Area is a mathematical term defined as the two-dimensional space taken up by an object, notes , adding that the use of area has many practical applications in building, farming, architecture, science, and even how much carpet you'll need to cover the rooms in your house.
Sometimes the area is quite easy to determine. For a square or rectangle, the area is the number of square units inside a figure, says "," because such polygons have four sides, and you can determine the area by multiplying the length by the width. Finding the area of a circle, however, or even a triangle can be more complicated and involves the use of various formulas. To truly understand the concept of area—and why it's important in business, academics, and everyday life—it's helpful to look at the history of the math concept, as well as why it was invented.
"Farmers knew that if one farmer planted an area three times as long and twice as wide as another farmer, then the bigger plot would be 3 x 2 or six times as large as the samller one."
The architects of the pyramids at Giza, which were built about 2,500 B.C., knew how large to make each triangular side of the structures by using the formula for finding the area of a two-dimensional triangle.
The Chinese knew how to calculate the area of many different two-dimensional shapes by about 100 B.C.
Johannes Keppler, who lived from 1571 to 1630, measured the area of sections of the orbits of the planets as they circled the sun using formulas for calculating the area of an oval or circle.
Sir Isaac Newton used the concept of area to develop calculus.
So ancient humans, and even those who lived up through the Age of Reason, had many practical uses for the concept of area. And the concept became even more useful in practical applications once simple formulas were developed to find the area of various two-dimensional shapes.
where "A" represents the area, "H" is the height, and "W" is the width.
where "A," as noted, stands for the area, "B" is the base of the triangle, and "H" is the height.
In this formula, "A," is, again, the area, "r" represents the radius (half the distances from one side of the circle to the other), and π is a Greek letter pronounced "pi," which is 3.14 (the ratio of a circle's circumference to its diameter).
There are many authentic and real-life reasons where you would need to calculate the area of various shapes. For instance, suppose you are looking to sod your lawn; you would need to know the area of your lawn in order to purchase enough sod. Or, you may wish to lay carpet in your living room, halls, and bedrooms. Again, you need to calculate the area to determine how much carpeting to purchase for the various sizes of your rooms. Knowing the formulas to calculate areas will help you determine the areas of the rooms.
A = 252 square feet.
You would then round that figure off to 12.6 square feet or even 13 square feet. So you would need 13 square feet of tile to complete your bathroom floor.
So, you'd need a whopping 40 square feet of carpet to cover the floor of that room. Make sure you have enough credit remaining on your card before heading to the home-improvement or carpeting store.


The World in Miniature (WIM) metaphor allows users to interact and travel efficiently in virtual environments. In addition to the first-person perspective offered by typical VR applications, the WIM offers a second dynamic viewpoint through a hand-held miniature copy of the environment. In the original WIM paper the miniature was a scaled down replica of the whole scene, thus limiting its application to simple models being manipulated at a single level of scale. Several WIM extensions have been proposed where the replica shows only a part of the environment. In this paper we present a new approach to handle complexity and occlusion in theWIM.We discuss algorithms for selecting the region of the scene which will be covered by the miniature copy and for handling occlusion from an exocentric viewpoint. We also present the results of a user-study showing that our technique can greatly improve user performance on spatial tasks in densely-occluded scenes.


The increase is largely in line with the increments that its peers have given. India's largest IT services company TCS gave an 8% hike to employees in India and 2%-4% for overseas employees.
BENGALURU: Cognizant has given a salary increase of 7%-9% for employees in India and around 3% for onsite employees (those in customer locations) effective July 1.
The increase is largely in line with the increments that its peers have given. India's largest IT services company TCS gave an 8% hike to employees in India and 2%-4% for overseas employees. Infosys gave an average salary increase of 6.5%, though the average increment for top performers was 9%. Wipro's average salary increase was 7% for employees in India.
The company, which has most of its employees in India, added 6,200 in the March quarter taking its global headcount to 217,700.
The $146-billion IT outsourcing industry, which for many years rewarded employees with double digit increments, today face pricing pressure thanks to traditional IT services like application development and maintenance becoming commoditized. "Companies are battling cost and pricing pressures. They are keeping their base salaries lower and instead reward their employees with stock options to manage their cost structure more efficiently and protect their bottomline," said H V Harish, partner in consultancy firm Grant Thornton.


Where this journey began! We had the space, a kitchen, and a team willing to try something new! Our first evening open on 04/04/14 was pretty wild but incredibly busy which made us think we may be onto something!
We are open every Friday (Saturdays June/July/August) night from 6pm – 10pm and serve a range of burgers, sides, and deserts. We are fully licensed and also boast Galloway's largest gin selection of over 30 premium gins from around the world. Children Welcome. Booking recommended.


text:
Katherine Newbegin at Lesley Heller Workspace
Artists in Dialogue: Katherine Newbegin & Jim Osman
Lesley Heller Workspace
October 23 – December 4
Leslie Heller Workspace: Artists in Dialogue: Katherine Newbegin & Jim Osman
October 23 – December 4, 2016
Katherine Newbegin "Auditorium circa 1972 (Eglés Sanatorium, Druskininkai, Lithuania)"
2016, C-Print, 40 x 50 in. Ed. of 2 + 1AP
From the Leslie Heller Workspace website:
Artists in Dialogue presents the work of photographer Katherine Newbegin and sculptor Jim Osman.
Katherine Newbegin's photographs explore vacant and long unused places of leisure, travel and transitional occupancy. All of these spaces are deeply informed by the traces of the human activities that had once taken place there, and linger now only in the remnants left behind. The architecture of these hotel rooms, sanatoriums, and auditoriums, holds a stifling sense of deadness, as if already ossified, channeling imagery of a distant yet recent history. Newbegin's newest series of photographs explore Polish and Lithuanian hotels and sanatoriums which were used in the 1970's as vacation and therapeutic destinations by citizens of the former Soviet Union.
Jim Osman's sculptures center on explorations of structure, architecture and space. Working with wood, paint, and construction paper, Osman instinctively combines materials, forms and colors to create dynamic 3-dimensional compositions. The sculptures presented in this exhibition range from complex free-standing floor pieces, to smaller and more intimate sculptures with simplified geometric contours. The sculptures excavate formal relationships of line and structure and invite contemplations on architecture, furniture and the materiality of wood.
Katherine Newbegin "Couples (Eglés Sanatorium, Druskininkai, Lithuania)", 2016
C-print, 30 x 40 inches, Ed. of 3 +1AP
LTI/Lightside has worked with Katherine Newbegin for a number of years — we printed this series of 30 x 40 and 40 x 50 conventionally enlarged c-prints directly from her original negatives.
Katherine Newbegin (b.1976) received her MFA from Hunter College and her BA from Yale. Newbegin has been the recipient of a Tiffany grant in 2009, a DAAD fellowship in 2008, and has been awarded residencies at the Marie Walsh Sharpe Foundation, Yaddo, the Camera Club of New York, and the Catskills Mountain Foundation. Newbegin has shown her work nationally and internationally, including at: Dina4Projekte, Haas & Fischer Gallery, Galerie Open, Pinakothek der Moderne, Kunstverein Munich, Kommunale Galerie Berlin, the Loeb Art Center at Vassar College, Deutsches Haus, and the Chelsea Art Museum. Newbegin has published catalogues with Revolver in Germany, and the Loeb Art Center at Vassar College. Her work has been featured in Berlin Zitty, Time Out New York, Lettre International, Camera Austria, Neues Deustchland, ParisBerlin, Zuricher Zeitung, Die Welt, and the Berliner Morgenpost. She lives and works in Brooklyn, New York.
Tags: conventional c-prints, Exhibitions, Film Processing, Katherine Newbegin

redpajama_set_name: RedPajamaCommonCrawl


Who's ready to get their hands on the infant version of the adidas Yeezy Boost 350? If you were one of the lucky few today then you were able to reserve your pair through the adidas Confirmed app. But if not, you're probably going to have to try your luck online this weekend.
Today we give you a closer look at the Pirate Black pair that will be arriving at retailers alongside the Turtle Dove pair on August 27th. This baby version of the Yeezy Boost 350 comes with a Primeknit upper and Boost midsole just like the adult version and also includes all of the details for that authentic look.
The adidas Yeezy Boost 350 Infant Pirate Black will release on August 27th for a retail price of $130. Be sure to visit our adidas Yeezy Boost 350 Infant hub page for all the latest images and info regarding this upcoming release.


