing compares to or satisfies like the sweet Presence of Jesus you have been experiencing. Wow, what a grateful heart I have. My Father loves me so much that when I take time and spend it with Him, seeking Him, loving on Him; He comes within those special moments and transform who I am. I want to abide there, dwell there and never, ever have to leave that place of His Presence. His light shines so intensely that it caused every dark place in my life to become light before me, my enemies scatter for a season when I'm in these most blessed times of visitation in Gods Presence.
During these times, nothing seems too heavy to bear or so difficult that this awesome God I serve can't fix it, after all He is Jehovah. Believing what He speaks is effortless, as the inner man is in full agreement with all that He is whispering to my heart. He says that His word is a lamp unto my feet and a light unto my path and I believe that Jesus is the word and therefore when He speaks to me, things are getting brighter before me. In this season when the Holy Spirit is moving upon me and I'm hearing this wonderful word that is bringing me life, I feel like an un-defeatable worshiper. God is on my side and this thing called life is going to be glorious. I come out of this wonderful season feeling refreshed, strengthened and in all ways encouraged that life is not hopeless and there is a brighter future than what I currently see.
One of the things I am assured of by the word of God is that when you're pushing toward God, He is pushing towards you. He loves us so much and enjoys our times of fellowship as much as we do. He loves us sitting at His feet or crying on His shoulder as we pour our hearts out and lay our burdens down. This is true faith that pleases God and it's seen by the desperation of those who need Him to live and exist. He stands proud as we dedicate out lives to His Kingdom and honor Him with our bodies. He couldn't be more pleased, by these acts of faith. He encourages us to never stop praying, to always press into His Kingdom, knocking and asking all the way. His reward is wonderful outpourings of the Holy Spirit, intimate moments of refreshing with the King of Kings, where secrets are whispered from His heart to yours and He reveals the promises He has for your life. Who wouldn't serve such a wonderful savior? I come out of my prayer room, having had one of these precious moments I long for and delight in, thinking to myself, it just doesn't get any better than this and I couldn't love Jesus any more than I love Him right now. He is my entire joy and my hearts desire, times like these are priceless to a worshipping heart.
A day goes by after this wonderful time with the Father and I feel as if I have a hold of the devils tail, my spirit is soaring, and nothing can take away my joy, my hope or my promises. Then after a while something happens and my world is suddenly occupied with some sort of trouble, trial, or test and I find myself thinking, no way, where is GOD? Suddenly after being on the mountain with the Lord, I'm wondering where my helper is. Although I don't feel abandoned because He's always with me, my promises on the other hand, seem like utter impossibilities. What the Lord just told me is falling apart, crumbling before my very eyes, going south as some would put it. Did I hear you Lord? Was that really your Spirit that visited me in those sweet moments of worship and fellowship, of course it had to be, your word says when I ask for bread you'll never give me a stone, when I ask for an egg, you'll never give me a scorpion, so when I ask you for the Holy Spirit you'll give me the Holy Spirit.
Satan suddenly begins his quandary of questions he throws at the human mind. My life has now darkened, the word you gave me has somehow slipped from me as I gaze on this devastation and disappointment has found a place in me, now I'm sad and feel bereaved of what you've promised. Satan moves in to strengthen my fears by creating many more thoughts of doubt; attracting every dark spirit from hell to harass the very validity of the voice of God in my life. I feel the foundation of my life shaking as tornado winds tear through my thoughts, my circumstances and my heart; screaming convincingly louder and louder with each passing moment in this valley of death; Hath God said?, Hath God said? He bellows and belches from the mouth of hell itself, challenging me, testing me to see if I will question or worse, deny this God I've loved and served and if He really knows me. I'm feeling as if Jesus, whom I love, didn't show up when I needed Him the most, He left me helpless and undone. This is how Mary felt when Jesus allowed Lazarus to die, for the specific purpose of revealing the Glory of the Lord to her.. He said to Mary, " Did I not say to you that if you would believe, you would see the Glory of the Lord? ' He is still asking us this today.
s faithful, He won't forget His promise to you" and peace once again fills my heart and I feel the strength of the Lord rising within me. Today, I've fought against this enemy of doubt that wages war against the very words you speak Lord, and today, you've caused me to overcome. I can once again believe for what I do not yet see. It's only Jesus that gives me life and helps me to overcome my enemies; which are many in this world; we must hold onto Him. Through this battle I've learned that I can't be passive nor can I let my guard down when I've been in the Presence of God and He's revealed His dreams for me. I need to always be alert and guard my mind with His word, realizing that all promises come with a test and a fight but through it all, even when I'm weak, when I cry out to Him, He will sustain me and now today, I can say thank you Lord, take a deep breath, pause and look ahead with my eye on the prize of His promises.


