Researchers at the Child Mind Institute say 50 percent of U.S. children will have a diagnosable mental illness, but less than 8 percent will get treatment in any given year.
There is a cavernous gap between the number of children struggling with mental health conditions and the number who actually get help. That's one of the conclusions of the Children's Health Report released recently by the Child Mind Institute.
The report states that nearly 50 percent of youth in the United States will have had a diagnosable mental illness at some point during childhood. Of those diagnosed, 22 percent will have a serious impairment. The problem is that not only are these kids not getting care now, they're not getting care tomorrow, or in five years.
Image Attribution: There are many barriers to mental healthcare for families but stigma and misunderstanding are the big ones. Mental health needs are still perceived as something to be ashamed of in the United States. Parents often don't want to accept that their child may be different either. "If parents were knowledgeable and unafraid, then early and routine mental healthcare would be the norm. It would be expected, training would be adequate, and we would not have shortages of providers," says Koplewicz.
Mental Health Issues Can Start Early: The data show that the median onset for anxiety disorders is 6 years of age. That may be because mental illness and development go hand in hand Koplewicz explained. "It's possible that, because fear and anxiety are such fundamental functions of the brain, when developmental processes go 'off course' in those areas they manifest early," he said. If your child has frequent, drawn-out, intense episodes of fear, stress, or anxiety that seem out of proportion and affects their daily life and happiness, they may have an anxiety disorder. Other symptoms include trouble sleeping or concentrating, irritability, fatigue, and restlessness.
Image Attribution: "Anxiety disorders are real, common, and treatable," said Koplewicz. "Knowledge is your best friend, and fear and shame have no place when it comes to the health of your child, physical or mental." The same goes for any mental health concerns, not just anxiety. If you suspect a problem, don't be afraid to discuss it with your child's doctor. It boils down to improving your child's quality of life. "Kids are amazingly resilient if they have the support and the tools to overcome these challenges — but the dangers are real," warns Koplewicz.
You wonder if your kindergartener's spending long periods of time alone in his room is normal. How many times does your teen have to throw her math book against the wall before you know her problem is not quadratic equations? Your college sophomore stopped texting you—should you worry?
Our thoughts and feelings influence our actions—how we perceive ourselves and others, how we communicate, how we learn and mature, and how we face obstacles. Crises, life transitions, hurts, and other negative forces often can challenge a child's sense of well-being. The University of Michigan describes a helpful mental health continuum that moves from mental health to mental problems and diagnosable mental illness. Our responses move along this continuum from mild and temporary, to moderate, disabling, long-lasting distress.
Famous psychotherapist Alfred Adler once said, "The only normal people are the ones you don't know very well." When problems arise in your family, you may be tempted to think the family next door has their act together. But take heart—you know your children best, and it's their normal that matters most.The opposite temptation is to think your family is the standard for normal. As you might expect, "normal" is a moving target. The mental health continuum is fluid and changeable, depending on how you manage stresses at any given time.
Resources: You have probably already equipped yourself for positive parenting by reading books such as Ages & Stages: A Parent's Guide to Normal Childhood Development(birth to 10 years) or The Teen Years Explained: A Guide to Healthy Adolescent Development. However, there are many other resources to help you lay a strong foundation for your children's mental health. Contact your child's school counselors, get support at your local community center, or tap into your local library's endless supply of knowledge.
To access services from our team of independently licensed therapists please call 843-884-0025 to schedule an appointment.


text:
The following is an incomplete list of films set or shot primarily in Dunedin, New Zealand.

 The Royal Treatment (2022) (partly filmed in Dunedin)
 The Power of the Dog (2021) (partly filmed in Dunedin)
 Black Christmas (2019) (partly filmed in Dunedin)
 The Light Between Oceans (2014) (partly filmed in Dunedin and Port Chalmers)
 I Survived A Zombie Holocaust (2012) (filmed in Dunedin)
 Paradise at the End of the World (Out of Ashes) (2009) (filmed on Otago Peninsula, Dunedin)
 X-Men Origins: Wolverine  (partly filmed in Dunedin)
 Perfect Creature (2007) (filmed in Dunedin)
 Out of the Blue (2006) (set in Aramoana, Dunedin; filmed at Aramoana and Long Beach, Dunedin)
 Sylvia (2003) (filmed in Dunedin)
 Jaal: The Trap (2003) (partly filmed in Dunedin)
 Scarfies (1999) (filmed and set in Dunedin)
 The Grasscutter (1990) (filmed and set in Dunedin)
 An Angel at My Table (1990) (filmed and set partially in Dunedin)
 Pictures (1981) (filmed and set in Dunedin)
 Phar Lap's Son (1936)  (filmed in Dunedin)

References

External links
 https://www.imdb.com/search/title?locations=Dunedin

Culture in Dunedin
Dunedin
Dunedin
Dunedin
Mass media in Dunedin
 Dunedin
 Dunedin

redpajama_set_name: RedPajamaWikipedia


Jul. 31, 2014 6:00 a.m.
VANCOUVER – Newly posted documents show a dramatic disparity in the salaries and travel expenses paid to a handful of Canada's First Nations chiefs, ranging from thousands of dollars to almost $1 million.
Following the passage of a financial-transparency law by the federal government in 2013, First Nations are now required to publish audited financial statements of salaries and expenses online within 120 days of the end of the financial year ending March 31, 2014.
But Metro Vancouver's Kwikwetlem First Nation has published, and the website shows that economic development officer and Chief Ron Giesbrecht was paid $914,219 in remunerations and $16,574 in expenses for the financial year ending March 31, 2014.
Remunerations are defined in the document as salaries, wages, commissions, bonuses, honorarium, dividends and any other benefits, other than reimbursements, and non-monetary benefits. Expenses are defined as the costs of transportation, accommodation, meals, hospitality and incidentals.
A person answering the phone at band's office had promised a statement, then later said there would be no comment at this time.
Still, the band states on its website that it is creating an environment that promotes a higher quality of life.
"We are committed to transparency, responsibility, financial accountability, social, health, education, and economic development," the website states.
Aboriginal Affairs and Northern Development Canada reports the Kwikwetlem band has a registered population of 37 and 33 people living on the reserve.
Earlier this month, the Kwikwetlem claimed title to all lands associated with now-closed Riverview Hospital in Metro Vancouver and other areas of its traditional territory, citing the recent Supreme Court of Canada ruling in Tsilhqot'in v. British Columbia.
The O'Chiese First Nation of Rocky Mountain House, Alta., reported Chief Darren Whitford received remunerations of $164,453 and travel and meeting expenses of $100,778. The First Nation's six councillors reported remunerations starting at just over $102,261 and expenses starting at $27,433.
The band's total population reported by Statistics Canada in the 2006 census was 450.
The Taku River Tlingit First Nation in the northwestern, B.C., community of Atlin also published a document showing a salary of $72,800 to band spokesman John Ward and travel expenses $6,400.
The Canadian Taxpayers Federation expressed "jubilation" over the publication, and noted more and more information would be available over the coming weeks as the federal government scans and posts the documents.
He said many aboriginal people have been bullied or harassed for asking for the basic information in the past.
In March 2013, Aboriginal Affairs Minister Bernard Valcourt and others tried to speak in Winnipeg on the First Nations Financial Transparency Act but were interrupted by protesters who opposed the law.
Protester Pam Palmater of the Idle No More movement said at the time she opposed the law because the financial information is already transparent.


Midweek Fiction: Stephen King, "Beachworld"
We haven't had science fiction here on Midweek Fiction in a while, and there may be some of you who, after reading this story of a shipwreck and a beach, say we still haven't. There may be some of you who say this story is horror. I know it leaves me unsettled.
Read more about Midweek Fiction: Stephen King, "Beachworld"
Remember Donkey from the Shrek movies? Of course you do—who could forget his love affair with the dragon, his body-swapping with Puss, or his "tiny mutant babies"? Sure, Shrek is the hero of these movies, and it is his actions (and those of the various villians, including Lord Farquaad and Prince Charming) that move the plot along. But Donkey serves another function in these movies; he is the perfect example of the sidekick as comic relief. His primary purpose is to relieve the tension created between the hero and villain. Although he may stray into the occasional thoughtful or insightful conversation, his reason to exist is to brighten up the tone of the narrative.
Sidekicks do, however, serve in other positions than comic relief. They are partnered with their hero, providing many needed services. Throughout fiction there are hundreds, if not thousands of famous hero/sidekick pairings: Donkey and Shrek, Sherlock Holmes and Watson, and Batman and Robin are just a few examples. In each of these pairings, the sidekick helps out the hero. As Bronwyn Williams explains, "The sidekick tends to be the more passive, literate character who fulfills the groundwork in order to free his or her hero to perform the action." Sidekicks vary in power and in abilities, but they share many common characteristics and are always beneath the hero.
I would like to propose that the role of the sidekick is not, however, the only role that the friend of the hero may play. There is something more than comic relief with sporadic insight available to characters who support the hero and develop the plot. The sidekick has its place, but in most fantasy literature this role should more truly be called the second, as this character is often a hero in his or her own right.
Midweek Fiction: Catherynne M. Valente, "White Lines on a Green Field"
There is, perhaps, no story more thematically appropriate for a back to school week than the story of Coyote going to high school. And the state football championship. The fact that it is a great story is a bonus.
Read more about Midweek Fiction: Catherynne M. Valente, "White Lines on a Green Field"


Your purchase is protected by Paypal Buyer Protection Policy and by our own word. If there is a problem contact us immediately and we will respond quickly with a solution. We want you to be happy and satisfied always. We refund the same day the part is returned. With overseas customers we can work out any issues that might arise. We can ship any size item or part, crates, pallets, boxes or envelopes.


text:
{{Infobox basketball club
| name = Sharjah SC
| color1 = white
| color2 = blue
| color3 = red
| logo = Sharjah SC logo.png
| nickname =
| league = UAE National Basketball League
| conference =
| division =
| founded = 1966 (as An Nahl Sharjah)
| dissolved =
| history = An Nahl Sharjah1966–2017''Sharjah SC2017–present
| arena =
| capacity =
| location =
| colors =
| current =
| sponsor =
| media =
| chairman =
| president =
| vice-presidents =
| manager =
| coach = Abdul Hamid Ibrahim
| captain =
| ownership =
| championships =
| conf_champs =
| div_champs =
| season =
| position =
| website =
| 1_title =
| 1_body =
| 1_pattern_b =
| 1_shorts =
| 1_pattern_s =
| 2_title =
| 2_body =
| 2_pattern_b =
| 2_shorts =
| 2_pattern_s =
}}Sharjah SC, also known as Al Sharjah, is an Emirati professional basketball team based in Sharjah. The team plays in the UAE National Basketball League, the highest national level. It is the basketball section of the Sharjah FC club, mainly known for its football team.