CHICAGO -- Oprah Winfrey is giving fans a chance to own some of her clothes and accessories via a charity auction of items from her Chicago office closet.
In her March issue of O, The Oprah Magazine, she gives readers an inside look at the closet clean-out - which will include more than 250 pieces of clothing and accessories. Oprah called her Chicago office home for nearly 30 years.
"What I hang on to will have meaning for me. What I give away will be put to good use by someone else. When I'm sure something of mine is going to someone who will really use and appreciate it, I'm completely fine with letting go," she said in a statement Thursday.
The auction will begin at 12 a.m. EST on March 1 and end on March 4. Proceeds will benefit the Oprah Winfrey Leadership Academy for Girls.


text:
\section{\label{Intr}Introduction}
The main modern achievements in studying processes of double beta
decay ($\beta^-\beta^-$-decay) can be attributed to detection of its
two-neutrino mode. This process has been discovered in as many as
ten nuclei (see reviews
\cite{Zd2002_DNDT},\cite{Bar2002_Cz},\cite{Cremonesi06}). The data
obtained for the two-neutrino mode offer a chance to directly
compare different models of the nuclear structure, which form the
basis for calculations of nuclear matrix elements $\|M^{2\nu}\|$,
and to select the optimal one. Though direct correlation between the
values of nuclear matrix elements for the two-neutrino and
neutrinoless modes of $\beta\beta$ decay is absent lacking, the
methods for calculating $\|M^{2\nu}\|$ and $\|M^{0\nu}\|$ are very
close, and a chance possibility to estimate their accuracy in
calculating $\|M^{0\nu}\|$ appears only when comparing experimental
data and theoretical results calculations for the probability of
$2\beta (2\nu)$ decay.

It can be expected that acquisition of experimental data on the
other types of $2\beta$ transitions ($2\beta^+, \rm{K}\beta^+$, and
$2\rm{K}$ processes) will make it possible to considerably increase
the quality of calculations for both $2\nu$ and $0\nu$ decays. Much
efforts have been currently made in searching for these processes
(\cite{r3},\cite{r4},\cite{r5}) in spite of the fact that the
$2\beta^+(2\nu)$ and $K\beta^+(2\nu)$ modes are strongly suppressed
relative to $2\beta(2\nu)$ decay due to the Coulomb barrier for
positrons, and a substantially lower kinetic energy attainable in
such transitions. Positrons are absent in the final state of the
$2K(2\nu)$ decay, and the kinetic energy of the transition may be
rather high (up to 2.8 MeV), which dictates determines an increased
probability of a decay. However, this process is also difficult to
detect, since it is only characteristic radiation that is detectable
in it. The state-of-the-art experimental limit on the $^{78}$Kr
half-life period with respect to the $2K(2\nu)$ capture is $T_{1/2}
\le 1.5\times10^{21}$ yr (90\% C.L.) \cite{r6}. The theoretical
calculations based on different models predict the following
$^{78}$Kr half-lives for this process: $3.7\times10^{21}$ yr
\cite{r7}, $4.7\times10^{22}$ yr \cite{r8}, and $7.9\times10^{23}$
yr \cite{r9}. The last two values were obtained from the estimates
of the $^{78}$Kr half-life with respect to the total number of
$2e(2\nu)$ captures including in view of the 78.6\% fraction of
$2K(2\nu)$ capture events which makes 78.6\% \cite{r10}. From
comparison of the experimental and theoretical results, it is
apparent that the sensitivity of measurements has reached the lower
limit of theoretical estimates.

\section{\label{sec1}The technique of the experiment}
The $^{78}$Kr$(2e_\texttt{K},2\nu)^{78}$Se reaction produces a
$^{78}$Se$^{**}$ atom with two vacancies   in its $K$-shell. The
technique for seeking this reaction is based on the assumption that
the values of   energies of characteristic photons, and of the
probability that they will be emitted when the double vacancy is
being filled, coincide with the   corresponding values   when two
separate single vacancies   in the $K$ shells of two isolated singly
ionized Se$^*$ atoms are being filled. In this case, the total
measured energy is $2K_{ab} = 25.3$ keV, where $K_{ab}$ is the
binding energy of a $K$ electron in a Se atom (12.65 keV). The
fluorescence yield  upon filling of a single vacancy   in the
$K$-shell of Se is 0.596. The energies and relative intensities of
the characteristic lines in the $K$ series are $K=11.22$ keV
(100\%), $K=11.18$ keV (52\%), $K=12.49$ keV (21\%), and $K=12.65$
keV (1\%) \cite{r11}. There are three  possible ways  for
deexcitation of a doubly ionized $K$-shell: 1) emission of  Auger
electrons only ($e_a$, $e_a$), 2) emission of a single
characteristic quantum and an Auger electron ($K,e_a$), and  3)
emission of two characteristic quanta and low-energy Auger electrons
($K,K,e_a$) , with probabilities $p1=0.163$, $p2=0.482$, and
$p3=0.355$, respectively. A characteristic quantum   can travel a
long enough distance in a gas medium between the points of its
production and absorption. For example, 10\% of characteristic
quanta with energies of 11.2 a nd 12.5 keV is absorbed in krypton at
a pressure of 4.35 atm ($\rho=0.0164$ g/cm$^3$) on a path 1.83 and
2.42 mm long, respectively (the values of absorption factors   are
taken from \cite{r12}). The  paths of photoelectrons   with the same
energies are 0.37 and 0.44 mm, respectively. They produce almost
pointwise charge clusters of primary ionization in the gas.  In case
of the event with the escape of two characteristic quanta   absorbed
in the working gas and a single Auger electron, the energy will be
distributed among three pointwise charge clusters. It is these
three-point (or three-cluster) events possessing a unique set of
features that were the subject of the search in \cite{r6}.

A large proportional counter (LPC) with a casing made of M1-grade
copper is used to detect   the above considered processes. The LPC
has a cylindrical shape with inner and outer diameters of 140 and
150 mm, respectively; its section along the axis is schematically
shown in Fig.\ref{LPC}. A gold-plated tungsten wire of 10 $\mu$m in
diameter goes along the LPC axis   and  serves as the anode. The
potential of +2400 is applied to the wire,   and the casing (the
cathode) is grounded. Both ends of the anode are lead to the
appropriate end cap flanges via high-voltage pressure-sealed
bushings-ceramic insulators with a central electrode taken from
spark plugs.

\begin{figure}[!htb]
\resizebox{0.45\textwidth}{!}{%
  \includegraphics{fig1.eps}}
\caption{ Schematic view of the LPC in section along the anode wire:
1 -- wire (collecting electrode), 2 -- load-carrying insulator, 3 --
cathode, 4 -- tubular bulge of the anode.} \label{LPC}
\end{figure}

To reduce the influence of edge effects on the operating
characteristics of the counter, the end segments of the wire are
passed through the copper tubes with dimensions of $3.0\times38.5$
mm, which are electrically connected to the anode. Gas amplification
is absent on these segments, and charges are collected in an
ionization mode. With   the fluoroplastic insulator, the distance
from the working region to the flange is 70 mm.

The working part of the LPC is 595 mm in length (the distance
between the end caps of the tubes); therefore, the LPC s operating
volume is 9,159 l. The total capacitance of the counter and the
outlet insulator is $~30.6$ pF. The total resistance of the anode
and two output electrodes is $~600$ Om. All detachable joints are
sealed with indium wire. All nipple joints are sealed with
fluoroplastic gaskets. The internal insulators are made of
fluoroplastic. Their thickness was selected so as to be the smallest
possible in order to improve the degassing conditions during vacuum
treatment of the counter and stabilize its operating characteristics
in the course of measurements.

The LPC is filled with a pure Kr sample to a total pressure of 4.51
att; no quenching or accelerating gases are added. Prior to filling,
Kr is purified of electronegative impurities in a Ni/SiO$_2$
reactor.

The LPS's signals are read out by a charge-sensitive amplifier (CSA)
from one end of the anode wire. The CSA parameters have been
selected so that the signal is transmitted with minimum distortions,
and information of the spatial distribution of primary-ionization
charges in a projection onto a counter radius is fully represented
by the pulse shape. When amplified in an auxiliary amplifier, the
pulses arrive at the input of the   digital oscilloscope
LA-n20-12PCI, the output data of which (the pulse waveform digitized
with a frequency of 6.25 MHz) are recorded   with a personal
computer. The length of the scanning frame with a resolution of 160
ns is 1024 points (163.8 $\mu$s), of which $~50$ $\mu$s is the
"prehistory"  and $~114$ $\mu$s is the "history".

The counter is calibrated through the wall of its casing   by
$\gamma$ rays of a $^{109}$Cd source ($E_\gamma=88$ keV; relative
yield 0.036 photons/decay). Figure \ref{pic2} presents ({\it0}) the
total pulse amplitude spectrum and the energy spectra of ({\it1})
single-, ({\it2}) two-, and ({\it3}) three-point events from the
source located in the middle of the LPC length. The procedure for
obtaining them from digitized pulses is described in what follows.
The following factors make their contribution to the low-energy part
of the spectrum: characteristic radiation Ag$_{K_{\alpha\beta}}$
($E\approx22$ keV) from this source, which "survived"  after passing
through a 5-mm-thick copper wall; scattered radiation from the wall,
which is in equilibrium with the characteristic radiation, and
Compton electrons from scattering of 88-keV photons in the gas with
the escape of a Compton photon beyond the counter.
\begin{figure}[!htb]
\resizebox{0.45\textwidth}{!}{%
  \includegraphics{fig2.eps}}
\caption{ Pulse amplitude spectrum from the external $^{109}$Cd
source located in the middle of the LPC length: (\emph{0}) all
events, (\emph{1}) single-point events, (\emph{2}) two-point events,
(\emph{3}) three-point events, and (\emph{4}) escape peak of
characteristic $\gamma$-ray photons.} \label{pic2}
\end{figure}

The 88-keV peak is wider on the low-energy side due to the
contribution of 88-keV $\gamma$ rays scattered from the wall. The
energy resolution of this peak, determined by its right half, is
6.5\%. Peak \emph{4} at an energy of 75.4 keV corresponds to the
escape of Kr characteristic radiation ($E_{Kr_\alpha}=12.6$ keV)
beyond the counter.