text:
Microdosing on Psychedelic Drugs Linked to Broad Range of Effects
April 21, 2021 12:50:01
In recent years, microdosing has become popular as a wellness trend, both in the United States as well as overseas in countries such as Australia. Microdosing involves consuming a low dose of a psychedelic drug to reduce anxiety and stress or boost performance.
While there have been some accounts by consumers who sing the praises of psychedelics, questions about how much of the reported benefits stem from the substances' pharmacological effects rather than the partaker's expectations and beliefs, and how microdosing works, still remain.
To help answer some of these questions, we'll look at a few studies on microdosing and highlight what they uncovered during their research. Research on psychedelics in Australia has advanced speedily, with many studies focusing on the science of microdosing. It is also evident that more Australians are experimenting with psychedelics, as the proportion of adults in Australia who have used psychedelics in their lifetime grew to 10.9% in 2019 from 8% in 2001.
An earlier study conducted by a researcher Vince Polito found that after a six-week period of microdosing, levels of stress and depression in some users were found to have reduced. The participants also admitted that their mind wandered less, which suggests that microdosing causes improved cognitive performance. Conversely, the research findings also note that there was a surge in neuroticism.
Another recent study, led by Stephen Bright, recruited participants who took part in both yoga and microdosing; the study also included participants who did neither of the two. The researchers found that yoga practitioners had higher levels of anxiety and stress in comparison with individuals who practiced microdosing and those who did not engage in microdosing or yoga. They also found that those who engaged in microdosing had higher levels of depression.
When compared to the control group though, the researchers found that both the microdosing and yoga group recorded higher overall scores on psychological well-being. Additionally, those who took part in both microdosing and yoga reported lower levels of stress, anxiety and depression, which suggests that yoga and microdosing may have synergistic effects.
Another study, conducted in collaboration with Germany's University of Göttingen, Macquarie University and Edith Cowan University, discovered an increase in conscientiousness and a reduction in neuroticism in the 76 study participants who engaged in microdosing. The findings were reported in the "Journal of Psychedelic Studies."
While there is still much that is unknown about psychedelics and microdosing, these studies provide a level of insight into what one may expect when taking psychedelics under supervision, which may help ease users' minds.
Researchers hope that in the future, scientific results on microdosing will be less mixed and more valid so that a clearer way forward can be determined.
These researchers' hopes could be answered sooner than they think as a number of companies, such as Cybin Inc. (NEO: CYBN) (OTCQB: CLXPF), are currently engaged in studying several psychedelic drug formulations for use in treating various ailments, particularly mental health conditions.
NOTE TO INVESTORS: The latest news and updates relating to Cybin Inc. (NEO: CYBN) (OTCQB: CLXPF) are available in the company's newsroom at https://ibn.fm/CYBN
About PsychedelicNewsWire
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PsychedelicNewsBreaks – Cybin Inc. (NEO: CYBN) (OTCQB: CLXPF) Announces Data Providing Strong Support to Advance Drug Development Candidates
First-of-a-Kind Study Identifies Benefits of Group Psychedelic-Assisted Therapy Sessions


This is the video of Get Rid Of Stretch Marks. Today i will show you Get Rid Of Stretch Marks In 30 Days Using Aloe Vera | Stretch Marks Removal.
First take aloe vera in a steel Pan.
Boil it for 30 minutes.
Now stain and put into a container.
Apply it on your stretch marks area.
You can use this oil 1-2 months.


text:
Вучедольська голубка — найвідоміша керамічна посудина з археологічних розкопок на Вучедолі. Схожа на голубку, керамічна посудина стала символом міста Вуковар, біля якого розташоване Вучедол. Мала культове призначення як кадильниця.