Sharjah has won the UAE League championship one time, in 2020. In 2017, An Nahl Sharjah Club and Shaab merged into one new club named Al Sharjah.

HonoursUAE National Basketball LeagueChampions (1):''' 2020

References

Basketball teams in the United Arab Emirates
Basketball teams established in 1966
Sport in Sharjah (city)


Ansiedlung von ausländischen Mitarbeiter, Betreuung, integration von ausländischen Arbeitskräften, Einschulung von Kinder, Haussuche, Wohnungsuche, Kulturelle information, Unterstützung von Ausländer bei neustart in der Schweiz, Leben in der Schweiz.
Our interaction with Roberto Canali started prior to our move during a pre-visit and the interaction at that time including getting us to see what is on offer despite the fact that we would be making a choice much later was really appreciable as it gave us clarity on what to expect and come prepared when we actually move. Next, although we had a limited time to make a decision, the decision was not forced upon us rather we were told to look into options and than make an informed decision.
We also wish Roberto Canali well and hope that he is able to provide similar help to others to make it comfortable.


The Australian government has said that it will remove some 40 children who remain in migrant detention camps on the Pacific island Nauru by the end of the year.
The announcement came under pressure from the international community which criticised the country's policy of intercepting asylum seekers attempting to reach Australia and detaining them in offshore detention facilities.
More than 240 child detainees have been relocated in the past few years from the facilities.
"Children have been transferred off Nauru. That's been happening for some time," Prime Minister Scott Morrison told 2GB radio on Thursday.
Over a thousand asylum-seekers remain on Nauru and 46 children have been born in detention since 2012, many of whom are suffering from medical and psychiatric problems.
The government has said that it would not settle the migrants in Australia once they get the medical treatments.


text:
\section{\label{sec:Intro}Introduction}
Due to continued nanoelectronics scaling, metal interconnects as well as
transistors in integrated circuits are becoming ever smaller and
are approaching atomic  scale dimensions \cite{ITRS}.
As a consequence, understanding the effects of size-dependent phenomena on
material properties is becoming ever more critical to enable efficient device
performance.
Present day transistor technologies use copper as an interconnect material,
however it is unknown if at the small cross-sections required for future
technologies copper will be able to fulfill this function effectively due
to increased resistances; measured line resistivity increases dramatically
for Cu nanowires (NWs) compared to bulk materials.
\cite{Steinhogl2002,Zhang2007}
It is required that the electrical conductivity of small cross section
copper nanostructures be understood to maintain acceptable power consumption in
future nanoelectronics generations.
In particular the contribution of the individual scattering sources, such
as surfaces,\cite{Fuchs1938} grain boundaries,\cite{Mayadas1970} electron-phonon interaction \cite{Plombon2006} and
impurities, to overall resistivity needs to be assessed to aid development
of interconnects which minimize line resistance.
A succinct overview of these issues can be found in the review of
Josell, Brongersma and T\H{o}kei.\cite{Josell2009}

In general the dominant scattering mechanism in metal nanostructures is
dependent on processing conditions and the geometry of the resulting
nanostructures.
For example \citet{Henriquez2010,Henriquez2013} have reported electron scattering
to vary with grain size in the case of gold thin films.
Grain boundary scattering is found to dominate for grain sizes much smaller
than the electron mean free path, while for much larger grain sizes
it is the surface that is critical to resistivity.
For grain sizes comparable to the mean free path, both mechanisms are
responsible for the increases resistances relative to bulk gold.
Meanwhile, in the case of copper thin films \citet{Sun2009,Sun2010} have reported
that it is grain boundary scattering which dominates.
\citet{Zhang2007} report that the temperature dependence
of resistivity in Cu NWs is consistent with surface scattering
as the dominant scattering source.
This report is corroborated by \citet{Graham2010},
who find that diffuse surface scattering and line edge roughness is
consistent with the temperature dependence of resistivity for Cu NWs down
to 25 nm diameter and that the role of grain boundary scattering is minimal.
Similarly, \citet{Wang2012} report that resistivity is dominated by
diffuse surface scattering for 20 - 100 nm Cu NWs.
Thus though the situation for metal nanostructures can vary by material
and process conditions, the literature to date as pertains to Cu NWs
seems quite emphatic; the surface is the dominant scattering source.

In low dimension Cu films the surface environment has been reported to
drastically influence conductivity.
In a series of studies,\cite{Chawla2009,Chawla2010,Chawla2011} Chawla and
co-workers have investigated the scattering at the surfaces of Cu thin films.
They report that scattering at a Cu-vacuum surface is partially specular,
whereas after tantalum deposition the surface scattering becomes diffuse
.\cite{Chawla2009,Chawla2011}
The effect of oxygen has also been reported, with diffuse scattering again
reported after oxidation.\cite{Chawla2010}
The effect of a variety of coating metals on Cu thin films has also been
reported from first principles simulations.\cite{Zahid2010}
Metals with a density of states (DOS) comparable to the DOS
of surface Cu atoms (Al and Pd) lower
resistivity, while those which do not (Ta, Ti and Ru) increase resistivity.

Against this backdrop, it is probable that surface scattering is of
particular importance for small diameter Cu NWs and thus we study
unterminated (i.e., in vacuum) and oxidized 1 and 3 nm Cu NWs using
\textit{ab initio} and semi-empirical computational
techniques.
A high degree of anisotropy of Cu NW conductivity with crystal orientation
has previously been reported using tight-binding computational
methods,\cite{Hegde2014} thus we also consider the effects of crystal
orientation.
We calculate transmission spectra and transmission pathways
\cite{Solomon2010} in each case for geometry optimized structures.
We find a strong dependence of transmission on crystal orientation
and termination.
[110] NWs consistently show a larger transmission than [100] and [111] NWs.
Surface oxidation reduces transmission substantially compared to
unterminated NWs.
Additionally we find that transmission even for 1 nm unterminated NWs is
larger at the NW surface than the core due to the existence of surface states.
We provide a simple analysis of transmission in nanoscale Cu
wires, which accounts for the
trends in transmission we obtain.

\section{\label{sec:Method}Method}

\begin{figure}[b]
\includegraphics[scale=1.0]{fig1.pdf}
\caption{Structures of the geometry optimized 1 nm NWs. (a), (b) and (c) show
the unterminated [100], [110] and [111] NWs, (d), (e) and (f) show the
respective O-terminated NWs. Cu is orange and O is red.}
\label{fig:Small-Structures}
\end{figure}

\begin{figure}[h]
\includegraphics[scale=0.95]{fig2.pdf}
\caption{Structures of the geometry optimized O-terminated 3 nm NWs. (a), (b)
and (c) show the [100], [110] and [111] NWs, respectively. Cu is orange and
O is red.}
\label{fig:Large-Structures}
\end{figure}

The NW structures studied in this work are based on the bulk fcc Cu structure,
with [100]-, [110]- and [111]-oriented NWs chosen with approximately 1 and
3 nm diameters.
Due to the small diameter of the NWs studied in this work, atoms at the NW
surface will  have an especially large contribution to the NW properties
e.g., 57\%, 59\% and 49\% of the atoms are at the surface for the [100], [110]
and [111] 1 nm NWs, respectively.
Hence in these nanostructures, electrical resistivity can be expected to
be dominated by surface scattering.
While standard complimentary metal oxide semiconductor (CMOS)
technologies employ Ta based materials as barrier layers
to prevent Cu diffusion, deposited Ta has been shown to cause diffusive
scattering at the surface of thin Cu films.\cite{Chawla2011}
As scaling continues, the relative contribution of surface scattering to
total scattering increases dramatically and along with the barrier
thickness means that Ta-based barrier layers may well become unsuitable
for efficient interconnect design.
To isolate barrier effects we have chosen to restrict this work to
consideration of unterminated  (i.e., in vacuum) and oxygen terminated
(i.e., surface oxidized) NWs.
The relaxed (i.e., zero strain) structures of the NWs studied are shown in Fig.
\ref{fig:Small-Structures} and Fig. \ref{fig:Large-Structures}.

Density functional theory (DFT) as implemented in the OpenMX software package
\cite{OpenMX} is used to study the electronic properties of the 1 nm diameter
Cu NWs.
The PBE\cite{PERDEW96} formulation of the generalized gradient approximation
(GGA) exchange and correlation functional is used in conjunction with
norm-conserving pseudopotentials\cite{MORRISON93} and a strictly localized
pseudo-atomic orbital (PAO) basis,\cite{OZAKI03,OZAKI04} which enables
us to perform the decomposition of the transmission into
localized pathways.
The basis sets used are 6.0H-s4p2d2 and 7.0-s2p2 for Cu and O respectively.
The first part of the basis set notation gives the PAO cutoff radius in Bohr,
while the second part indicates the orbitals used for the valence electrons,
e.g., O 7.0-s2p2 gives a cut-off radius of 7.0 Bohr and 8 basis functions
(2 s functions and 6 p functions).
This Cu basis set agrees reasonably with experiment, giving an optimal fcc
lattice parameter of 3.63 \AA\ and a bulk modulus of 135 GPa compared to
experimental values of 3.615 \AA\ and 137 GPa, respectively.
The supercell approach is used and because the NWs are periodic only along
their axis, a cell size incorporating a minimum of 1 nm of vacuum in the
transverse directions is used such that the interaction between periodic
images is minimized.
The first Brillouin zone is sampled using 11 k-points generated according
to the Monkhorst-Pack method \cite{Monkhorst1976} and
an energy cutoff of 200 Ry is used to generate the grid by which real space quantities are discretized.
The atomic positions in the NWs are relaxed until all forces are
less than 3x10$^{-4}$ Hartree/Bohr; total energy is also minimized with
respect to the lattice cell parameter along the NW axis for each NW
orientation. Optimized lattice parameters along the NW axis are given in
Table \ref{tab:Cell_Parameter}.