The 88-keV full-energy peak contains events with different internal
structures. Quanta with this energy are   absorbed in Kr mostly by
photoeffect   in the $K$-shell (86.7\%). The photoeffect in other
shells makes 13.3\% \cite{r12}, \cite{r13}. Filling of the vacancy
in the $K$-shell of Kr is accompanied by emission of characteristic
radiation in 66.0\% of cases and Auger electrons in 34.0\%
\cite{r13}. The theoretical efficiency of characteristic radiation
absorption in the counter s working volume is 86.9\%. Therefore, the
photoeffect is responsible for 49.7\% of two-point events
$(0.867\times0.660\times0.869)$ and 42.8\% of single-point events
$(0.133+0.867\times0.340)$ out of the total number of absorptions
due to photoeffect in the full-energy peak. By single-point events,
we mean all events in which only electrons escaping from the shell
of a single atom (photoelectrons $+$ Auger electrons), including
events of photoelectric absorption in the upper shells of Kr. Only
single-point events in an amount of 7.5\%
$[0.867\times0.660\times(1.000-0.869)]$ of the total number of
photoabsorption events will be presented in peak {\it4}.

Some primary quanta can be absorbed as a result of two-step process
of  "Compton scattering-photoeffect".  A Compton electron creates
one ionization point. A Compton photon absorbed by photoeffect
participates in the above-described processes. Therefore, the
two-step process makes its contributions to the full-energy peak in
the form of two- and three-point events and to peak {\it4} in the
form of two-point events. Upon normalization to the peak area, the
estimated final composition of events for the full-energy peak
contains 44.1\% (single-point events) + 51.2\% (two-point events)
due to photoeffect + 2.2\% (two-point events) + 2.5\% (three-point
events) due to the two-step process. In peak {\it4}, there are
95.3\% single-point events + 4.7\% two-point events.

\begin{figure}[!htb]
\resizebox{0.5\textwidth}{!}{%
  \includegraphics{fig3.eps}}
\caption{ Examples of pulses (dark lines) of two types of events:
(\emph{a}) for photoabsorption of an 88-keV photon with an escape of
electrons only (a single-point event), (\emph{b}) simultaneous
escape of a 12.6-keV characteristic photon Kr$_{K\alpha}$ and a
photoelectron (${\rm E}_\gamma -{\rm E}_{KrK\alpha}$)=88.0 keV--12.6
keV = 75.4 keV (a two-point event). The calculated, area-normalized
current pulses of primary ionization electrons are shown with light
lines in Figs. 3\emph{c} and 3\emph{d}, while the respective voltage
(charge) pulses obtained by integrating these current pulses are
depicted with light lines in Figs.3\emph{a} and 3\emph{b}.}
\label{exam_pulse}
\end{figure}
Examples of pulses (dark  lines) corresponding to events of two
types are presented in Fig.\ref{exam_pulse}. The pulse due to
photoabsorption of a 88-keV photon with escape of electrons only (a
single-point event) is shown in Fig.\ref{exam_pulse}a, and
simultaneous escape of characteristic photon Kr with an energy of
12.6 keV and a photoelectron $(E_\gamma-E)=88$~keV - 12.6 keV=75.4
keV (a two-point event) is illustrated in Fig.\ref{exam_pulse}b. The
maximum distance between pointwise charge clusters in projection
onto the counter s radius is equal to the radius. For pure Kr, the
evaluated time it takes for ionization electrons to drift from the
cathode to the anode is 53 $\mu$s. From Figs.\ref{exam_pulse}a and
\ref{exam_pulse}b, it is apparent that the second pulse with a
$\sim3\div5$ times smaller amplitude is produced in the counter in
about $\sim53$ $\mu$s after the first one. This pulse is generated
by secondary photoelectrons knocked out of the cathode by photons
produced during development of an avalanche from the primary
ionization. The probability of photoeffect   on the cathode is
rather high, since the working gas contains no quenchers.

\section{\label{shape} Determining the shape of the LPC current
signal}
The digitized output pulse from the measuring channel can be
presented as direct convolution of sought signal $x(t_i)$ with
response pulse $\widehat{G}$ from the linear system, which is
distorted by stochastic or determinate noise $z(t_i)$:
\begin{eqnarray}\label{Eq1}
  y(t_i )&:=& \widehat{G}x(t_i ) + z(t_i ), i = 0,...,N - 1\\
  &:=& (g \otimes x)(t_i ) + z(t_i ).
  \nonumber
\end{eqnarray}

The noise level determines the lower limit on the sensitivity of the
measuring channel, while the instrumental function defines the
resolution value.

Given the values of $y$ and $\widehat{G}$, one can try to estimate
$x(t)$ in the presence of noise $z(t)$; i.e., in principle, it is
possible to state the inverse problem (deconvolution) of determining
the signal at the linear system output by the values of the output
signal:
\begin{eqnarray}\label{Eq2}
\widetilde{x}(t_i ) = \widehat{G}^{ - 1} y(t_i ) = x(t_i ) +
\widehat{G}^{ - 1} z(t_i ),
\end{eqnarray}
where $\widehat{G}^{ - 1}$ is the operator inverse.

To determine the values of charges released in individual clusters
of a multipoint event, one can differentiate the original charge
pulse $\left( {\widehat{G}^{ - 1}  = \frac{d}{{dt}}} \right)$ and
represent the obtained shape by a set of Gaussian curves. The
evaluated area under an individual Gaussian curve will correspond to
the charge (energy) value in the relevant cluster. From
Figs.\ref{exam_pulse}\emph{c} and \ref{exam_pulse}\emph{d}, it is
apparent that direct differentiation provides  an asymmetric bell
shape (dark line). Such shape results from the nearly Gaussian
distribution of the current pulses due to electrons of primary
ionization from a pointwise  energy deposit, which arrive at the
boundary of the gas amplification region near the anode wire.

This shape is determined by the spatial distribution of the charge
density in projection onto the radius. The parameters of this
distribution depend on the time it takes for the primary charge
cluster to drift to the anode. As it drifts, the charge cluster
spreads out into a cloud due to electron diffusion. The pulse read
out from the anode wire is mostly produced by a negative charge
induced on the anode moving toward the cathode by positive ions
produced near the wire in gas amplification process and moving
toward the cathode i.e., the ion component (i.c.). The estimated
total ion drift time is 0.447 s. The contribution of the equilibrium
(with ions) electron component (e.c.) to the total induced charge is
$\sim7$\%. The electron collection time is $\sim1$ ns.

The output pulse shape is defined by the superposition of induced
charges from single electron avalanches distributed in time and
intensity according to: the shape of the current pulse from primary
ionization electrons, the shape of a pulse from an individual
avalanche, and a finite time of the CSA self-discharge. The last two
parameters are responsible for the asymmetry of the output current
pulse. The output current pulse can be transformed to a symmetric
shape by taking into account the analytical dependence of the
amplitude of the output voltage pulse generated by a point (in
projection onto the radius at the boundary of the gas amplification
region) group of primary ionization electrons as a function of time
and discharge constant of the output storage capacitor \cite{r14}:
\begin{eqnarray}
 V_{\emph{k}} (t_i ) &=& K_{{\rm{i.}}{\rm{c.}}} n_\emph{k} \exp \left( {
- \frac{{t_i  + B}}{{RC}}} \right) \times\\
& & \times\left\{ {ln\left( {1 + \frac{{t_i }}{\emph{B}}} \right) +
\frac{{t_i }}{{RC}} +
\frac{{t_i ^2 }}{{2 \cdot 2!(RC)^2 }} + ...} \right\}+ \nonumber\\
 & & +
K_{{\rm{e.}}{\rm{c.}}} n_\emph{k} \exp \left( { - \frac{{t_i
}}{{RC}}} \right),\nonumber
\end{eqnarray}
where $V_k(t_i)$ is the amplitude of the voltage pulse from the
$k$th group of electrons, $n_\emph{k}$ is the number of primary
electrons in the $k$th group, $t_i=t(t_0 + t_{i0})$ is the current
time for the dependence of the voltage pulse amplitude from the
$k$th group, $t_0$ is the time of origin of the total pulse, and
$t_{i0}$ is the time of origin of the pulse from the $k$th group,
$K_{\rm{i.c.}}= MV_{(1)i.c.}$, $M$ is the gas amplification factor,
\begin{eqnarray}
V_{(1){\rm i.c.}}=(e/C)\cdot\ln({\emph{r}}_{\rm{k}}/{\emph{r}}_0)
\ln({\emph{r}}_{\rm{k}}/{\emph{r}}_{\rm{a}})\nonumber
\end{eqnarray}
is the total voltage pulse amplitude produced at output capacitor
$\emph{C }$  by a single ion generated in the gas discharge,
$\emph{e}$ is the electron charge, $\emph{r}_0$ is the radius
corresponding to the avalanche's center of gravity, $\emph{r}_a$ is
the anode radius, $\emph{r}_{\rm{k}}$ is the cathode radius,
\emph{B} is the time parameter associated with the motion of
positive ions of the gas discharge in a particular gas (for the LPC
filled with Kr at 4.51 at, $\emph{B} = 2.28$ ns), $RC=\tau_d$ is the
CSA discharge constant, $R$ is the leakage resistance, $K_{\rm
{e.c.}}= MV_{(1){\rm{e.c.}}}$, and
\begin{eqnarray}
V_{(1){\rm
e.c.}}=(\emph{e}/\emph{C})\cdot\ln(\emph{r}_0/\emph{r}_{\rm{a}})
\ln(\emph{r}_{\rm{k}}/\emph{r}_{\rm{a}})\nonumber
\end{eqnarray}
is the total voltage pulse amplitude produced at output capacitor
$\emph{C }$ by a single electron generated in the gas discharge. In
Eq.(3), the electron component is assumed to appear instantly.