Опис пам'ятки
Посудина темного кольору, прикрашена білим орнаментом (банти, намисто, низка хвилястих та зигзагоподібних ліній на крилах) у гравірованому орнаменті та орнаменті, створеному штампованим стібком. На шиї є три інкрустовані символи пісочного годинника, тобто подвійна сокира. Вона служила кадилом і є унікальним зразком (сьогодні він служить історичним матеріальним джерелом).

Хоча керамічну посудину називають голубкою, вчені-археологи вважають, що насправді це куропатка. Археологічна знахідка змайстрована між 2800 і 2400 рр. до н. е. Була знайдена в 1938 році. В даний час знаходиться в Археологічному музеї в Загребі.

Вучедол знаходиться неподалік Вуковара, на честь ньогоназвана вучедольська культура, що включає широкий культурний комплекс від Карпат до Східних Альп та Дінари. Вважається, що воно виникло з приходом індоєвропейських поселенців близько 3000 р. до н. е. і тривало приблизно до 2200 р. до н. е. Характеристиками цієї культура є нові металургійні процеси, надзвичайно кваліфіковані гончарі. Вучедольська культура поширювалась у Східній Славонії на правому березі річки Дунай. На думку деяких дослідників, у них також був календар, записаний на керамічних посудинах. Вучедольська голубка є свідченням високого розвитку культури на той час.

Посилання

 Вучедолська культура

Джерела

Посуд
Доісторична скульптура

redpajama_set_name: RedPajamaWikipedia


text:
Q: WPF databinding: Why doesn't my copy display on the screen? What simple thing am I missing here? Why doesn't my copy display on the screen?
<Window x:Class="DeleteThis.MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="MainWindow" Height="350" Width="525" >
<Grid>

    <StackPanel>

        <TextBlock Text="{Binding Path=SomeCopy}" Height="35" Width="100" Margin="10"/>

    </StackPanel>
</Grid>

and my code-behind.
    public partial class MainWindow : Window
{

    private string _someCopy;
    public string SomeCopy
    {
        get
        {
            return _someCopy;
        }

        set
        {
            _someCopy = value;
        }
    }

    public MainWindow()
    {

        InitializeComponent();

        SomeCopy = "why doesn't this display";
    }
}

A: You never set the DataContext of the Window. Change your XAML to this...
<TextBlock Text="{Binding}" Height="35" Width="100" Margin="10"/>

...and change your code behind to add the DataContext line...
    public MainWindow()
    {
        InitializeComponent();

        SomeCopy = "why doesn't this display";

        this.DataContext = SomeCopy;
    }

Your current issue has nothing to do with needing a DependencyProperty as mentioned in the other answers.

A: WPF never finds out that the property changed.
To fix it, you can turn the property into a dependency property.
EDIT: You also need to bind to the property on the Window itself, like this
<TextBlock Text="{Binding Path=SomeCopy, RelativeSource={RelativeSource Self}}" ... />

A: SLaks's answer is the correct one. But making dependency properties manually is annoying, so I link you to my favorite solution: A custom PostSharp NotifyPropertyChangedAttribute that, when used in conjunction with PostSharp, makes all the properties of any given class into dependency properties.