The 3 nm O-terminated NWs are also relaxed using the OpenMX
software package using the same parameters.
[100] and [110] NW structures are fully optimized whereas we take a
hollow-core approach (described in the supporting information) for the [111]
NW due to the number of atoms in the unit cell. Due to
its reduced computational demand, Density Functional Tight Binding (DFTB) as implemented by the QuantumWise
software package\cite{QW,Brandbyge2002,Soler2002} is used to calculate the electronic transport properties
of the 3 nm NWs, using a density mesh cutoff of 15 Hartree
and an 11 k-point Monkhorst-Pack grid. DFTB results were
compared to DFT in a carefully chosen set of cases
in order to explicitly assess their validity in NW structures.

The electrical properties of these
NWs are modeled in the context of the Landauer-B\"{u}ttiker formalism, \cite{Landauer1957, Datta1995}
which includes the concepts of wide \emph{reflectionless} contacts and
electrodes.  This formalism relates the electric current through
a NW attached to two electron reservoirs (contacts) with the probability
that an electron can be transmitted via the relation
\begin{eqnarray}
I = \frac{e}{h} \sum_{\sigma} \int T_{\sigma} (E,V)& \nonumber \\
\times \left[ f  \left( E , \mu_R , \right. \right. & \left. \left. T_R \right) -
f \left( E, \mu_L , T_L \right) \right] \, dE \, ,
\end{eqnarray}
where $e$ is the electron charge, $h$ Planck's constant, $T_{\sigma} (E,V)$ is
the transmission coefficient per spin channel $\sigma$ at energy $E$ and applied bias $V$,
$f$ is the Fermi-Dirac distribution, $T_{L}$ ($T_{R}$) and $\mu_L$
($\mu_R$) are the temperature and chemical potential
of the left (right) electrode, and the applied bias is given by

\begin{equation}
V=\frac{\mu_R - \mu_L}{e}.
\end{equation}
In the case of a NW directly attached to
identical electron reservoirs (i.e., same chemical potential and temperature)
we may write the linear response conductance in the zero-temperature limit as

\begin{equation}
G = \frac{I}{V}=\frac{e^2}{h} \sum_{\sigma} T_{\sigma}(E_F, V=0).
\end{equation}

Given that the NW is modeled as a
perfectly periodic structure, all Bloch waves propagate with unit probability. This leads to
the expression for the NW contact resistance

\begin{eqnarray}
G_C^{-1} (E_F) =& \left[ \frac{e^2}{h} \sum_{i} T_i M_i \right]_{T_i = 1; E=E_F}^{-1} \nonumber \\
=& \left[ \frac{e^2}{h} M(E_F) \right]^{-1} \, ,
\end{eqnarray}

where the NW acts as a ballistic waveguides for the total number of modes at the Fermi level
$M(E_F)$, which includes all Bloch waves $\psi_{k \sigma}(E_F)$. This quantity
provides information on the electrical resistivity intrinsic to the
NW's electronic structure. Throughout this work the reported
transmission then corresponds to a sum over the total
number of modes $M(E)$ for each structure as a measure
of their maximum potential conductivity as affected by
their reduced scale and in the absence of
scattering sources such as structural defects,
grain boundaries, and phonons. Even though surface scattering is expected
to be the most important contribution to resistance at these
dimensions at zero temperature, the contribution of electron-phonon scattering
at finite temperatures cannot be neglected.
\citet{Plombon2006} report a decomposition of the resistance
of copper lines with widths ranging from 75 to 500 nm with electron-phonon
scattering estimated to account for 60\% of the resistivity
at 300K. The effects of electron-phonon interactions on
resistivity in sub 5nm copper NWs are currently unknown and have been excluded from this study.

It is worth noting that for
interconnect applications these NWs' function would be
to provide electrical contact between devices (e.g., transistors)  across a short length and with small voltage drops
- ideally zero. Hence the use of the linear response conductance
applies and its validity can be extended to
arbitrarily high temperatures as long as the transmission coefficient remains approximately constant over the energy
range in which the transport takes place.

With the aim of providing some insight into
the influence of the local chemical environment on
electronic transport,
a decomposition of transmission into spatially
resolved pathways is computed according to the formalism
described by \citet{Solomon2010}, as implemented
in the QuantumWise software package, in which the transmission
through a plane perpendicular to the transport direction
that divides the system in two regions $A$ and $B$ is decomposed as

\begin{equation}
T(E) = \sum_{i \in A, j \in B} T_{ij}(E) \\,
\label{eq:pathways}
\end{equation}

where $i$ and $j$ are atoms on each side of said plane.
We note that the use of a
Green's function implementation to the Landauer approach
is required for decomposing the transmission into
local contributions between pairs of atoms and hence this
approach is taken for computing all electronic transport
properties.

\section{\label{sec:Results}Results and Discussion}
\subsection{Nanowire structure}

The optimized cell parameters along the periodic direction of the NWs for
a single repeat unit are given in Table \ref{tab:Cell_Parameter}.
In the case of the unterminated NWs, the optimized cell parameter is very
similar to the calculated bulk cell parameter;
this agreement is reflected in the NW structures wherein
the atoms move only slightly from their bulk positions after geometry
optimization (see Fig. \ref{fig:Small-Structures}).
When oxygen atoms are placed on the NW surface the situation changes
dramatically with significant surface reconstruction seen for both
the 1 nm and 3 nm NWs.
There is a strong tendency for O to pull surface Cu atoms away from the
NW bulk-like core until the bonded Cu and O atoms lie in a single plane.
In bulk Cu(I) and Cu(II) oxide, each Cu bonds to 2 or 4 O atoms for Cu$_2$O
and CuO respectively, conversely each O atom bonds to 4 or 2 Cu atoms for
Cu$_2$O and CuO, respectively.
The surface reconstruction seen in this work emulates the kinds of structural
motifs seen in these oxides.
The ratio of copper to oxygen (Cu:O) at the NW surface is 1.5, 1.7, and 1.9
for the 1 nm oxidized [100], [110], and [111] NWs respectively, i.e., it lies
between bulk CuO and bulk Cu$_2$O.
In all cases, each O atom at the surface bonds to 3 Cu, thus the oxidation is
intermediate to the situation seen for the bulk oxides.
The surface oxide in the NWs consists of a very thin curved layer
which locally is essentially two dimensional.
Thus the NW surfaces are well oxidized as the Cu:O ratio is comparable
to bulk copper oxide.
For the [100] and [110] NWs, each Cu at the surface bonds to 2 oxygen atoms.
Thus while the Cu:O ratio at the surfaces are different, in the case of [100]
and [110] NWs, each O bonds to the same number of Cu atoms and each Cu bonds
to the same number of O atoms.
In spite of the similarity in the surface environment the surface geometries
differ.
For [100] the O-Cu-O motif is linear at Cu, while for [110] most O-Cu-O are
V-shaped, a minority are linear.
The [111] NW surface has 13 Cu atoms bonded each to 2 O atoms and 8 Cu atoms
bonded each to 1 O atom, thus in line with the higher Cu:O ratio, this
surface appears to be less oxidized than the [100] and [110] surfaces.
The Cu atoms at the [111] surface which bond to two O have a mix
of linear and V-shaped O-Cu-O structural arrangements.

\begin{table}[h]
\caption{\label{tab:Cell_Parameter}Optimized cell parameter in \AA\ along the
NW periodic direction. Unterminated NWs have cell parameter comparable to the
calculated bulk value, while terminated NWs have a longer cell parameter.}
\begin{ruledtabular}
\begin{tabular}{l *{5}{c}}
& & \multicolumn{2}{c}{Unterminated} & \multicolumn{2}{c}{O-terminated} \\
& Bulk & 1 nm & 3 nm & 1nm & 3nm \\
\hline
{[}100{]} & 3.63 & 3.60 & 3.63 & 3.75 & 3.64 \\
{[}110{]} & 2.57 & 2.56 & 2.59 & 2.86 & 2.73 \\
{[}111{]} & 6.29 & 6.26 & - & 6.46 & -\\
\end{tabular}
\end{ruledtabular}
\end{table}

The surface reconstruction does not strongly affect the positions of Cu atoms
below the surface layers, this is clearly evident in the 3 nm NW structures
shown in Fig. \ref{fig:Large-Structures}, beyond the first two Cu surface
layers the Cu atoms occupy approximately equivalent configurations with
respect to their bulk positions.
The reconstruction at the surface is associated with a lengthening of the
optimized cell parameter relative to the bulk and unterminated NW, which
is more severe for the 1 nm NWs than 3 nm NWs.
This suggests that there is competition between the surface of the NW and
core over the relaxed cell parameter along the axis.
The oxidized surface favors an increase in length along this axis,
presumably to better incorporate the surface O atoms in a layer.
Conversely the core of the NW consists only of Cu atoms with their
geometry similar to bulk fcc Cu and therefore favors a bulk-like cell
parameter.
Thus while unterminated NW cell lengths are similar for 1 and 3 nm NWs, the
oxidized 3 nm NWs have a smaller (i.e., closer to the bulk value) cell
parameter than the oxidized 1 nm NWs.
A concomitant increase in NW diameter is not observed, therefore this change
in cell parameter occurs exclusively along the NW axis.
The surface structural rearrangement seen here for the O-terminated [100] NW,
shown in Fig. \ref{fig:Small-Structures}(d) and Fig.
\ref{fig:Large-Structures}(b), is very similar to that seen in experiment
for surface oxidized Cu(100) slabs\cite{Baykara2013}
suggesting the structural rearrangement we see for the NWs in our simulations
is representative of experimental structures with highly prepared surface
treatments.