At $\tau_d=\infty $, Eq. (3) assumes the form
\begin{equation}\label{Eq4}
V_{\emph{k}} (t_i ) = K_{{\rm{i.}}{\rm{c.}}} n_\emph{k} \times
ln\left( {1 + \frac{{t_i }}{B}} \right) +
K_{{\rm{}}{\rm{e.}}{\rm{c.}}} n_\emph{k}.
\end{equation}
In our case, $\tau_d\approx192$ $\mu$s. For a time interval
satisfying condition $t/\tau_d < 2$, Eq. (3) can be reduced to the
first two expansion terms.

If its is assumed that the gas discharge from $n_k$ of primary
electrons happens at the beginning of the digitization interval, the
pulse amplitude at the end of this interval can be described by Eq.
(3) for $t=160$ ns, since the influence of the output capacitor
discharge over this time is negligible. If a contribution of the
earlier discharges is absent in this time interval, the pulse
amplitude at the upper bound of the interval can be used to
determine the $n_k$ value.  In this case, it is taken into account
that, at the end of a 160-ns interval, the contributions of the
terms to the total $V_k(t_i)$ value in Eq. (3) make 74 and 26\%,
respectively. These conditions are satisfied in the recorded actual
pulse in the first time channel from the beginning of the pulse. The
$n_1$ value obtained from the actual pulse is used in Eq. (3) to
calculate the total shape of the partial pulse in the entire time
interval from the beginning to the end of the frame. The pulse
obtained thereby is subtracted from the actual one. Therefore, the
above condition is now fulfilled for the first digitization interval
of the residual pulse or for the second interval of the original
pulse. This procedure is repeated until the last time channel in the
frame.

The sequence of $n_k$ values for a single-point event has a
symmetrical distribution with a nearly Gaussian shape. It is this
distribution that is used for further analysis. The area under the
Gaussian curve or, in the case of a multiparticle event, the sum of
the Gaussian areas on a time interval of 53 $\mu$s from the
beginning of the pulse yields the total number of primary ionization
electrons. To plot the spectra in Fig.2, this sum is multiplied by
the coefficient equal to the averaged ratio of areas of the actual
current pulse and of the calculated Gaussian curve for purely
single-point events.

The calculated, area-normalized current pulses of primary ionization
electrons at the boundary of the gas amplification region are shown
with light curves in Figs.\ref{exam_pulse}\emph{c} and
\ref{exam_pulse}\emph{d}, and the corresponding voltage (charge)
pulses obtained by integrating these current pulses are depicted
with light lines in Figs \ref{exam_pulse}\emph{a} and
\ref{exam_pulse}\emph{b}.

From Figs.\ref{exam_pulse}\emph{c} and \ref{exam_pulse}\emph{d}, it
is apparent that, at an energy deposit of 88 keV, the
signal-to-noise ratio (SNR) is rather high. In the energy range of
$20\div30$ keV, in which the $2K$-capture in $^{78}$Kr is sought,
the SNR for individual components of the total energy deposit
corresponding to the possible effect (25.3 keV) is not so favorable.

Figures \ref{Pic4}\emph{a} and \ref{Pic4}\emph{b} present examples
of recalculated current pulses for two types of two-point energy
deposits due to the $K$-capture of $^{81}$Kr isotope. The total
energy deposit corresponds to the binding energy of an electron in
the $K$-shell of a daughter $^{81}$Br (13.5 keV). The energies of a
characteristic quantum ($E_{K\alpha}=11.9$ keV) and concomitant
Auger electrons ($E_a=1.6$ keV) are close to the energies of
individual components for events of the $2K$-capture of $^{78}$Kr.
More detailed information on the $^{81}$Kr source is given in what
follows.
\begin{figure}[htp]
\resizebox{0.45\textwidth}{!}{%
  \includegraphics{fig4.eps}}
\caption{Primary ionization signals for two types of two-point
energy deposits from $K$-capture of $^{81}$Kr isotope accompanied by
an escape of a characteristic photon and a concomitant Auger
electron: (\emph{a}, \emph{b}) recalculated voltage (charge) pulses
and (\emph{c}, \emph{d}) corresponding current pulses from primary
ionization electrons.} \label{Pic4}
\end{figure}

From Fig.\ref{Pic4}, it is apparent that these signals have a high
noise level. Noises and possible electric pickup may both mask the
low-energy component and create a false one. The use of traditional
methods of frequency filtering with different window functions,
e.g., in the form of the Hamming \cite{r15}, Wiener \cite{r16}, and
Savitzky-Golay \cite{r17} filters, sometimes fail to ensure reliable
extraction of closely spaced (Fig. 4a) and masking each other
components of a compound event.

\section{\label{filters} Wavelet-based filter}

Mathematical studies carried out in late 1980s initiated intense
development of a principally new class of orthogonal transforms
based on the use of wavelet functions \cite{r18}. Wavelet transforms
are distinguished by a high degree of locality of their base
functions both in the time and frequency regions, which allows one
to use them for processing of many nonstationary processes. "In the
preliminary processing of our LPC data it is expedient to use
multiresolutional signal analysis \cite{r19} based on the {\it
dyadic transform of discrete signals}, and often called discrete
wavelet transform (DWT). In this case, the analyzed signal
$\widetilde{x}(t)$ is presented as the decomposition
\begin{equation}\label{Eq5}
x^J (t) = \sum\limits_{m = 0}^{N_{j_o }  - 1} {\widehat{a}_{j_0 ,m}}
\varphi_{j_0,m}(t) + \sum\limits_{j = j_0 }^J {\sum\limits_{m =
0}^{N_j  - 1}{\widehat{d}_{j,m} \psi_{j,m}}} (t),
\end{equation}
where are the well-known orthonormal scaling (scaling functions) and
wavelet functions- "ancestor" wavelets; $\widehat{a}_{j_0 ,m}  =
\left\langle {\widetilde{x},\varphi _{j_o ,m} } \right\rangle $ are
the empirical approximation coefficients and $\widehat{d}_{j,m}  =
\left\langle {\widetilde{x},\psi _{j,m} } \right\rangle $ are the
empirical detailing coefficients; $j,m\in Z$ are the current values
of the scale and the shift; $N_{j_0}(N_j)$ is the number of
approximation (detailing) coefficients considered at the relevant
levels of the decomposition; $j_0$ is the initial scale value; and
$J$ is the final scale value.

Parameter $J$ specifies the resolution of wavelet reconstruction
$x^J(t)$ of original signal $x(t)$. Actually, in the case of
tendency $J \rightarrow \infty$, the norm tends to $\|x^J-x\|
\rightarrow 0$.