redpajama_set_name: RedPajamaStackExchange


text:
No. 8 Michigan State holds off No. 14 Ohio State 86-77
Michigan State guard Cassius Winston, left, goes up for a shot against Ohio State forward Kaleb Wesson during the first half of an NCAA college basketball game in Columbus, Ohio, Saturday, Jan. 5, 2019. (AP Photo/Paul Vernon)
Cassius Winston scored 25 points, Nick Ward added 21 and No. 8 Michigan State extended its unbeaten streak to eight games with an 86-77 victory over No. 14 Ohio State on Saturday.
The second half was tied six times before the Spartans took the lead on a Ward foul shot, and a layup by Kenny Goins put them up by three with 3:28 left.
A Kyle Ahrens put-back at the 2:35 mark, a turnover by Ohio State's Keyshawn Woods and a pair of Aaron Henry foul shots all but sealed it for Michigan State. Ohio State got to within six points twice in the last minute but couldn't get closer.
Kaleb Wesson scored 25 points despite being in second-half foul trouble, and Luther Muhammed had 12 for the Buckeyes (12-2, 2-1 Big Ten), who saw a six game winning streak snapped.
Michigan State (13-2, 4-0) hasn't lost since Nov. 27.
Ohio State led 43-36 at halftime, boosted by a late 3-pointer from Duane Washington Jr. and another from Kaleb Wesson with 13 seconds left in the half.
Michigan State: Despite missing injured junior guard Joshua Langford, the Spartans bore down late in the second half and won their first of the new year after going 6-0 in December.
Ohio State: Matched Michigan State every step of the way until its shooting went cold and it faltered late. Kaleb Wesson continues to be the featured player on a fairly talented team, but the Buckeyes need a clone of him to help out.
Michigan State: Hosts Purdue on Tuesday.
Ohio State: At Rutgers on Tuesday.
Michigan State forward Nick Ward, left, goes up for a shot against Ohio State forward Kyle Young during the first half of an NCAA college basketball game in Columbus, Ohio, Saturday, Jan. (AP Photo/Paul Vernon)
Ohio State forward Kaleb Wesson, right, goes up for a shot against Michigan State guard Kyle Ahrens, left, and forward Nick Ward during the first half of an NCAA college basketball game in Columbus, Ohio, Saturday, Jan. (AP Photo/Paul Vernon)
Michigan State guard Matt McQuaid, right, goes up for a shot against Ohio State guard Duane Washington during the first half of an NCAA college basketball game in Columbus, Ohio, Saturday, Jan. (AP Photo/Paul Vernon)
Ohio State guard C.J. Jackson, left, goes up for a shot against Michigan State guard Matt McQuaid during the first half of an NCAA college basketball game in Columbus, Ohio, Saturday, Jan. (AP Photo/Paul Vernon)
Ohio State guard Duane Washington, right, puts up a shot against Michigan State, forward Xavier Tillman, left, and forward Kenny Goins during the first half of an NCAA college basketball game in Columbus, Ohio, Saturday, Jan. (AP Photo/Paul Vernon)
Michigan State forward Xavier Tillman, right, goes up for a shot against Ohio State forward Andre Wesson during the first half of an NCAA college basketball game in Columbus, Ohio, Saturday, Jan. (AP Photo/Paul Vernon)
Tags:Michigan Ohio College basketball Nick Ward Men's college basketball Kenny Goins Kaleb Wesson Keyshawn Woods Aaron Henry Kyle Ahrens
Kentucky tornadoes aftermath: Nearly 26,000 customers still without power
Ethan Crumbley's parents had their own troubles with law before their son's shooting
Michigan school: bullied suspect already thought of killing before the deadly shooting
Michigan school shooting: 3 killed and 8 injured, a 15-year-old suspect detained
Ohio Army National Guard Specialist has been AWOL for over a month
Father sacrifices himself to shield his daughter during plane crash on Michigan's Beaver Island


text:
Q: Mocha cannot find module 'factories' (and it's an npm module) In my test file:
const factory = require('factories');

I installed the node-factories package two ways:
npm install --save-dev node-factories
// npm test fails to find module
npm install --save node-factories
// npm test also fails to find the module