\subsection{Electron transmission}
\begin{figure}
\includegraphics[scale=0.95]{fig3.pdf}
\caption{Transmission for (a) 1 nm and (b) 3 nm Cu NWs. Unterminated NWs
(dashed lines) have a larger transmission than oxidized NWs (full lines)
irrespective of diameter or crystal orientation. Transmission is strongly
influenced by crystal orientation, with [110] NWs having larger transmission
than [100] and [111] NWs. The zero of energy is taken to be
at the Fermi level.}
\label{fig:Transmission}
\end{figure}

\begin{table}[b]
\caption{\label{tab:Transmission_Area}Calculated transmission per unit area
for unterminated and oxidized 1 nm and 3 nm NWs. The area of each NW is
the area of a circle with diameter the sum of the NW width and twice the Cu atomic
radius.}
\begin{ruledtabular}
\begin{tabular}{l *{5}{r}}
& & \multicolumn{2}{c}{Unterminated} & \multicolumn{2}{c}{O-terminated} \\
& Bulk & 1 nm & 3 nm & 1nm & 3nm \\
\hline
{[}100{]} & 28.0 & 22.8 & 19.4 & 7.3 & 8.8 \\
{[}110{]} & 29.7 & 26.7 & 24.3 & 15.3 & 15.1 \\
{[}111{]} & 27.9 & 15.3 & 11.8 & 3.7 & 4.0 \\
\end{tabular}
\end{ruledtabular}
\end{table}

The transmission spectra calculated for the terminated and oxidized 1 nm and
3 nm Cu NWs are shown in Fig. \ref{fig:Transmission} for a narrow energy range
of $\pm$50 meV centered about the Fermi energy.
In each case, we find that the oxidized NW has a substantially lower electron
transmission than the corresponding unterminated NW.
This result is consistent with the increase in resistance after chemical
oxidation previously been reported by \citet{Chawla2010}
for Cu thin films and arises from  the reduction of the DOS at
the surface upon oxidation.
Additionally, we find a strong dependence of transmission on NW orientation.
In all cases we find that the [110] NW has a larger transmission than [100],
which in turn has a larger transmission than [111], irrespective of
termination.
As expected the transmission of the NWs increases going from 1 nm to 3 nm
diameter due to the increasing cross-sectional area.
The cross-sectional areas of the NWs are not identical as diameters
deviate from exactly 1 nm and 3 nm due to the different atomic arrangements of
the crystal orientations.
Thus, we also calculate the transmission per unit area $t$, presented in
Table \ref{tab:Transmission_Area}, to ensure that this variation in
transmission with orientation is not due to deviation in cross sectional
area.
There is ambiguity in how to define the cross sectional
area of the NWs due to atomic structure.
The atoms in the NW have volume which extends beyond the nuclear positions
and the smaller the NW the greater this contribution will be to the NW
cross section.
For simplicity we have taken the cross-section to be circular,  elliptical, or octagonal
as appropriate, with dimensions equal to the maximum inter-nuclear width of the
NW plus twice the Cu atomic radius (1.28 \AA).
We find that the transmission per area $t$ follows the same trend as the
total transmission plotted in Fig. \ref{fig:Transmission}; [110] has
the largest $t$ and [111] the smallest, regardless of diameter
or termination.
This result is consistent with the anisotropy
in Cu conductivity with crystal orientation reported recently by \citet{Hegde2014}.
In fact, this orientation dependence is of such significance that for the
3 nm NWs the \textit{oxidized} [110] NW has a transmission comparable to
the \textit{unterminated} [111] NW at the Fermi energy;
a remarkable result consistent with the shape of the
Fermi surface of bulk fcc copper, in
which the Fermi surface exhibits a vanishing DOS along the  $\left\langle 111 \right\rangle$ directions.
The extent of the orientation dependence on transmission is also clearly
evident in Table \ref{tab:Transmission_Area}.
In the case of unterminated NWs, the transmission for a given cross sectional
area for [110] is approximately twice that of [111] NWs, after oxidation this
margin further increases with the [110] transmission per unit area
approximately 3.5 times larger than for the [111] NW.
It may be anticipated that a more oxidized NW would show greater suppression
in transmission, however the 1 nm [111] NW is in fact less oxidized than the
[110] NW; each surface Cu in the [110] NW bonds to 2 oxygen atoms while
surface [111] atoms bond to either 1 or 2 oxygen atoms.
Meanwhile, unterminated [100] and [110] NWs show similar transmission
per unit area; [100] is about
4 units smaller than [110] for both 1 nm and 3 nm NWs.
After oxidation, the transmission per unit area for [100] NWs is
approximately 60\% of [110] NWs, i.e., transmission suppression on
oxidation is relatively larger for [100] than [110].
Thus both the surface chemical environment and the NW orientation play
a critical role in determining the overall transmission of the copper
NW.

\subsection{Local transmission paths}
\begin{figure}
\includegraphics[scale=1.0]{fig4.pdf}
\caption{Transmission pathways at the Fermi energy for
unterminated 1 nm [111] Cu NW.
The arrows show the direction of transmission paths.
The arrow thickness represents the magnitude of the transmission
while the color represents the orientation of the path
with respect to the NW axis. Forward transmission is shown in
blue, radial transmission in green, and backscattering in
red. Pathways with transmission below 10\% of the maximum value
are omitted for clarity. The dashed
black lines mark the positions of the planes shown Fig. \ref{fig:1nm-Cross-Section}(e).}
\label{fig:1nm-Pathways}
\end{figure}

\begin{figure}
\includegraphics[scale=1.0]{fig5.pdf}
\caption{Cross-section view of the transmission pathways at the
Fermi energy. (a) Unterminated [100],
(b) O-terminated [100], (c) Unterminated [110], (d) O-terminated [110],
(e) Unterminated [111] and (f) O-terminated [111]. Atomic
positions are shown as "+" (Cu) or "x" (O). The 'dot' size
represents the absolute size of the transmission pathway crossing the plane,
while the 'dot' color indicates the size and direction of the
transmission pathway.
Blue 'dots' correspond to forward transmission and red 'dots' to
backscattering. Note the difference in the color scales ranges.}
\label{fig:1nm-Cross-Section}
\end{figure}

The transmission results show that orientation and surface environment
drastically impact on Cu NW electron transport.
These effects are not easy to decouple, however, a greater
understanding of the relationship between them can be established
by examining transmission through the NW at an atomic scale.
We have calculated transmission pathways in the NWs\cite{Solomon2010} at the Fermi level, which
are shown in
Fig. \ref{fig:1nm-Pathways} for the unterminated [111] NW, to particularly elucidate the effects of NW
crystal orientation and surface oxidation on transmission.
Transmission pathways provide a visual representation of transmission
through the NW with the arrow width representing the size
of the transmission between an atom pair.
As described in the caption of Fig.
\ref{fig:1nm-Pathways}, the arrows are colored according to
their angle with respect to the NW axis; blue arrows
correspond to forward transmission, green arrows to radial
transmission (i.e., atoms within the same transverse plane),
and red arrows backscattering or reflection. As expressed in
Eq. (\ref{eq:pathways}), the transmission pathways crossing a
given plane perpendicular
to the transport direction always sum to give the total
transmission coefficient.

A more convenient visual representation is portrayed
in Fig. \ref{fig:1nm-Cross-Section} in which
the intersections of transmission pathways
with planes located halfway between non-equivalent atomic planes
give a clear image of the decomposition of the total transmission
into pathways per cross-sectional area per NW.
Such planes are indicated by
dashed black lines in Fig. \ref{fig:1nm-Pathways} for
the case of the unterminated [111] NW.
These projections provide
a heuristic representation of localized transmission
and allow quick
identification of where the most important contributions
lie within the NW cross-section.

Fig. \ref{fig:1nm-Cross-Section}(a) shows transmission pathways for the
unterminated [100] NW.
There are
transmission pathways both parallel ('dots'
centered at atomic positions) and angled to the NW axis (centered
between atomic positions). Angled pathways are larger
in magnitude than parallel pathways as represented by their larger
'dot' diameter and their color.
This difference in magnitude can be
attributed to the distance between the Cu atoms being larger if a direct route
parallel to the axis is taken (3.60 \AA\ versus 2.53 \AA).
It is is readily seen that pathways along the surface
dominate electron transmission for this NW as the 'dots' in the
surface are larger than below the surface, where the parallel
pathways are smaller and
obscured by the symbols indicating the atomic positions.

The unterminated [110] NW transmission pathways are shown in Fig.
\ref{fig:1nm-Cross-Section}(c).
Transmission involving only surface atoms occurs along the NW axis and is
large (indicated by the darker blue 'dots' centered about atomic
positions) while pathways at an angle to the axis exhibit much lower transmission.
Below the surface the situation is similar, transmission along the axis is larger than off-axis.
In this orientation the Cu atom separation is similar for both parallel and
off axis transmission and thus the more direct parallel route is favored.
As for the unterminated [100] NW, transmission is larger at the NW surface
than below the surface with the largest 'dots' corresponding to
pathways located at the surface and parallel to the NW axis.
The transmission pathways for the unterminated [111] NW, shown in Fig.
\ref{fig:1nm-Cross-Section}(e).
In this case, there is no significant transmission directly
parallel to the NW axis, this is presumably
because the Cu interatomic distance along the NW axis is simply too large
compared to the off axis distances (6.26 \AA\ versus $\sim$2.5 \AA\ reflecting
that no nearest neighbors align along the NW axis).
As previously mentioned, this result is consistent with the
vanishing density of states found along the $\left\langle 111 \right\rangle$ directions in the Fermi surface of fcc Cu; there are no transmission paths parallel to
the [111] direction as shown by the absence of arrows parallel to the
NW axis in Fig. \ref{fig:1nm-Pathways} and of
'dots' centered about atomic positions in Fig. \ref{fig:1nm-Cross-Section}(e).
As shown in Fig. \ref{fig:1nm-Pathways} transmission pathways tend to flow along the NW surface until they reach
a Cu atom with a low coordination number (such as the one at the
top center of the figure), at which point the electrons
are scattered into the NW core where they continue to propagate
along angled paths until they reach another
surface where this process repeats. The lack of transmission
pathways parallel to the [111] NW axis makes the surface critical
as all paths inevitably lead to the surface.
While there are some transmission pathways inside the core of the
NW, transmission
\textit{through} the NW occurs primarily at the NW surface; and much like the
unterminated [100] and [110] NWs, transmission is larger at the surface.
However, in this case as well as 'dots' representing forward transmission,
the 'dots' representing negative values (i.e., electron
backscattering or reflection paths) are much larger than for the
unterminated [100] and [110] NWs.