Scaling functions $\{\phi_{j,m}(t)\}$ and mother wavelet functions
$\{\phi_{j,m}(t)\}_{j,m\in{Z}}$, which have $2K$ nonzero
coefficients, satisfy the so-called two-level relations \cite{r18}:
\begin{equation*}
\varphi (t) = \sqrt 2 \sum\limits_{n = 0}^{2K - 1} {h(n)\varphi (2t
- n)} ,
\end{equation*}
\begin{equation*}
\psi (t)=\sqrt 2 \sum\limits_{n = 0}^{2K-1}{g(n)\varphi (2t-n)} ,
\end{equation*}
where $h(n)$ and $g(n)$ are the coefficients of low- and
high-frequency filters of the wavelet transform, when $g(n) = \left(
{ - 1} \right)^n h(2K - n - 1)$. As distinct from other types of
transforms, in which the base functions are explicitly specified,
one succeeds in analytically obtaining the base functions in the
wavelet analysis only in rare cases, and the basis is most
frequently specified by coefficients $h(n)$ and $g(n)$. In this
paper, we use wavelets of the Daubechies family. The scaling
functions and the Daubechies wavelets are continuous functions that
are not identically equal to zero on a finite segment and are not
differentiable anywhere on this segment. Table \ref{tab1} contains
the filter coefficients used in the Daubechies scaling functions
$db4$ and $db6$ (numbers 4 and 6 denote the number of nonzero
coefficients in the filters). They are rational numbers and fully
define the Daubechies wavelet transform (DVT) \cite{r18}.
\begin{table} \label{tab1}
\caption{Coefficients of the low-frequency filters for wavelets with
compact carriers \emph{db}4 and \emph{db}6. The \emph{h}(\emph{n})
values are normalized so that $\sum\nolimits_{n=0}^{2K -
1}{h(n)=\sqrt 2}$ \cite{r18} }\label{tab1}
\begin{tabular}{|c|c|c|c|c|c|c|}
  \hline

  \emph{h}(\emph{n)} & $db4$ $(K=2)$ &  $db6$ $(K=3)$ \\
  \hline \hline
  \emph{h}(0) & ${{\left( {1 + \sqrt 3 } \right)} \mathord{\left/
 {\vphantom {{\left( {1 + \sqrt 3 } \right)} {4\sqrt 2 }}} \right.
 \kern-\nulldelimiterspace} {4\sqrt 2 }}$
 & ${{\left( {1 + \sqrt {10}  + \sqrt {5 + 2\sqrt {10} } } \right)} \mathord{\left/
 {\vphantom {{\left( {1 + \sqrt {10}  + \sqrt {5 + 2\sqrt {10} } } \right)} {16\sqrt 2 }}} \right.
 \kern-\nulldelimiterspace} {16\sqrt 2 }}$ \\
  \emph{h}(1) & ${{\left( {3 + \sqrt 3 } \right)} \mathord{\left/
 {\vphantom {{\left( {3 + \sqrt 3 } \right)} {4\sqrt 2 }}} \right.
 \kern-\nulldelimiterspace} {4\sqrt 2 }}$
 & ${{\left( {5 + \sqrt {10}  + 3\sqrt {5 + 2\sqrt {10} } } \right)} \mathord{\left/
 {\vphantom {{\left( {5 + \sqrt {10}  + 3\sqrt {5 + 2\sqrt {10} } } \right)} {16\sqrt 2 }}} \right.
 \kern-\nulldelimiterspace} {16\sqrt 2 }}$
 \\
  \emph{h}(2) & ${{\left( {3 - \sqrt 3 } \right)} \mathord{\left/
 {\vphantom {{\left( {3 - \sqrt 3 } \right)} {4\sqrt 2 }}} \right.
 \kern-\nulldelimiterspace} {4\sqrt 2 }}$
& ${{\left( {10 - 2\sqrt {10}  + 2\sqrt {5 + 2\sqrt {10} } }
\right)} \mathord{\left/
 {\vphantom {{\left( {10 - 2\sqrt {10}  + 2\sqrt {5 + 2\sqrt {10} } } \right)} {16\sqrt 2 }}} \right.
 \kern-\nulldelimiterspace} {16\sqrt 2 }}$
\\
  \emph{h}(3) & ${{\left( {1 - \sqrt 3 } \right)} \mathord{\left/
 {\vphantom {{\left( {1 - \sqrt 3 } \right)} {4\sqrt 2 }}} \right.
 \kern-\nulldelimiterspace} {4\sqrt 2 }}$
 & ${{\left( {10 - 2\sqrt {10}  - 2\sqrt {5 + 2\sqrt {10} } } \right)} \mathord{\left/
 {\vphantom {{\left( {10 - 2\sqrt {10}  - 2\sqrt {5 + 2\sqrt {10} } } \right)} {16\sqrt 2 }}} \right.
 \kern-\nulldelimiterspace} {16\sqrt 2 }}$
 \\
 \emph{h}(4) & -- & ${{\left( {5 + \sqrt {10}  - 3\sqrt {5 + 2\sqrt {10} } } \right)} \mathord{\left/
 {\vphantom {{\left( {5 + \sqrt {10}  - 3\sqrt {5 + 2\sqrt {10} } } \right)} {16\sqrt 2 }}} \right.
 \kern-\nulldelimiterspace} {16\sqrt 2 }}$
 \\
  \emph{h}(5) & -- & ${{\left( {1 + \sqrt {10}  - \sqrt {5 + 2\sqrt {10} } } \right)} \mathord{\left/
 {\vphantom {{\left( {1 + \sqrt {10}  - \sqrt {5 + 2\sqrt {10} } } \right)} {16\sqrt 2 }}} \right.
 \kern-\nulldelimiterspace} {16\sqrt 2 }}$
 \\
  \hline
\end{tabular}
\end{table}
In contrast both to the Fourier transform, which localizes
frequencies, but fails to provide time resolution for the process,
and to the apparatus of $\delta$-functions, which localizes moments
of time, but have no frequency resolution, the DVT makes it possible
to reveal the local properties of any structure of an individual
event on different scales, eliminating smooth polynomial
characteristics and emphasizing fluctuation structures. It is
possible to completely eliminate statistical fluctuations by
selecting only strong correlated fluctuations, which will allow one
to observe exactly those dynamic fluctuations that exceed the
statistical component (noise).

\subsection{Noise elimination using the wavelet
method}

Among the modern noise suppression techniques, the Donoho-Johnstone
method has received the widest acceptance \cite{r20}. This method is
rather simple in implementation and time-saving in computational
aspect, since it implies the use of only fast algorithms of wavelet
transform. It consists of three steps, which, being successively
applied to the original signal, produce a noise-suppression effect.
At the first step, signal under investigation $x(t)$ is subjected to
DWT; afterward, the threshold noise elimination procedure is applied
to each of the detailing coefficients of level $j$ and, sometimes,
to the approximation coefficients of the same level; and, finally,
inverse wavelet transform is performed, which results in
reconstruction of the signal that is characterized, as expected, by
a higher SNR.

This technique is a nonparametric estimate of the regression signal
model with the use of an orthogonal basis \cite{r21}-\cite{r23}; it
operates with high efficiency with signals in the decomposition of
which only a few detailing coefficients significantly differs from
zero. Selection of a particular wavelet form depends on the problem
under investigation and is not predetermined beforehand \cite{r24}.
The depth of decomposition generally depends on the properties of
the analyzed signal. Smooth wavelets produce a smoother signal
approximation, and vice versa- "short"  wavelets better search for
peaks of the approximated function. The depth of decomposition
affects the scale of rejected details; i.e., as the depth of
decomposition increases, the model subtracts the noise of a steadily
increasing level until the scale of details becomes too large  and
the transform starts distorting the original signal shape. Upon
further increase in the depth of decomposition, the transform starts
forming a smoothed version of the original signal; i.e., apart from
the noise, some local peculiarities of the original signal are also
filtered off. Decomposition of the signal and its reconstruction by
the approximation and detaining coefficients that have passed
threshold processing is carried out using the Malla algorithm
\cite{r19} and the lifting procedure \cite{r25}. The threshold
processing itself is performed with the aid of one of the threshold
noise suppression operations. In accordance with the {\it hard
threshold} processing \cite{r20}, all coefficients $\left\{
{\widehat{d}_{j,k} \left| {k \in Z} \right.} \right\}$ of level $j$,
which are greater than or equal to the threshold, are held constant,
while the other coefficients that do not satisfy this condition are
are reduced to zero:
\begin{equation}\label{Eq6}
    d_{j,k}^h  = \widehat{d}_{j,k} I\left( {\left| {\widehat{d}_{j,k} } \right| > \theta _j } \right),\begin{array}{*{20}c}
   {} & {\theta _j  = \rho _j \sigma _i ,}  \\
\end{array}
\end{equation}
where $\rho_j$ is the threshold factor for the specified scale
\cite{r19}, and $\sigma$ is the noise variance  on the $j$th scale.
Hard threshold processing is a straight-out procedure. It should
nevertheless be taken into account that a hard threshold has two
drawbacks that can lower its usefulness for the noise suppression
task. The first consists in the fact that retaining of detailing
coefficients above a predetermined threshold value also implies
retaining of their noise. The other drawback is in the presence of
parasitic harmonics generated in the resulting signal by artificial
introduction of lacunas (gaps) formed due to the coefficients
reduced to zero. The use of {\it soft threshold} processing implies
recalculation of detaining coefficients $d$ in the following way:
\begin{equation}\label{Eq7}
d_{j,{}^{}k}^s  = {\rm{sign}}\left( {\widehat{d}_{j,{}^{}k} }
\right)\left( {\left| {\widehat{d}_{j,{}^{}k} } \right| - \theta
_{trh} } \right),
\end{equation}
where $\theta$ is a certain threshold value.