In the docs for node-factories, it specifies to require('factories') in the sources...
But no matter what, I keep getting this stack trace for JUST this module (and my local modules are in scope after I installed the dependencies),
Error: Cannot find module 'factories'
    at Function.Module._resolveFilename (module.js:489:15)
    at Function.Module._load (module.js:439:25)
    at Module.require (module.js:517:17)
    at require (internal/module.js:11:18)
    at Object.<anonymous> (/Users/sjcbsolo/Engineering/flex/io-server/src/encryption/decrypthandler.tests.js:9:17)
    at Module._compile (module.js:573:30)
    at Object.Module._extensions..js (module.js:584:10)
    at Module.load (module.js:507:32)
    at tryModuleLoad (module.js:470:12)
    at Function.Module._load (module.js:462:3)
    at Module.require (module.js:517:17)
    at require (internal/module.js:11:18)
    at /Users/sjcbsolo/Engineering/flex/io-server/node_modules/mocha/lib/mocha.js:222:27
    at Array.forEach (<anonymous>)
    at Mocha.loadFiles (/Users/sjcbsolo/Engineering/flex/io-server/node_modules/mocha/lib/mocha.js:219:14)
    at Mocha.run (/Users/sjcbsolo/Engineering/flex/io-server/node_modules/mocha/lib/mocha.js:487:10)
    at Object.<anonymous> (/Users/sjcbsolo/Engineering/flex/io-server/node_modules/mocha/bin/_mocha:459:18)
    at Module._compile (module.js:573:30)
    at Object.Module._extensions..js (module.js:584:10)
    at Module.load (module.js:507:32)
    at tryModuleLoad (module.js:470:12)
    at Function.Module._load (module.js:462:3)
    at Function.Module.runMain (module.js:609:10)
    at startup (bootstrap_node.js:158:16)
    at bootstrap_node.js:598:3
npm ERR! Test failed.  See above for more details.

Any thoughts out there from node sharks?

A: node-factories has an error in docs, it seems.
const factory = require('node-factories');

will yield the results you're looking for.
As a rule, what you require is what it looks like on the file system as the folder the module installs to in node_modules, which is also what it looks like when you do npm install.


Grants are available of up to £8,750 for SME businesses to grow and innovate.
The IMAGE programme, supported by the European Regional Development Fund, is offering funding opportunities for SME businesses to work with universities and tap into their leading expertise.
Cranfield University in partnership with the University of Bedfordshire, can support you in conducting a range of activities – from prototyping, development and testing of your product through to management coaching, finding business solutions and networking solutions.


text:
People are stealing mattresses from luxury hotels
By CBS News
Published: Dec. 12, 2019 at 6:00 PM EST
By: Megan Cerullo | CBS News
Some hotel guests wake so rested at luxury properties that they purchase the same kind of mattress they slept on. Then there are those patrons who steal them.
At least 48 mattresses have disappeared from guest rooms in the more than 1,100 four- and five-star European hotels surveyed by German review site Wellness Heaven. Guests at five-star hotels were 8% more likely to take mattresses, perhaps because they were more comfy, according to the survey.
That's far less than the nearly 900 towels or 753 bathrobes that hotels say went missing. Hangers, pens, cutlery, cosmetics and blankets were among the other most commonly lifted items. Personal electronics and small appliances, including tablet computers, hair dryers, coffee makers and TV sets were also reported missing from hotel rooms across the properties.
Upscale hotels often make their mattresses or pillows available for purchase to guests who've slept soundly during their stays. What's less clear is how thieves escape without paying for the not-so-compact pieces of hotel property. Some hoteliers told the survey company that guests snuck away with mattresses in the dark of night using elevators that led directly to underground parking.
Another guest threw a mattress out of the room's window, according to the site's hotel reviewer, Tassilo Keilmann.
"The nice thing about mattresses is they bounce so they don't really get damaged, and the guest then collected it from the road," Keilmann told CBS MoneyWatch.
Wellness Heaven pegs the value of a single stolen mattress at a couple thousand dollars. He estimates that roughly $60 million worth of mattresses are lifted from hotels worldwide each year.
Some hotels say they charge guests for missing property, while others turn a blind eye.
"Especially in the case of towels and bathrobes, they don't do anything, because they don't want to confront the guest and lose repeat visitors," he said. "They also want to avoid calling the police and making a scene."
Others simply factor the anticipated losses into their room rates, or make clear that desirable items are available to purchase through the hotel's shop.
Other unusual — and valuable — items that have gone missing from hotels include a grand piano from a hotel lobby in Italy, bathroom fixtures in Germany, a taxidermied head and guest room numbers from a hotel in England, according to Wellness Heaven.
"We didn't notice until the next guest could not find his room," the director of an unnamed British hotel told Wellness Heaven of the missing room numbers.