\begin{figure}
\includegraphics[scale=1.0]{fig6.pdf}
\caption{Average local density of states for an atom at the surface
(dashed) and at the center (solid) of unterminated 1nm NWs. The
zero of energy is taken to be at the Fermi level.}
\label{fig:1nm-LDOS}
\end{figure}

The transmission pathways of the unterminated NWs consistently show
that transmission is larger at the NW surface than in the core and also
that backscattering for these NWs is relatively small, particularly
for the [100] and [110] NWs in which the total magnitude of
all reflecting paths is 14\% and 13\% of that of forward paths,
whereas for [111] NWs this value increases to
25\%. This surface-dominated
transmission can be explained in terms of the increased local
density of states (LDOS)
of surface atoms at the Fermi level as a result of their low
coordination. This allows electrons otherwise localized
at bonds to become available
for transmission at the surface atoms.
Fig. \ref{fig:1nm-LDOS} shows the average local density of
states (LDOS) of an atom situated at the surface and of an
atom close to the center
of the NWs' cross section; the atoms at the surface show
a larger density of states in the range around the Fermi level
studied in this work. Unterminated [111]
NWs exhibit the
largest boost with the average LDOS value of a surface atom being
2.55 times that of an atom near the center of the NW
at the Fermi level;
similarly, atoms at the surface of [100] NWs have an average
surface-to-center LDOS ratio of 2.41 and a considerably
lower ratio of 1.39 is found for [110] NWs.

As might be expected from the transmission spectra shown in
Fig. \ref{fig:Transmission} and the previous analysis, oxidation
of the NWs changes the behavior at the
NW surfaces considerably.
In the [100] NW, transmission at and just below the NW surface is
reduced upon oxidation, in fact Fig. \ref{fig:1nm-Cross-Section}(b)
shows that near the surface forward transmission
is largely
suppressed and backscattering pathways are enhanced.
In the core of the NW the transmission is similar to the
unterminated NW as shown by similarly arranged,
sized and colored 'dots'.
Thus in the case of the [100] NW, oxidation appears to affect the surface
and immediate subsurface almost exclusively.
In the case of the [110] NW, more significant back scattering is seen upon
surface oxidation with the appearance of the large red 'dots' indicating
a relatively large magnitude in Fig. \ref{fig:1nm-Cross-Section}(d).
Unlike the [100] NW, transmission is also reduced in the core of
the [110] NW upon surface oxidation.
A suppression of the pathways parallel to the NW axis can be
clearly seen all the way to the center when comparing to the
unterminated NW (\ref{fig:1nm-Cross-Section})(c).
Thus it appears that the effect of surface oxidation is felt deeper in the NW
for the [110] orientation compared to [100].
However, transmission per unit area for the oxidized [100] NW actually drops
more relative to the unterminated NW compared to the [110] orientation, as
reported in Table \ref{tab:Transmission_Area}.
This is likely caused by a reduction of transmission at the
surface and immediate subsurface in the [100] oxidized NW,
in which the surface has a larger
contribution relative to the core in the
unterminated case as shown in Fig. \ref{fig:1nm-LDOS} and
discussed above.
The surface of the oxidized [111] NW is more disordered than the oxidized
[100] and [110] NWs studied in this work.
This disorder along with the indirect transmission associated with transport
along this crystal orientation leads to a complicated, disordered
transmission pathways (Fig. \ref{fig:1nm-Pathways}(f)) consistent with the low
transmission calculated for this structure.
In contrast to the [100] and [110] oxidized NWs, there is large forward
transmission at the surface for the oxidized [111] NW, which can be seen
clearly in the mapping of the transmission pathways onto a cross sectional
area of the [111] NW shown in Fig. \ref{fig:1nm-Cross-Section}(f). However, the large backscattering paths
in the core of the NW result in a lower overall transmission;
all paths in the core lead either to the surface (where
oxidation has largely suppressed forward transmission) or are backscattered.

\subsection{Transmission model}

To understand the behavior of the total transmission per NW
given in the previous sections, we provide an analysis for a simple
model describing the electron transmission behavior of round NWs
which partitions the NWs into regions of similar behavior
based on the magnitudes of the transmission pathways within the
them.
The generalization of the model to other geometries is straightforward.
The model provides insight into the observation that transmission per
unit area decreases as area increases for the unterminated NWs and that the
transmission per unit area is relatively constant for oxidized NWs for a
given orientation.

\begin{figure}
\includegraphics[scale=0.7]{fig7.pdf}
\caption{Schematic representing the copper NW model, with surface,
sub surface and bulk regions indicated.
$R$ is the radius of the NW, $r$ is the radius of the bulk region,
$d$ is the width of the subsurface region, i.e., the depth to which $t$ is
affected by the surface, and $\delta$ is the width of the surface.}
\label{fig:Model}
\end{figure}

The total transmission $T$ of a round NW of radius $R$ is divided into
contributions from three distinct regions of the NW; the surface, the
subsurface and the bulk regions; as shown in Fig. \ref{fig:Model} for a
cross section of the NW.
The surface region is described by a thickness $\delta$, the subsurface
region by a thickness $d$ and the bulk-like core is described by a
radius $r$; therefore

\begin{equation}
\label{eq:radius}
R = r + d + \delta.
\end{equation}

To each region is assigned a transmission per unit area $t$.
The surface transmission per unit area $t_{surf}$ is assumed constant,
whereas the subsurface transmission per unit area $t_{sub}$ can vary
with depth into the NW as signified by the grading in Fig. \ref{fig:Model}.
However, it is assumed that an effective transmission per unit area
can be assigned to the subsurface region.
The bulk region is defined as the core atoms for which the transmission
per unit area approaches the bulk behavior $t_{bulk}$.

The area of the surface region can be expressed as

\begin{equation}
\label{eq:surface}
A_{surf} = \pi [R^2 - (R-\delta)^2] = (2 \pi R) \delta - \pi \delta ^2,
\end{equation}

which for $R \gg \delta$ can be approximated as

\begin{equation}
\label{eq:surface-2}
A_{surf} \approx (2 \pi R)\delta.
\end{equation}

Similarly the area for the subsurface region can be expressed as

\begin{equation}
\label{eq:sub}
A_{sub} = \pi [(R-\delta)^2 -r^2] = 2\pi (R-\delta)d - \pi d^2,
\end{equation}

which for $R \gg d + \delta$ is given as

\begin{equation}
\label{eq:sub-2}
A_{sub} \approx (2 \pi R)d.
\end{equation}

The core region displaying bulk-like behavior has an area given by

\begin{equation}
\label{eq:bulk}
A_{bulk} = \pi r^2 = \pi (R - d - \delta)^2
\end{equation}

which for $R \gg d + \delta$ becomes

\begin{equation}
\label{eq:surface}
A_{bulk} \approx  \pi R^2.
\end{equation}

The fact that $A_{surf}$ and $A_{sub}$ scale linearly with $R$ whereas
$A_{bulk}$ scales as $R^2$ for large values of $R$ simply describes
the fact that the surface and subsurface play decreasing roles as
the NW's radius is increased.
An effective transmission per unit area $t$ is then defined for each
region and the total transmission is expressed as

\begin{equation}
\label{eq:surface}
T = t_{surf}A_{surf} + t_{sub}A_{sub} + t_{bulk}A_{bulk}.
\end{equation}

To explore the role of the surface and subsurface transmission per
unit area in small cross section NWs we consider four cases.

\textit{Case I: $R \approx \delta$}.
In this limit, the surface dominates and transport is given purely
by the surface and represents, for example, the case of an atomic chain.

\textit{Case II: $R \approx d + \delta$}.
This condition describes when the cross sectional area of the NW is
of a scale that a subsurface region is present but the NW diameter
is not large enough for the core of the NW to display bulk behavior
for transmission (it should be noted that the subsurface region is not
sharply defined as represented by the grading of the gray region used
to define it in Fig. \ref{fig:Model}).
In the transmission plots of Fig. \ref{fig:1nm-Cross-Section} for the
unterminated Cu NWs, it can be seen that the subsurface region has a
lower transmission per unit area compared to the NW surface regions.
Hence by decreasing the NW diameter from 3 nm to 1 nm, a larger
transmission per unit area is obtained consistent with the results listed
in Table \ref{tab:Transmission_Area}.

\textit{Case III: $r \approx d + \delta $}.
As the NW radius increases, eventually a core region is formed
whereby local transmission pathways approach the values obtained in
bulk copper.
When this core region is of a comparable dimension to the surface and
subsurface layer, the transmission per unit area will reflect
the contributions from the different regions.
As the subsurface region in unterminated Cu NWs has a lower
transmission per unit area than the bulk, the overall transmission per
unit area will increase relative to Case II as the region forms.

\textit{Case IV: $ R \approx r$}.
As the NW's radius is further increased, the core region's contribution
will quickly dominate due to the area increasing as $R^2$ as opposed to the
linear dependence on NW radius for the surface and subsurface regions.
Hence the transmission per unit area for the NW will increase with
increasing $R$ until asymptotically approaching the bulk value.

The following picture emerges in the case of unterminated NWs.
For extremely small diameter NWs with diameters of approximately 1 nm,
surface and subsurface transmissions combine to provide a transmission per
unit area that is comparable to bulk copper for [100] and [110]
and less than bulk copper for [111].
As the NW diameter increased, for example up to 3 nm, the lower
subsurface transmission with respect to surface transmission results in a
net lowering of overall transmission per unit area compared to smaller
diameter NWs. As the NW diameter is increased further, the
core region begins to behave like a bulk conductor and the transmission
rises and asymptotically approaches the bulk transmission per
unit area.