In this case, apart from the reduction to zero of the coefficients
$d$ actually containing only the noise component, the detailing
coefficients are decreased by the $\theta_{thr}$ value, which
corresponds to noise suppression in the informative coefficients as
well. Threshold $\theta_{thr}$, which defines the analyzed signal,
is a sole parameter that cannot be exactly estimated directly from
actual data. Mathematical solutions in determining the threshold
value seem unsatisfactory to be a priori  accepted. In an ideal
case, we tend to specify this threshold so as to minimize the
root-mean-square error (rmse):
\begin{equation}\label{Eq8}
\varepsilon  = \sqrt {\frac{1}{N}\sum\limits_{i = 1}^N {\left[
{x(t_i ) - \widetilde{x}(t_i )} \right]} ^2 } .
\end{equation}

Therefore, by analogy to \cite{r19},\cite{r25}, we determine the
basic signal component relying on threshold processing of the model
signal. Ideal threshold processing minimizes the rmse, making all
coefficients with the signal component below $\sigma$ vanish
\cite{r19}. In other words, it is assumed that the free from noise
signal component above $\sigma$ is an original signal; i.e.,
$\theta_{thr}=\sigma$. This selection can be tested on the model
signals. Our experience gained in working with natural signals
confirms that the ratio of the signal peaks to the noise level
reaches its maximum near $\theta_{thr} = \sigma$.

\subsection{Test of model signal with noise}
 To illustrate the efficiency of different approaches to the
deconvolution problem, let us select model signal $x(t_n)$, which is
specified on a set of points $N=2^{10}$ and consists of three
closely spaced Gaussian peaks
\begin{equation*}
  a_k \exp \left( { - {{(t - t_k )^2 } \mathord{\left/
 {\vphantom {{(t - t_k )^2 } {2\mu _0^2 }}} \right.
 \kern-\nulldelimiterspace} {2\mu _0^2 }}} \right),
\end{equation*}
where $a_k=[1.32, 7.0, 7.0]$, $t_k=[277, 307, 327]$, and $\mu_o=7$.
Let us add Gaussian noise and a harmonic term to it:
\begin{equation*}
\widetilde{x}(t_n ) = x(t_n ) + \kappa \Delta (\tau ) + {\rm{g}}(t_n
),
\end{equation*}
where $\Delta (\tau)$ is ordinary Brownian process analyzed on
$\tau\in[0,1]$, $\kappa$ is a certain coefficient, and $g(t_n)$ is
the harmonic term.

For the variance $\sigma^2$ of the noise component in model signal
$W(t_n ) = \kappa \Delta (\tau ) + {\rm{g}}(t_n )$
 to be estimated by the $x(t_n)$ data, it is necessary
that the influence of signal $x(t_n)$ be suppressed. A rough
estimate can be obtained from the mean values of the smallest-scale
wavelet coefficients \cite{r20}. The signal with length $N$ has
$N/2$ wavelet coefficients $\left\{ {\left\langle {\widetilde{x}(t_n
),\psi _{j,m} } \right\rangle } \right\}_{0 \le m \le {N
\mathord{\left/
 {\vphantom {N 2}} \right.
\kern-\nulldelimiterspace} 2}}$ of the smallest scale $2^j=2N^{-1}$.
Coefficients $\left| {\left\langle {x(t_n ),\psi _{j,m} }
\right\rangle } \right|$ are small if signal $x(t_n)$ is smooth on
carrier $\psi_{j,m}$, and in this case, $\left\langle
{\widetilde{x}(t_n ),\psi _{j,m} } \right\rangle  \approx
\left\langle {W,\psi _{j,m} } \right\rangle $. However, if $x(t_n)$
has a sharp differential on carrier $\psi$, coefficients $\left|
{\left\langle {x(t_n ),\psi _{j,m} } \right\rangle } \right|$
 are rather large. In the case of a piecewise-smooth signal, we have several
differentials, which results in a certain number of large
coefficients. This number is small in comparison with $N/2$. At the
smallest scale, signal $x(t_n)$ defines the value of a small portion
of large-amplitude coefficients $\left| {\left\langle {x(t_n ),\psi
_{j,m} } \right\rangle } \right|$, which are considered to be
"overshoots".  All the other coefficients are approximately equal to
$\left\langle {W,\psi _{j,m} } \right\rangle $; they are independent
random Gaussian variables with variance $\sigma^2$. Therefore,
$\sigma^2$ can be roughly estimated, with the influence of $x(t_n)$
being ignored, by the mean of absolute values $\left\{ {\left\langle
{\widetilde{x}(t_n ),\psi _{j,m} } \right\rangle } \right\}_{0 \le m
\le {N \mathord{\left/
 {\vphantom {N 2}} \right.
 \kern-\nulldelimiterspace} 2}} $, divided  by 0.6745 \cite{r21}.

Daubechies filters $db4$ were used in a direct wavelet transform and
when the estimate of the useful signal was synthesized from
coefficients after their threshold processing, whereas higher-order
filters $db6$ were employed to estimate the threshold values.

Calculations of all wavelet coefficients, testing of the noise
suppression algorithms, and selection of required signals for
further analysis were performed using MATLAB and its web libraries
\cite{r26}.

\begin{figure}[!htb]
\resizebox{0.4\textwidth}{!}{%
  \includegraphics{fig5.eps}}
\caption{ (\emph{a}) Model signal from three closely spaced Gaussian
peaks; (\emph{b}) additive mixture of the model signal with noise;
noise suppression using (\emph{c}) the Savitzky--Golay filter and
(\emph{d}) Wiener filter; (\emph{e}, \emph{f}) Daubechies wavelet
filters, $db4$, with hard and soft threshold processing,
respectively.} \label{test_pulse}
\end{figure}
The results are shown in Fig.\ref{test_pulse}. It is apparent that
all filters provide good noise suppression efficiency (the SNR is
$>30$ dB), but the signals passed through the wavelet filters with
the use of the hard or soft threshold processing better represents
the shape of the original signal (Figs.\ref{test_pulse}\emph{e} and
\ref{test_pulse}\emph{f}), which ensures more reliable signal
resolution into individual components.  For our purposes, hard
threshold processing is quite satisfactory both in the quality
factor and in the computational time.

\section{\label{reliability} Reliability in identifying multipoint
events}

In order to verify the efficiency of the algorithm for the noise
suppression and pulse shape discrimination for multipoint events
from an actual source the LPC was filled with natural Kr containing
cosmogeneous radioactive isotope $^{81}$Kr ($T_{1/2}=2.1\times10^5$
yr) with a bulk activity of $\sim0.1$ $min^{-1}l^{-1}$Kr \cite{r27},
\cite{r28}.
\begin{figure}[!h]
\resizebox{0.4 \textwidth}{!}{%
\includegraphics{fig6.eps}}
\caption{Amplitude spectra (\emph{1}) of single-, (\emph{2})
two-point, and (\emph{3}) three-point events that form the total
analyzed pulse amplitude spectrum of the counter detecting both
background and $^{81}$Kr decays.} \label{spcKr81}
\end{figure}
It decays by electron capture into $^{81}$Br$^*$. In
87.5\% of cases, an electron is captured from the $K$-shell of a Kr
atom ($K$-capture) \cite{r29}. Filling of the vacancy at the
$K$-shell of a daughter Br atom is accompanied in 61.4\% of cases by
an escape of two characteristic quanta with energies of 11.92 keV
($K_{\alpha1}$, 100\%), 11.88 keV ($K_{\alpha2}$, 50.9\%), 13.29 keV
($K_{\beta1}$, 21.0\%), and 13.47 keV ($K_{\beta2}$, 1.07\%)
\cite{r11} and concomitant Auger electrons with energies of 1.55
keV, 1.60 keV, 0.27 keV, and 0.01 keV, respectively (the relative
intensities of $K_{\alpha,\beta}$ lines are presented in brackets).
From this list, it is apparent that, when photons $K_{\alpha1}$ and
$K_{\alpha2}$ escape, the energy of Auger electrons is sufficient
for a distinguishable two-point event to be formed. In 38.6\% of
cases, filling of the vacancy at the $K$-shell of Br is accompanied
by an escape of a cascade of Auger electrons that produce  a
single-point energy deposit. Events with an escape of characteristic
photons $K_{\beta1}$ and $K_{\beta2}$ should also be placed into a
category of single-point events. Taking into account the absorption
efficiency for characteristic photons in the LPC working gas
$(\epsilon_{abs}=0.869)$ and using the above data, one can calculate
the composition of a 13.5-keV full-energy peak: 49.4\% of all events
are single-point, and 50.6\% are two-point.