text:
What is the average age of students at UCLA?
Can I get into UCLA with a 3.7 GPA?
What benefits does UCLA Career Center provide?
What career is UCLA known for?
What is the lowest GPA UCLA has accepted?
What was UCLA acceptance rate 2020?
Is a 3.6 GPA good for UCLA?
Is UCLA hard to get into?
What is a 90 GPA on a 4.0 scale?
Can I get into med school with a 3.1 GPA?
Which is best for you? The "traditional" college student is thought to be between the ages of 18-21. At University of California – Los Angeles, 56.7% of students are in the age 18 to 21 bracket, compared to the national average of 60%. We rank UCLA #2,900 in the nation for student age diversity.
3.7 is not bad at all. A good SAT or ACT would easily counteract that. Add on some ECs and you have as good a chance as anyone.
Paid micro-internship opportunities for UCLA students of all majors, years, and degree levels. A smart resume platform that allows you to build your resume and get detailed feedback anytime, anywhere, 24/7.
Now, more than ever, there are countless professional options no matter what your degree. The most popular majors at UCLA are biology, business economics, film and television, political science and psychology. If you have a B.S.
UCLA gets enough applicants to accept only students with perfect GPA (beyond just A's as many take AP classes) however, student average GPA is not perfect because they accept students based on other merits that makes them better rounded as a person. If your weighted GPA is a 3.8, you may not get into UC Irvine.
You must have a 3.0 GPA (3.4 for non-residents) or higher and no grades lower than a C in required high school courses. You can also substitute SAT subject tests for courses. If you don't meet the requirements, it is possible to gain admission with a high enough score on the ACT/SAT plus on two SAT subject tests.
The total acceptance rate across UC campuses rose by 6.5% to 69.5% in 2020. At UCLA, the total acceptance rate also rose by 2.3% to 16.3%. In total, 47% of new UC admits are first-generation students and 47% come from low-income families. 5% of UC's in-state freshmen are African American and 21% are white.
Is your high school GPA good enough for UCLA? The average high school GPA for admitted students at UCLA is 3.89 on a 4.0 scale. (You can calculate your high school a GPA here.) This is a very competitive GPA, and UCLA is clearly accepting students at the top of their high school class.
How Hard Is It to Get Into UCLA? It's very competitive to get into UCLA. Each year, UCLA accepts around 14% of its applicants. Put another way, that means that UCLA accepts 14 out of every 100 students that apply.
How to Convert Your GPA to a 4.0 Scale
Percent Grade
4.0 Scale
A 93-96 4.0
A- 90-92 3.7
B+ 87-89 3.3
B 83-86 3.0
It will be a bit difficult, but not impossible, to get into medical school with a 3.1 GPA. The average median GPA was 3.72, and generally fell around 3.4 or higher, based on U.S. News 2019 Best Medical School rankings.
Is it bad to take the MCAT twice?
Should I learn C++ or Python?


As the first ever UKFL Championship fast approaches TimeFlyZ are busy preparing for this exciting event on the 4th and 5th August 2018 at Lincolnshire Showground. Our League team will consist of Nera, Roxy, Hartley and Willow. They are looking competition ready and we are currently fine-tuning their starts and passes in readiness for the big day.
We also have some of our younger dogs showcasing in their first ever Little League competition at the event where we hope they gain some vital ring and competition experience.
We owe huge thanks to our sponsors Green Pantry, Seraquin and Cambridgeshire Canine Massage for their support over the last twelve months. TimeFlyZ hope to do you proud in the lanes!