The picture needs to be slightly modified for the case of NWs with
surface oxidation.
As seen in Fig. \ref{fig:1nm-Cross-Section}, the surface transmission is
reduced significantly due to surface oxidation.
From Table \ref{tab:Transmission_Area}, it is seen that the transmission per
unit area for the 1 nm and 3 nm diameter NWs are comparable.
Once oxidized, the transmission at the surface is suppressed and the
transmission of the subsurface region dominates.
We anticipate that the transmission per unit area of the subsurface region
for a given orientation is similar for 1 nm and 3 nm NWs and this combined with
the low surface transmission (see Fig. \ref{fig:1nm-Cross-Section}) leads
to the transmission per unit area for each orientation being approximately
constant going from 1 nm to 3 nm diameter,
as reported in Table \ref{tab:Transmission_Area}.
However, the transmissions of both  1 nm and 3 nm oxidized NWs
are much lower than
found for the bulk, and hence larger cross section NWs are required
before significant bulk-like behavior from the core contributes to the
net transmission per unit area.

\section{\label{Conclusion}Conclusion}
The electron transport properties of 1 nm and 3 nm diameter
copper NWs have been calculated in each case for unterminated and
surface oxidized NWs of [100], [110] and [111] crystal orientations.
We find even 1 nm diameter copper NWs to be metallic, however electron
transmission is strongly dependent on both surface termination and crystal
orientation.
Surface oxidation suppresses electron transmission compared to unterminated
copper NWs,
consistent with previous reports for copper thin films.
The [110] oriented NWs consistently show a higher electron transmission
than [100] oriented NWs which in turn have a higher electron
transmission than [111] NWs.
Transmission in unterminated copper NWs is larger at the NW
surface than below the surface, irrespective of crystal orientation.
A different picture emerges for surface oxidized NWs wherein
transmission is lower at the NW surface than in the subsurface for
[100] and [110] oriented NWs. However while the oxidized [111] NW
surface transmission is reduced compared to the unterminated NW,
it nonetheless continues to show larger surface transmission
than subsurface transmission.
Transmission per unit area decreases with increasing diameter for
unterminated NWs but remains approximately constant for the surface
oxidized NWs studied.
A simple model of transmission in round NWs which divides the NW
into regions based on local transmission pathways explains the differing
behaviors of unterminated and oxidized NWs.
Briefly, transmission per unit area is lower in the subsurface region than
at the surface for the unterminated NWs studied, thus when the diameter
is increased from 1 nm to 3 nm the transmission per unit area of the NW
decreases as the subsurface region becomes relatively more important.
In oxidized NWs, the overall transmission per unit area is comparable
for 1 nm and 3 nm NWs.
The suppression of the surface transmission in this case increases the
contribution of the subsurface to overall transmission and a similar
subsurface transmission per unit area may be expected for 1 nm and 3 nm
oxidized NWs for the same crystal orientation resulting in similar
overall transmission per unit area.
Overall, our results suggest that conductivity in sub 3 nm copper NWs
is highly sensitive to crystal orientation and
surface termination, and that careful material preparation and processing will be
essential in order to maximize conductivity.

\begin{acknowledgments}
This work was performed as part of the Intel-Tyndall research
collaboration sponsored by Intel Components Research.
ASS was funded under an Irish Research Council postgraduate scholarship.
We are grateful to QuantumWise A/S for providing access to the QuantumWise
simulation software.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


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I am not happy buying anything direct from NVidia as I don't think the support is anywhere near as good as OcUK.
Not really the jumps in performance vs price increase will really bring high end gaming PC's to an end and when sales drop so will developer support. Any honest person will admit that generational upgrades are getting more and more an expensive extravagance than a necessity or even just a justified performance boost based on cost.
The truth is people who grow up playing console generally stay on that platform in adult life, most of us on this forum grew up in a time when PC gaming was vastly superior to consoles and the price difference much closer, when we have consoles which can produce the same level of gaming experience with PC basically providing higher frame rates how many people are going to game on PC when a mid tier PC would cost you over triple the price of the console and high end could easily be 8- 10 times the price, the question we should be asking is how can a console manufacturer put mid-high end hardware into £500-700 console but PC users are priced double that just for a stand alone GPU card.
Yup +1 I always get my gear from ocuk only time I don't is when there's no stock or they just don't sell something I'm after.
I grew up in a time when PCs were more than 20x the price of consoles and the former are still going strong.
Now I think about it my first gaming machine was a console that played Space Invaders, it's strange how things have come full circle with ultra high end PCs also running the game.
Only question is , FTW3 or Lightning Z ???
Rightly or wrongly I'm seeing the Lightning Z as a real OC enthusiasts card that can get hot and noisy and should probably be under water with a warranty service I know northing about and the FTW3 as clocked slightly lower out of the box but with the same OC potential and has the best warranty in the business? Fair?
I'm happy with my purchase if my 2080ti I no ppl don't like them .but to me I'm happy with my card and can't say enough about OCuk they have been really exellent with all my rma s with all my kit and I'll be gettin all my kit of them in future best support ever!.
Obviously can't disagree with the gist here, and I do agree with you that high end gaming PCs aren't going away any time soon but I personally see (at least) two big things that threaten it in the relatively near future.
Firstly, you are completely correct that the latency can only be improved by so much, but do bear in mind that there may be other solutions to this both in the near future and others further away that haven't been thought of yet. Microsoft has been making noises about their upcoming gaming cloud infrastructure, and I believe I remember reading that they have been putting a lot of work into splitting the games into latency sensitive and non sensitive tasks, the former runs locally and the latter can be offloaded to the cloud. In theory at least it allows much lower end hardware at the user's end with a lot of the heavy lifting done elsewhere while still maintaining a local-esque latency feel.
Secondly, what will happen to the high end if the mid range money factory does indeed lose out to the cloud... will the money be there to fund all the R&D required for these high end cards? Obviously someone has to provide the processing clout needed for the cloud servers, but what do the margins look like compared to selling all the individual people their own cards?
Integrated graphics will cover the low end, Cloud gaming hasn't found its place yet because imho it cannot answer enough of the use cases.
I think what we'll see is a reluctance from developers to push the graphical demands because the buy-in too high end; PC gaming has never been more niche. So you'll just see these gimmicks and half hearted efforts for the next few years. It is what it is the market has basically stifled its of progression so here we will stay for a good year or two.
The AMD integrated graphics are now so good its really removed the need for stuff like RX 550's and 1030's which are not far off £100 anyway, so discreet for gaming is now really 1050 and RX 560 upwards. Plus discreet manufacturers prefer making high-end cards, better for both revenues and profits.


A huge part of my job involves reading actuarial and insurance-industry-related articles. Mic drop: If that sentence doesn't hook 999 out of 1000 readers, I don't know what will.
These three traits lead to a number of structural problems in most articles that I don't want to nitpick now, but one of the most common (and easiest to fix) is the introduction problem.
The typical conclusion section of an unedited article is something the author wrote very last, meaning the author wrote it at the point when he or she had finally figured out what they wanted to say by writing the preceding words of the body.
In almost every case, a "conclusion" paragraph can be cut and pasted to the beginning of the article—completely overriding the original introduction—with almost no additional editing at all.
People don't have a lot of time these days, and editing resources are increasingly scarce. If you're asked to write something for a newsletter or industry publication (in any field), try moving your conclusion to the introduction after you write your thing. It will make your article significantly more accessible and relevant from the moment time-pressed readers lay eyes on it.
See what I mean? If I had just put that paragraph first, wouldn't this have been a better and shorter blog post?


The dream of boating, fishing and camping your way around Australia sounds amazing right? But the decision to take a boat or not, is a hard packing question. We explore what's involved in making the right decision for you, and tell you what we did?
Our good friends at On the Roam Again – Trip Straya, are the mad keen fisher type. Check out their set up!
If you are a mad keen fisher person, than this question would have already been answered for you! But for those who just enjoy boating and fishing as a hobby, you really need a lot of forethought and planning. Space in your camping set up is already prime real estate, so you really can't afford to take something that just isn't going to be used sufficiently.
Here are your points to consider when making your decision to take a boat or not?
1. How often are you getting out now in a boat?
2. Where do you plan to fish? Be sure to consider the time you will be in the Top End with crocs!
3. Where will a boat be stored in your camp set up?
5. How much extra fuel will it cost to take your boat with you?
6. How much enjoyment does it bring to you?
7. What type, size and capacity does the boat need to be?
8. Do you already have a boat, or is this an additional purchase?
10. Will hiring boats or charters in amazing locations work out cheaper, easier and be sufficient?
11. What will you sacrifice to fit the boat?
We considered all these questions and decided …. to compromise!
We decided that a marine quality 5 person INFLATABLE tender boat, with capacities to take a boat motor down the track if needed, suited our family's needs the best while travelling Australia.
Being inflatable and already having a pump on board for other uses, has meant the boat doesn't take up too much of our incredibly valuable space in our Goldstream pop top camper set up.
The main purpose of a boat for us was to have fun with our two young kids in the shallow water and for being able to explore more of the fresh water rivers and gorges we visit. For the times we wanted to go deep sea fishing, we decided hiring a charter with the knowledge and equipment, would be our better and ultimately cheaper option for us.
Almost 8 months on the road and we are still happy with our decision to take a boat, but choose a compact inflatable instead. To be honest we have only used our boat averaging once a month, but each one of those times has been incredibly worth it and we wouldn't consider getting rid of it!
To take a boat or not is such a personal choice. What is suitable for one, won't be suitable for all.
SO WHAT WOULD YOU DECIDE???
Tagged Travelling with Kids, Tips and Tricks, Plan your Trip, Get the right Gear, Lap of Australia, Travel Set Up.