Describing the noise-free signals by a set of Gaussian curves using
rmse minimization technique (7), one can discriminate between two-
and single-point events. Figure \ref{spcKr81} presents the energy
spectra ({\it 1}) of single-, ({\it 2}) two-~, and ({\it 3})
three-point events forming the total analyzed pulse-amplitude
spectrum of the counter that detects both background and $^{81}$Kr
decays. Similar components (spectra {\it 1-3}) of total spectrum
{\it 1} for a calibration measurement of 88-keV $\gamma$ rays are
shown in Fig.2.

Given the composition of events from the $^{81}$Kr and $^{109}$Cd
sources and results of simulation of these processes in the LPC, one
can, using the GEANT 4.8.2 program \cite{r30}, determine the quality
of suppression of the noise component and the efficiency of the
procedure for separating events by the criteria of a multipoint
event. Table II presents the percentage composition of three types
of events in the full-energy peaks with energies of 13.5 keV
($^{81}$Kr) and 88 keV ($^{109}$Cd), which was obtained by
estimation (column \emph{I}); by simulation of processes in the LPC,
ignoring the confluence of closely spaced primary charge clusters
(column \emph{IIa}), and taking into account their confluence
(column \emph{IIb}); and by separation of the experimental spectrum
into components after its wavelet purification of noise using hard
threshold processing (column \emph{III}).

Determining the parameters of individual components in a compound
event, it is possible to perform energy calibration in the energy
range under investigation and determine the energy resolution of
single-point components which form a multipoint event. The energy
distributions of individual components of two-point events from the
$^{81}$Kr and $^{109}$Cd sources are shown in Figs. 7 and 8,
respectively.
\begin{figure}[!htb]
\resizebox{0.45 \textwidth}{!}{%
\includegraphics{fig8.eps}}
\caption{Amplitude distributions of energy deposits  of  individual
components  for two-point events from the source placed in the
middle of the LPC length ($^{109}$Cd).} \label{matrCd109}
\end{figure}

\begin{figure}[!htb]
\resizebox{0.45\textwidth}{!}{%
\includegraphics{fig7.eps}}
\caption{Amplitude distributions of energy deposits in of individual
components of  for two-point events from the internal ($^{81}$Kr)
source with a total energy of 13.5 keV.} \label{matrKr81}
\end{figure}

\section{\label{conclusions}Conclusions} The analysis both of the
pulse shape variety and methods of LPC signal processing has been
performed  using a multiresolutional wavelet analysis. It has been
shown that the noise component can be suppressed successfully, and
the problem of separating of the events with closely spaced
clasters, partially or fully lapping over each other, can be solved
with a high efficiency, and the parameters of these events can be
estimated. The test measurements of signals from the krypton-filled
LPC irradiated by internal and external sources have made it
possible to determine the efficiency of discrimination between
single-, two-, and three-point events. The described technique helps
increase the sensitivity of detection of compound events in
gas-filled detectors and demonstrates its applicability to detection
of rare events from $2K(2\nu)$ capture in large proportional
counters.

\textbf{Acknowledgments}. The work has been carried out under the
financial support of the RFBR (grant no. 04-02-16037) and "Neutrino
Physics" Program of the Presidium of RAS.

\begin{widetext}

\begin{table*}[!htb]
\label{tab2} \caption{Relative composition of three types of events
in the full-energy peaks with energies of 13.5 keV ($^{81}$Kr) and
88 keV ($^{109}$Cd), obtained by estimation (column \emph{I}); by
simulation of processes in the LPC, ignoring the confluence of
closely spaced pointwise ionization regions (column \emph{IIa}) and
taking into account their confluence (column \emph{IIb}); and by
separation of the experimental spectrum into components after its
wavelet purification of noise using hard threshold processing
(column \emph{III}).}
\begin{tabular}{|c|c|c|c|c||c|c|c|c|}
  \hline

& \multicolumn{4} {c||}{13.5 keV ($^{81}$Kr)} & \multicolumn{4}{c|}
{88 keV ($^{109}$Cd)} \\ \hline &    calc., \% & \multicolumn{2}
{c|} {GEANT4.8.2, \%} &  \multicolumn{1} {c||} {empiric., \%}   &
calc., \% & \multicolumn{2} {c|} {GEANT4.8.2, \%}   &
\multicolumn{1} {c|} {empiric., \%}
           \\
type of events &\emph{I}&\emph{IIa}&\emph{IIb}&\emph{III}
&\emph{I}&\emph{IIa}&\emph{IIb}&\emph{III} \\ \hline\hline
  singl-point &  49.4 & 44.1 & 66.2 & 68.2 & 44.1 & 45.0 & 59.4 & 56.8  \\
  two-point   &  50.6 & 55.9 & 33.8 & 31.7 & 53.4 & 53.7 & 40.0 & 39.4  \\
  three-point &       &      &      & $<0.1$ &  2.5 &  1.3 &  0.6 &  3.4  \\
  \hline
\end{tabular}

\end{table*}

\end{widetext}

redpajama_set_name: RedPajamaArXiv


ABC News(WASHINGTON) — A whistleblower from the Environmental Protection Agency says that Administrator Scott Pruitt was "bold-faced lying" when he told members of Congress that no EPA employees were retaliated against for raising concerns about his spending decisions.
In an exclusive interview with ABC News' Kyra Phillips, former deputy chief of staff Kevin Chmielewski said he was "100 percent" forced out after raising concerns about Pruitt's spending on first-class travel.
Chmielewski said a manager called him into his office and said: "Hey — Administrator Pruitt either wants me to fire you or put you in an office so that he doesn't have to see you again," Chmielewski told ABC News.
The EPA declined to comment in response to questions about Chmilewski's allegations against Pruitt and his staff. ABC News obtained a personnel form filled out by an EPA HR officials that says he resigned on March 17.
The form is not signed by Chmielewski, who says he was actually forced to leave a month before that date.
Chmielewski said he had previously raised concerns about things like Pruitt's first-class flights and a request to spend $100,000 a month on a private jet, even meeting with the presidential personnel office about what he called lavish spending at the EPA. He said no one would look into his concerns further.
"They didn't wanna touch it with a ten-foot pole. Understandably. I mean, at this point I'm going up against a cabinet secretary. Who wants to do that? I sure didn't want to, and still don't want to. But that's apparently where I'm at now," he said.
The Trump campaign veteran says he believes he started being pushed out after he refused to sign off on first-class flights for one of Pruitt's aides. Chmielewski said there was no reason for that person to fly first class.
"I refused to do it. And, once again, I think that was some of the beginning of the retaliation, and why you know, cause I said absolutely not. And I kinda got in trouble behind closed doors for not signing that. Just Kevin, "Sign it. You know, be done with it." And the last thing I was doing was signing off on that," he said.
Months after he first raised concerns, Chmielewski said he returned from a trip to Japan with the vice president and was immediately told to surrender his parking pass. He said that after he declined, the head of Pruitt's security detail Nino Perrotta called him multiple times threatening to come to his house and physically take his pass, even though Chmielewski said that would be trespassing. He said he was ultimately told to resign or he would be fired but he still refused to resign.
Perrotta has not responded to ABC News request for comment.
When asked about Chmielewski's situation Pruitt said last week during congressional testimony that the former deputy chief of staff resigned, but Chmielewski says that he was fired and that the agency has been trying to discredit him.
When asked about reports that the agency pushed out employees that raised concerns about his spending, Pruitt told lawmakers last week that there was "no truth" to the reports and that the agency will work to protect whistleblowers.
"I just want to emphasize very very clearly to you that there's no actions that we have taken that I'm aware of related in any way to the issues you raise as far as reassignment or employment action based upon that," Pruitt told lawmakers.
The New York Times first reported that Chmielewski and four other EPA employees were reassigned or removed from their positions for raising concerns about Pruitt's spending. Chmielewski met with members of Congress and staffers earlier this month.
Pruitt, who is the subject of multiple ethics investigations and a White House probe, appeared before Congress on April 26 where he insisted he did not retaliate against employees in response to questions from both Democrats and Republicans.
"I have nothing to hide as it relates to how I've run the agency for the past 16 months," Pruitt said during his remarks before a House subcommittee last week.
The EPA's internal watchdog is looking into multiple questions about Pruitt's decisions since taking over at the EPA, including the allegations of retaliation against employees, his spending on travel and security, and his living arrangement.
In March, ABC News first reported that Pruitt had been living in a Capitol Hill condo co-owned by the wife of a prominent lobbyist with business interests before the EPA. Pruitt paid just $50 a night, claiming it was just for a one bedroom.
ABC News also reported that Pruitt's daughter was living in the condo for an extended period of time as she was completing a White House internship, without permission, according to his former landlord.
The report launched queries into other Pruitt and EPA expenditures, including questions about Pruitt's security spending, which far outpaced his predecessors, on things like first class flights, a 24-hour security detail, and a $43,000 soundproof phone booth for his office. It was also found that Pruitt's chief of staff had approved significant raises for some of Pruitt's top aids on the administrator's behalf.
Chmilewski said that he was involved in planning the phone booth and that Pruitt knew it would cost more than $40,000. "He knew what was going on, and what the ideas were," he said, though Chmielewski said he didn't personally see Pruitt sign anything authorizing the expense.
Chemeilewski also said that he isn't criticizing the administrator because he doesn't disagree with his political agenda. Chmielewski worked on President Donald Trump's campaign said he is still loyal to Trump and Vice President Mike Pence. He said he thinks the president doesn't have the full story when it comes to Pruitt.