I'm having a fine week – what is becoming a "normal" week. Soon I probably won't even use quotation marks.
I've been doing a good job of making dinner since I went grocery shopping last week – even if dinner has alternated between Mexican food and breakfast food. I've also cut waaaaaaay back on my trips to the Brewhouse – been going once a week, if that. this does mean that I have not been nearly as social, though, which hasn't really been a huge problem lately. yes, I'm lonely. no, the cats don't help that much (especially Lucille). I do enjoy being able to talk to people online though, whether the medium is emailing or chatting or blogging – it helps some.
I'm falling back in love with reading, I think. it's definitely better than other things I could fall in love with.
this is all I really have to say at the moment. if anyone wants to hang out with me tonight, let me know.
It's interesting to read entries from three, two, and even one months ago. It's interesting because I have changed a lot in that period of time – which has felt like a year and not a mere 15 weeks. On the other hand, I still have the same issues sometimes. I still feel desperate and broken – just not constantly. I don't even know what else to say about it (I feel like I've been gushing a bit much with the last several entries, anyway).
I'm going to a United Way meeting after work today. It's an organization that helps in the community a lot – they focus on education, health, financial security, and that kind of stuff. I found out that they sponsor the Survivors of Suicide group that I'm going to next week, too. Someone at work sent out an email to see if anyone would be interested in going to this informational meeting tonight, and another coworker kind of persuaded me to go with her. She has a baby so we won't be able to stay for the whole meeting (OK with me), but I'm interested in seeing what it's all about. I've been toying with the idea of volunteering and being more involved in the community. So, so many people are much worse off than I am, and I also have a lot of free time lately.
I wonder where I'll end up going in life. I have not been single without some kind of goal before – whether it be finishing school, or finding a boyfriend, I've just always had something to go towards. Right now I'm just trying to head towards healing, but thinking about the future isn't quite as depressing as it used to be so I just wonder. Matt dying pretty much tore all of my long-term plans into pieces; there's no way that I can buy property, build a house, and farm on my own. I don't know. I guess I'm glad that I'm not very old yet (though I'll be 30 here in a few months…).
I've been reading a lot lately. I read those two self-help grief books right after Matt died, and read a couple books of poetry cover-to-cover. I finished Childhood's End last week, and finished Truth and Beauty a couple of days ago. I'm making good progress re-reading the Heart is a Lonely Hunter too, and I think I'm going to try to pick up Bridget Jones's Diary the next time I'm a McKays.
I did not cook dinner last night (ended up hanging out with Ryan at his parents' house, and had a delicious sandwich there…) – there's not much food at my house right now anyway unless you could frozen soup and frozen poultry (a whole turkey AND a whole chicken). Though I've been craving sushi lately. Maybe I'll have that for dinner tonight since that meeting will last until 7 or so anyway.
Sorry…I know this entry is kind of rambly and probably not too interesting. But oh well.
This week has been better. I've spent some time with friends, and have made a couple of new ones. I've kept the house clean which always helps me to be in a better mood. I haven't been to the bar as much – I'm just getting tired of it because I can feel it not being so good for me. I mowed the lawn. I bought a new raincoat.
Ryan helped one of his friends move, and she gave him a ton of her old books that she couldn't keep because of moving into a smaller place. Helen also gave him some of her books, and we took them to McKay's last night and ended up with about $200 in store credit – with two boxes of books still left in my car to take back later! It was a great trip. 🙂 I ended up with a few new books and two DVDs – didn't go too overboard anyway. After, we went to Cafe Coco and did some reading. It was pleasant.
I don't have a ton to say at the moment, but I've been kind of trying to blog each Thursday just as a weekly update. Maybe someday I'll read back over these and be glad that I updated each week. We'll see.


Here you will find one or more explanations in English for the word Outbribe. Also in the bottom left of the page several parts of wikipedia pages related to the word Outbribe and, of course, Outbribe synonyms and on the right images related to the word Outbribe.
Outbribe Out*bribe", v. t. To surpass in bribing.


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Q: How to add multitext values seperated by commas to optionset and lookup field in cm 2015 using c# plug-in I have a plug-in. This plug-in should get the values seperated by commas from multitext field one by one and stores to an optionset field.
And also this plugin should get values(ids) from multitext field seperated by comma and searches the ids one by one in lookup field values. If found (the search operation should be done one by one in a loop;since there will be more thean one id to search), the value should be seen in the lookup field.
After theese opertaions the plugin should save the entity.
How can i do this in crm 2015 using c# visual studio plug-in? Can anyone help me please

A: So, in a nutshell, what do you want to do is to generate the CRM metadata dynamically from a comma separated input, like a CSV?
Have a look at the CreateOptionSetRequest  and InsertOptionSetValueRequest in CRM, this will allow you to insert new option set values for a given option set.
Those will allow you to dynamically create an option set field, and populate option set values for that field, respectively.
For lookups, If I understood correctly, you can link records to each other using AssociateRequest messages.
Hope this helps