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Atmospheric & Space Scientists
Also called: Forecaster, General Forecaster, Meteorologist, Warning Coordination Meteorologist
In the military: see titles from the Air Force, Army, Marine Corps, or Navy.
In the Air Force: Command and Control Battle Management Operations; Command and Control Battle Management Operations Apprentice, Weapons Director; Command and Control Battle Management Operations Helper; Command and Control Battle Management Operations Superintendent; Space Systems Operations Craftsman; Space Systems Operations Superintendent; Special Operations Weather Apprentice; Special Operations Weather Journeyman; Weather Apprentice; Weather Journeyman
In the Army: Space Operations
In the Marine Corps: Basic Meteorology and Oceanography (METOC) Marine; Basic Meteorology and Oceanography (METOC) Officer; Field Artillery Operations Man; Field Artillery Sensor Support Man; METOC Senior Forecaster; Meteorology and Oceanography (METOC) Analyst Forecaster; Meteorology and Oceanography (METOC) Officer; Space Operations Officer; Weapons and Tactics Instructor (WTI) METOC
In the Navy: Aerographer's Mate; CWO - Oceanography Warrant Officer; LDO - Meteorology/Oceanography; Master Meteorological And Oceanographic (Metoc) Forecaster; Meteorological And Oceanographic (Metoc) Analyst; Meteorological And Oceanographic (Metoc) Forecaster; Meteorology and Oceanography (METOC) Services Officer; Meteorology and Oceanography Watch Officer; RL - Special Duty Officer (Oceanography); Staff Meteorology and Oceanography (METOC) Officer
Even before breakfast, and certainly before leaving the house, most people consult the weather forecast. That essential item of news is provided by atmospheric and space scientists, who study the weather and climate, and examine how those conditions affect human activity and the earth. Atmospheric scientists collect data from the field using instruments such as weather balloons, radar systems, and satellite imagery. Many write their own computer programs to model or predict weather developments, and advise the public or their clients on risks caused by weather events and climate change. There are many types of atmospheric scientists… For example, weather forecasters use computer models to forecast short- and long-term conditions for airports, farmers, utility companies, and others. Climate scientists model climate change to help plan building design and adapt agricultural production to changing conditions. Atmospheric scientists generally work full time and may be called upon to work at odd hours, or overtime—keeping the public informed during severe weather or monitoring conditions around the clock at a field station. They may work in government weather stations, laboratories and offices, or television and radio stations. Atmospheric scientists need a bachelor's degree in meteorology or a related earth science field for most positions. To lead research or teach at the college level usually requires a Ph.D. or master's degree in the field.
Investigate atmospheric phenomena and interpret meteorological data, gathered by surface and air stations, satellites, and radar to prepare reports and forecasts for public and other uses. Includes weather analysts and forecasters whose functions require the detailed knowledge of meteorology.
Broadcast weather conditions, forecasts, or severe weather warnings to the public via television, radio, or the Internet or provide this information to the news media.
Gather data from sources such as surface or upper air stations, satellites, weather bureaus, or radar for use in meteorological reports or forecasts.
Develop or use mathematical or computer models for weather forecasting.
figuring out how a system should work and how changes in the future will affect it
make general rules or come up with answers from lots of detailed information
choose the right type of math to solve a problem
add, subtract, multiply, or divide
Visual Understanding
see hidden patterns
People interested in this work like activities that include ideas, thinking, and figuring things out.
Analytical Thinking
Achievement/Effort
Analytical or scientific software
The MathWorks MATLAB
Graphics or photo imaging software
AccuWeather Galileo
Adobe Systems Adobe Photoshop
Cartographers & Photogrammetrists
City & Regional Planning Aides
Geographic Information Systems Technicians
Geoscientists
Geospatial Information Scientists & Technologists
Professional, Science, & Technical
See more details at O*NET OnLine about atmospheric and space scientists.
Atmospheric & Space Scientists by U.S. Department of Labor, Employment and Training Administration is licensed under a Creative Commons Attribution 4.0 International License.

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AUSTIN, TX - May 5, 2014 —The National Alliance for Insurance Education & Research, in collaboration with the Council for Insuring Private Clients (CIPC), announces the development of the Certified Personal Risk Manager (CPRM) Program. CPRM is the newest designation program of The National Alliance with a purpose of training the insurance and risk management communities to better serve the high net worth and affluent client base. The program will contain a unique combination of risk management, technical information, and account development.
The National Alliance, based in Austin, TX, with its 45 year history of experience and leadership in insurance and risk management education and designation programs, is most qualified to provide comprehensive, relevant and practical training. The development and support of the program includes leading carriers such as AIG, Fireman's Fund, Ironshore, Lexington, and Lloyds Underwriters – Hiscox, Britt, and Amtrust, along with top agencies and brokers writing high net worth and affluent clients.
The five major areas of emphasis will include personal risk management, insurance coverage differences, evaluation and protection of the lifestyle, the practical application, and management of the business of high net worth and affluent clients. The initial CPRM courses will be presented in early October 2014 and will provide two distinct benefits to the participants. First, an exceptional opportunity to exchange ideas and practices specific to this client community; secondly, the formalized presentation of practical and relevant educational materials in conjunction with earning the CPRM designation.
The National Alliance for Insurance Education & Research is known for insurance and risk management education and designation programs such as Certified Insurance Counselor (CIC), Certified Risk Manager (CRM), Certified Insurance Service Representative (CISR), and Certified School Risk Manager (CSRM). The company advances the industry quality by providing insurance and risk management professionals of every experience level with integrated, practical continuing education, timely research and designation opportunities. For additional information, visit The National Alliance website: www.TheNationalAlliance.com, or call 800-633-2165.
The Council for Insuring Private Clients and High Net Worth Individuals (CIPC) was founded by MarketScout to provide a venue where agents and insurers may come together on how to better serve their private clients.


text:
Home > List of people > Vincent > Records confirmed by Vincent
Records confirmed by Vincent
Bingham, M.G., Willemen, A., Wursten, B.T., Ballings, P. and Hyde, M.A. (2023). Flora of Zambia: Records confirmed by Vincent.
https://www.zambiaflora.com/speciesdata/utilities/utility-display-confirmations-by-person.php?person_id=998, retrieved 31 January 2023


FAQs — Topa Topa Brewing Co.
We fill all growlers, as long as they fit under our tap handles. We also sell these awesome California Growlers that are fillable at most of the craft breweries in California.
We only sell the beer that we brew, but both of our locations have easy access to food vendors. Santa Barbara patrons can order from The Nook window in the Waterline and Ventura has a food truck most days of the week. View the Ventura taproom calendar for food truck schedule. You are always welcome to bring in any outside food as well!
Can I bring my dog/kids?
Yes! We are a family and dog-friendly brewery. Just be sure to keep all furry friends on a leash.
Can I submit a beer donation request?
We love donating beer to support local causes and organizations whose values align with our own. We are a 1% for the Planet member and, as such, we try to focus our giving on 1% for the Planet affiliated non-profits. Note that the ABC is very specific as to who we are are allowed to donate to. For more information, please see our donation information page.


text:
Laguna Nuevo Mundo är en sjö i Bolivia.   Den ligger i departementet Beni, i den centrala delen av landet,  km norr om huvudstaden Sucre. Laguna Nuevo Mundo ligger  meter över havet. Arean är  kvadratkilometer. Den sträcker sig 9,1 kilometer i nord-sydlig riktning, och 10,6 kilometer i öst-västlig riktning.

Runt Laguna Nuevo Mundo är det mycket glesbefolkat, med  invånare per kvadratkilometer.  Tropiskt monsunklimat råder i trakten. Årsmedeltemperaturen i trakten är  °C. Den varmaste månaden är november, då medeltemperaturen är  °C, och den kallaste är maj, med  °C. Genomsnittlig årsnederbörd är  millimeter. Den regnigaste månaden är februari, med i genomsnitt  mm nederbörd, och den torraste är augusti, med  mm nederbörd.

Kommentarer

Källor

Insjöar i Beni
Insjöar i Bolivia större än 10 kvadratkilometer


Specialised schools or grandes écoles.
Grandes écoles recruiting by competitive examination following two or three years of preparatory classes (CPGE mostly).
Obtaining the baccalauréat is a pre-requisite to being admitted to an institution of higher education. The baccalauréat is a diploma that acknowledges the successful completion of secondary education and the first level of university studies. This is a very important feature of the French education system, one which has several consequences, particularly with regard to university studies and student orientation during the premier cycle (first cycle) at university.
"Tertiary education is organised in cycles. The number, nature and duration of the cycles vary depending on the studies pursued. Each cycle has its own objectives and contributes to students' orientation, general education, acquisition of elements necessary for professional qualification, research, personality development, sense of responsibility, and ability to work both independently and as part of a team. At the end of each cycle, the student receives a national of institutional degree acknowledging the acquisition of specific knowledge, skills, and elements of professional qualification."


In adding the Facebook Recommendation Widget to RCG, I decided to try something a bit different and add it to the footer (along with the social scope plugin widget).
My hope is that if someone makes it through an article, but doesn't know what to do next, something in the plugin will catch their eye and keep them clicking articles. Your thoughts?
And you probably should pop over to a RCG article, like this one: Everybody LOVES Bank Fraud to see the recommendation plugin in action.
Yesterday, Jeff let me know how Facebook launched the "like" button yesterday and a bunch of other social plugins, and it's been a non-stop conversation around the M Realty office this morning.
The default "like" button didn't work so well within my P2 theme, but I was able to get the recommendation plugin working with almost no effort at all… and it rocks!
It not only shows the number of folks who are sharing each article on my site, but will make personalized recommendations to you for articles based on the articles that you're friends are sharing! So slick!
It's so darn easy, I decided to post it in this blog post!
I added the PuSHPress plugin that's suppose to push your new blog posts to sites like Google Reader in real time… and sure enough, I checked Google Reader JUST after publishing my last post, and it was already there!
I don't know about you, but the idea of adding Google Friend Connect to my blogs never really enticed me…. It seemed like just another MyBlogLog.
However, I'm kind of a Facebook Junkie, and so when I had a few minutes, I decided to look into Facebook Connect. It's pretty darn similar to Google Connect in that users (you!) can "join" a blog and it will display "recent" visitors. However, the one HUGE benefit is that when configured correctly (there's a bit more to this than I expected), users can push "comments" to their news feeds… and I'm pretty sure there'll be other ways of integrating content created on the blog into Facebook in the near future.
With that in mind I installed and configured the facebook connect plugin from sociable.es.
Why not go ahead and spread some luv, 4realz-style!
That's all for now. I thought I'd test it out on 4realz for a few days and if everything works well, then this is definitely something I'll push to Rain City Guide soon.