New England Neon, Susan's new book, will take readers up and down the main streets and back roads of the region, from the shores of Lake Champlain to the tip of Cape Cod. The volume celebrates the style and exuberance of these one-of-kind creations — Rhode Island hot weiners, tourist cabins in Maine and New Hampshire, Connecticut-style apizza, and restored movie palaces everywhere. You can purchase copies of her book and other works of hers this weekend at Mistletoe Art Fair, December 15-16, 10am-5pm.
Donna, the owner of "Inspired by the Sea Studio" will be exhibiting at the Mistletoe Art Fair this weekend. You can purchase her Fine Art, Prints, Calendars, Note Cards, and Coasters at the Cambridge Center for Adult Education.
Owner Liz Stewart has been making and teaching jewelry since 2000. She uses new and repurposed hardware in unexpected ways. You will find bracelets, necklaces, earrings and pendants in her collection. Come and see her creations this coming weekend, December 15-16 at Cambridge Center for Adult Education, 42 Brattle Street, Harvard Square.
In 1994 while recuperating from a motorcycle accident, Peter found his passion, a future in art. A physical therapist suggested stained glass as a hobby / therapy that would help to recapture the lost dexterity of his fingers. One operation lead to another with a lot of down time in between. One day while recovering, as he was watching a PBS program that explained the basics of stained glass, he found his creative path.
Later, while attending a retrospective at the San Francisco Museum of Modern Art, he was inspired by the work of Sol LeWitt. His signature Guilday Glass designs are a direct result of his exposure and discovery of abstract expressionism in contemporary art. His use of primary colors and simplistic shapes to create works of art that are complex and satisfying was all the inspiration he needed.
In early 2001, with the help and encouragement of his wife Patricia, he left his job with Charles Schwab & Co. Inc. They moved from beautiful San Francisco, CA to quaint Walpole, MA, and fulfilled his dream of opening his own business, Guilday Glass. Today having fully recovered from those injuries He has turned his much loved pastime into a successful business.
Judy Robinson-Cox creates temporary tabletop dioramas that capture humorous human events and the inner workings of the mind.
An award-winning Cape Ann, Massachusetts photographer and mixed media artist, Judy creates Lilliputian Landscapes, which are photographs of tabletop tableaus that she construct with food or found objects and populate with ¾" high miniature figures. The tiny people transform the scene into a world with a life of its own. Cauliflower becomes a snow-covered hill, a plate of grain is transformed into a beach, and a butternut squash turns into a construction site. She creates each scene entirely in front of the camera and does not use Photoshop or any other computer tool to construct the picture.
Fishtown Creations is the name of her business. Deborah Way loves working with metals.
Marian Ives, a native New Englander, studied art and metal smithing from an early age. Her ornaments are produced on a hundred-year-old, three-ton kick press, using dies hand-cut from tool steel, and hand painted.
To make her keen (and often whimsical) observations of our natural world accessible, she has made several series of unique hand-painted characters. Discerning collectors and those with a gentle eye will enjoy each of these handcrafted creations.
Using various elements such as antique keys and watch gears, hand-colored brass and wires, Kendra creates her jewelry. Sprouting leaves and wings with colors ranging from naturalistic to brilliant and fantastical are common themes in her work.
Kendra's work includes a wide range of pendants, earrings with titanium or niobium findings, alligator clips for hair or fabric, and hair pins that serve equally well as scarf or shawl pins.
Visit her during Mistletoe Art Fair on December 15-16, 10am – 5pm at Cambridge Center for Adult Education.
We are looking forward to seeing his new work at the Mistletoe Art Fair. Walter earned a degree in advertising and journalism from the University of Maine before deciding to run his own professional photography studio, a Marlborough-based business.
You can see his photography on December 15-16, at Cambridge Center for Adult Education, Mistletoe Art Fair.
She works in a traditional medium, but with a modern look. Liz Foss has been making quilts for over 30 years, often as a respite from various administrative work and business ventures.
Liz's quilts are based on traditional patterns, which evoke an emotional response, conjuring a sense of home and family.
She incorporates contemporary colors and design elements, creating various items for the home: table runners, pot holders, pillows that turn into lap quilts. Fabrics are 100% cotton and washable.
Liz enjoys custom work. Some customers have redecorated a whole room around one of her quilts. She lives in Spencer, MA.
MISTLETOE ART FAIR is the revival of Holly Fair, a holiday tradition for over 60 years at Cambridge Center for Adult Education. Holly Fair, a cherished event, was canceled a couple of years ago, but it has been reestablished and is now called 'Mistletoe Art Fair. Look for it this season on December 15th and 16th at CCAE, 42 Brattle Street, Harvard Square.


Monaco Kitchen Design is a kitchen and bathroom design company based in Downers Grove, serving the entire Chicagoland area. The owner of Monaco Kitchen Design was looking for a professionally designed, responsive website with great SEO to help establish his business. This website was built on the WordPress platform and features a full page responsive image slider, responsive grid design, informational pages for their services, a great image gallery, a contact form with custom fields, an SSL certificate, Google Analytics to track visitors, sitemap submission to Google and Bing and social media page creation and optimization. This website features great Search Engine Optimization (SEO) that should help Monaco Kitchen Design grow for years to come.


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The $28 Lip Mask Behind Jennifer Aniston's Stunning Smile on 'The Morning Show'
By Suzy Forman
Jennifer Aniston at Apple's 'The Morning Show' season two special premiere photocall on September 10, 2021. Eric Charbonneau/Shutterstock
Our lips don't get along very well with cold weather, to say the least. If they could, they'd tear each other apart. The cold weather definitely doesn't hold back on the offensive side of things, but our lips can't really fight back. Going on the defensive is our only real choice if we want to keep them soft and smooth!
We spend day after day slathering on lip balms that might be doing more harm than good. We try exfoliating with scrubs too, but sometimes that flakey, dry skin on our lips doesn't want to budge, or it pops right back up an hour later. Are there actually any lip products out there that could make a genuine, positive difference in our lives? Well…how about one used by Jennifer Aniston?
Jennifer Aniston's beauty team on set at "The Morning Show." Courtesy of Jennifer Aniston/Instagram
Get the Tatcha Kissu Lip Mask for just $28 at Amazon! Also available directly from Tatcha! Please note, prices are accurate at the date of publication, September 21, 2021, but are subject to change.
Aniston is one of the biggest beauty icons in the world, so when we see an Aniston-approved product, we immediately check it out. She's not too shy about sharing either. The actress actually posted a photo earlier this year from the set of The Morning Show, revealing a slew of products used by her hair stylist, Chris McMillan, and her makeup artist, Angela Levin. Season two just started airing on Apple TV+, so we can see for ourselves the effects of these products!
This Kissu lip mask was one of multiple Tatcha products to make the cut, claiming responsibility for Aniston's smooth and supple lips. It's a leave-on treatment made to "restore lips to full lushness" with key ingredients like squalene and Japanese peach to repair damage, calm irritation and lock in moisture, soothing chapped lips. It also contains Japanese camellia oil with contains oleic acid, vitamins and Omegas 3, 6 and 9!
This lip mask has a thick, jelly-like texture that's non-sticky and may help plump up lips to reduce the appearance of wrinkles. Tatcha shoppers say their lips "felt softer than any Chapstick" has made them in the past, calling this mask "a treat for your lips." They say it's "super luxurious" and "extremely hydrating," and that after just one application, their lips "feel amazing the entire day"!
You can use this mask any time you feel your lips need a little extra healing love and/or protection. It's a must just before bed, but you can also wear it with makeup, while working from home, while stepping out on a brisk winter day — any and every time your lips crave it!
Jennifer Aniston's Facialist Compared This Mascara to Having Lash Extensions
Looking for more? Shop more Tatcha products here and check out all skincare at Amazon here! Don't forget to explore all of Amazon's Daily Deals for more great finds!
Browse fashion, beauty and health products. Also, check out our gift guides.
This post is brought to you by Us Weekly's Shop With Us team. The Shop With Us team aims to highlight products and services our readers might find interesting and useful, such as wedding-guest outfits, purses, plus-size swimsuits, women's sneakers, bridal shapewear, and perfect gift ideas for everyone in your life. Product and service selection, however, is in no way intended to constitute an endorsement by either Us Weekly or of any celebrity mentioned in the post.
The Shop With Us team may receive products free of charge from manufacturers to test. In addition, Us Weekly receives compensation from the manufacturer of the products we write about when you click on a link and then purchase the product featured in an article. This does not drive our decision as to whether or not a product or service is featured or recommended. Shop With Us operates independently from the advertising sales team. We welcome your feedback at ShopWithUs@usmagazine.com. Happy shopping!