New year, new lashes with neuLASH! Our friends at Skin Research Laboratories have a fantastic product that will help you have thicker, longer lashes. neuLASH is a serum that is formulated with a special blend of amino acids, vitamins, and conditioning ingredients and is ophthalmologist and dermatologist- tested. Apply the clear liquid to your lash line daily and by the end of the month, expect to see beautiful, full lashes to frame your eyes. We found that it was gentle on our eyes, with no irritation at all and was easy to apply. No need to spend time fussing with mascara or falsies in the morning – just a quick application of neuLASH at night and you'll have luscious, strong, dark lashes. A must-have addition to your TrailblazerGirl beauty routine!


text:
Ontario- Mathematics: Grade 10 Academic
Ontario Curriculum Adopted: 2005
Province Correlations
Mathematics: Grade 10 Academic
2: Quadratic Relations of the Form y = ax² + bx + c
2.1: Overall Expectations
2.1.1: determine the basic properties of quadratic relations;
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
2.1.2: relate transformations of the graph of y = x² to the algebraic representation y = a(x - h)² + k;
2.1.4: solve problems involving quadratic relations.
2.2: Investigating the Basic Properties of Quadratic Relations
2.2.1: collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology (e.g., concrete materials, scientific probes, graphing calculators), or from secondary sources (e.g., the Internet, Statistics Canada); graph the data and draw a curve of best fit, if appropriate, with or without the use of technology (Sample problem: Make a 1 m ramp that makes a 15° angle with the floor. Place a can 30 cm up the ramp. Record the time it takes for the can to roll to the bottom. Repeat by placing the can 40 cm, 50 cm, and 60 cm up the ramp, and so on. Graph the data and draw the curve of best fit.);
2.2.2: determine, through investigation with and without the use of technology, that a quadratic relation of the form y = ax² + bx + c (a "not equal to" 0) can be graphically represented as a parabola, and that the table of values yields a constant second difference (Sample problem: Graph the relation y = x² - 4x by developing a table of values and plotting points. Observe the shape of the graph. Calculate first and second differences. Repeat for different quadratic relations. Describe your observations and make conclusions, using the appropriate terminology.);
Translating and Scaling Functions
Using Tables, Rules and Graphs
2.2.3: identify the key features of a graph of a parabola (i.e., the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum value), and use the appropriate terminology to describe them;
Polynomials and Linear Factors
2.3: Relating the Graph of y = x² and Its Transformations
2.3.1: identify, through investigation using technology, the effect on the graph of y = x² of transformations (i.e., translations, reflections in the x-axis, vertical stretches or compressions) by considering separately each parameter a, h, and k [i.e., investigate the effect on the graph of y = x² of a, h, and k in y = x² + k, y = (x - h)², and y = ax²];
2.3.2: explain the roles of a, h, and k in y = a(x - h)² + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry;
Defining a Line with Two Points
Dilations
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
2.3.3: sketch, by hand, the graph of y = a(x - h)² + k by applying transformations to the graph of y = x² [Sample problem: Sketch the graph of y =- 1/2(x - 3)² + 4, and verify using technology.];
2.3.4: determine the equation, in the form y = a(x - h)² + k, of a given graph of a parabola.
2.4: Solving Quadratic Equations
2.4.1: expand and simplify second-degree polynomial expressions [e.g., (2x + 5)², (2x - y)(x + 3y)], using a variety of tools (e.g., algebra tiles, diagrams, computer algebra systems, paper and pencil) and strategies (e.g., patterning);
Addition of Polynomials - Activity A
2.4.2: factor polynomial expressions involving common factors, trinomials, and differences of squares [e.g., 2x² + 4x, 2x - 2y + ax - ay, x² - x - 6, 2a² + 11a + 5, 4x² - 25], using a variety of tools (e.g., concrete materials, computer algebra systems, paper and pencil) and strategies (e.g., patterning);
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
2.4.3: determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts (i.e., the zeros) of the graph of the corresponding quadratic relation, expressed in the form y = a(x - r)(x - s);
2.4.4: interpret real and non-real roots of quadratic equations, through investigation using graphing technology, and relate the roots to the x-intercepts of the corresponding relations;
2.4.5: express y = ax² + bx + c in the form y = a(x - h)² + k by completing the square in situations involving no fractions, using a variety of tools (e.g. concrete materials, diagrams, paper and pencil);
2.4.6: sketch or graph a quadratic relation whose equation is given in the form y = ax² + bx + c, using a variety of methods (e.g., sketching y = x² - 2x - 8 using intercepts and symmetry; sketching y = 3x² - 12x + 1 by completing the square and applying transformations; graphing h = -4.9t² + 50t + 1.5 using technology);
2.4.7: explore the algebraic development of the quadratic formula (e.g., given the algebraic development, connect the steps to a numerical example; follow a demonstration of the algebraic development [student reproduction of the development of the general case is not required]);
2.4.8: solve quadratic equations that have real roots, using a variety of methods (i.e., factoring, using the quadratic formula, graphing) (Sample problem: Solve x² + 10x + 16 = 0 by factoring, and verify algebraically. Solve x² + x - 4 = 0 using the quadratic formula, and verify graphically using technology. Solve -4.9t² + 50t + 1.5 = 0 by graphing h = -4.9t² + 50t + 1.5 using technology.).
2.5: Solving Problems Involving Quadratic Relations
2.5.1: determine the zeros and the maximum or minimum value of a quadratic relation from its graph (i.e., using graphing calculators or graphing software) or from its defining equation (i.e., by applying algebraic techniques);
2.5.2: solve problems arising from a realistic situation represented by a graph or an equation of a quadratic relation, with and without the use of technology (e.g., given the graph or the equation of a quadratic relation representing the height of a ball over elapsed time, answer questions such as the following: What is the maximum height of the ball? After what length of time will the ball hit the ground? Over what time interval is the height of the ball greater than 3 m?).
3: Analytic Geometry
3.1.3: verify geometric properties of triangles and quadrilaterals, using analytic geometry.
Parallelogram Conditions
Triangle Inequalities
3.2: Using Linear Systems to Solve Problems
3.2.1: solve systems of two linear equations involving two variables, using the algebraic method of substitution or elimination (Sample problem: Solve y = 1/2x - 5, 3x + 2y = -2 for x and y algebraically, and verify algebraically and graphically);
Special Types of Solutions to Linear Systems
3.2.2: solve problems that arise from realistic situations described in words or represented by linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method (Sample problem: The Robotics Club raised $5000 to build a robot for a future competition. The club invested part of the money in an account that paid 4% annual interest, and the rest in a government bond that paid 3.5% simple interest per year. After one year, the club earned a total of $190 in interest. How much was invested at each rate? Verify your result.).
Solving Linear Systems by Graphing
Systems of Linear Equations - Activity A
3.3: Solving Problems Involving Properties of Line Segments
3.3.2: develop the formula for the length of a line segment, and use this formula to solve problems (e.g., determine the lengths of the line segments joining the midpoints of the sides of a triangle, given the coordinates of the vertices of the triangle, and verify using dynamic geometry software);
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
3.3.3: develop the equation for a circle with centre (0, 0) and radius r, by applying the formula for the length of a line segment;
3.3.4: Determine the radius of a circle with centre (0, 0), given its equation; write the equation of a circle with centre (0, 0), given the radius; and sketch the circle, given the equation in the form x² + y² = r²;
3.3.5: solve problems involving the slope, length, and midpoint of a line segment (e.g., determine the equation of the right bisector of a line segment, given the coordinates of the endpoints; determine the distance from a given point to a line whose equation is given, and verify using dynamic geometry software).
Slope - Activity B
3.4: Using Analytic Geometry to Verify Geometric Properties
3.4.1: determine, through investigation (e.g., using dynamic geometry software, by paper folding), some characteristics and properties of geometric figures (e.g., medians in a triangle, similar figures constructed on the sides of a right triangle);
Classifying Quadrilaterals - Activity B
Classifying Triangles
Perimeters and Areas of Similar Figures
Polygon Angle Sum - Activity A
Similar Figures - Activity A
Similar Polygons
Triangle Angle Sum - Activity A
3.4.2: verify, using algebraic techniques and analytic geometry, some characteristics of geometric figures (e.g., verify that two lines are perpendicular, given the coordinates of two points on each line; verify, by determining side length, that a triangle is equilateral, given the coordinates of the vertices);
Isosceles and Equilateral Triangles
4: Trigonometry
4.1.1: use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;
4.1.2: solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
4.2: Investigating Similarity and Solving Problems Involving Similar Triangles
4.2.1: verify, through investigation (e.g., using dynamic geometry software, concrete materials), the properties of similar triangles (e.g., given similar triangles, verify the equality of corresponding angles and the proportionality of corresponding sides);
4.2.2: describe and compare the concepts of similarity and congruence;
Congruence in Right Triangles
4.2.3: solve problems involving similar triangles in realistic situations (e.g., shadows, reflections, scale models, surveying) (Sample problem: Use a metre stick to determine the height of a tree, by means of the similar triangles formed by the tree, the metre stick, and their shadows.).
4.3: Solving Problems Involving the Trigonometry of Right Triangles
4.3.1: determine, through investigation (e.g., using dynamic geometry software, concrete materials), the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios (e.g., sin A = opposite/hypotenuse);
Sine Function
4.3.2: determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
4.3.3: solve problems involving the measures of sides and angles in right triangles in reallife applications (e.g., in surveying, in navigating, in determining the height of an inaccessible object around the school), using the primary trigonometric ratios and the Pythagorean theorem.
4.4: Solving Problems Involving the Trigonometry of Acute Triangles
4.4.2: explore the development of the cosine law within acute triangles (e.g., use dynamic geometry software to verify the cosine law; follow the algebraic development of the cosine law and identify its relationship to the Pythagorean theorem and the cosine ratio [student reproduction of the development of the formula is not required]);
Cosine Function
4.4.4: solve problems involving the measures of sides and angles in acute triangles.
This correlation lists the recommended Gizmos for this province's curriculum standards. Click any Gizmo title below for more information.