text:
Passport on Wheels – What You Need to Know About it
By Announcement PH Staff 3 Comments Filed Under: DFA, Tips
Even after the Department of Foreign Affairs (DFA) made the passport application easier, it's still a hassle for some people who live in far off places. Why? Because of the fact that they still need to travel in order for them to apply for a passport. This is why the DFA made a better and a much more convenient effort to serve the people who need to get a passport. And thus, the Passport on Wheels (PoW) came to life. In this article, we will be giving you more information on what this Passport on Wheels is, where you can see them, what you need to submit for your requirements, literally everything you need to know about it.
Image was taken from the Department of Foreign Affairs Website | dfa.gov.ph
Read: A Guide to Getting your Philippine Passport
What is the Passport on Wheels?
Based on what it's called, the Passport on Wheels is a service from the DFA to extend its efforts in serving the public. It was a nationwide move and aims to assist thousands of Filipinos daily.
As per the DFA, with this Passport on Wheels, they will be able to accommodate at its maximum capacity and they will serve more passport applicants than the usual. When it first launched in January 2018, the number of POW applicants in the first six (6) months were already equivalent to the service of four (4) medium-sized consular offices.
Alan Peter S. Cayetano, Department of Foreign Affairs Secretary said that this will provide service and can accommodate hundreds and thousands of more passport applicants.
Through the Passport on Wheels, we are not only able to bring our consular services closer to the people but, more importantly, serve more people, accommodating more than 138,000 applicants since January."
What services can the Passport on Wheels accommodate?
Image was taken from ABS-CBN NEWS | news.abs-cbn.com
If you think that this will only provide service to new passport applicants, think again. Other services like renewal and claiming of loss and stolen passports can also be done in the PoW.
Read: Read: Requirements and Procedure for Applying Driver's License in the Philippines
Adult and minor new and renewal passport applicants can be served in the PoW. So, if you are looking for an easy way for your passport to be finished, you can resort to the PoW.
Just to be clear, the Passport on Wheels is a group of teams which visit schools, municipalities, and government offices to be able to give aid for them to have their passports.
How can the PoW give service to establishments and institutions?
According the Cayetano, any company, organization, school, or LGU, can get the PoW service via a formal written request to the Assistance Secretary for Consular Affairs of the Department of Foreign Affairs via email. The email needs to be sent to [email protected] and [email protected].
NOTE: The letter must specify the number of applicants in estimation. It needs to be at a minimum of 500 applicants; maximum of 2,000, the name and contact details of the coordinator of the requestor, with the preferred schedule, of course.
What are the requirements if you are to apply for a passport via the PoW?
The requirements are pretty much the same as to how you would apply for a passport in a consular office. To give you a rundown, you would need:
Duly accomplished application form
Personal appearance
PSA-certified birth certificate (original copy) or PSA-authenticated marriage certificate (for married females)
Original and photocopy of two (2) valid IDs
If you are a student, you can submit your original copy of the registrar's certificate, your school ID (original and photocopy), and your PSA-certified birth certificate.
How about passport renewals?
In renewing the Maroon passport (machine readable passport) and the green ones, those will be treated as new applicants so you can refer to the above instructions.
Read: How do you Apply and Register for the CSC-Computerized Examination?
Renewal of ePassports, on the other hand, would have a different set of instructions:
Personal appearance of the person
Current ePassport with the photocopy of the data page
PSA-authenticated documents like birth certificate or marriage certificate
For minor renewal applicants:
Passport of the applicant (current one)
School ID (original and photocopy)
PSA-certified birth certificate
Personal appearance of both the authorized adult companion (guardian or parent) and the minor applicant
In the event that the applicant is not a legitimate child, there would be additional requirements:
If the minor is not accompanied by his or her mother during the time of the appearance, the applicants need to submit a verified Special Power of Attorney (SPA) accomplished by the mother, anointing the companion to be allowed in the process.
More so, if the minor is not traveling with the mother, the applicant must submit an Affidavit of Support and Consent (ASC) and a DSWD Clearance accomplished by the mother of the minor.
If the mother of the minor is deceased, the father can take place of the mother and submit these documents. In the event that the father is not known, the following addition requirements must be submitted:
Affidavit of Guardianship
DSWD Clearance
Valid government ID of the adult guardian or the valid passport.
With the fees, it's just like the fees you would need to settle if you are to proceed with the process in a consular office. The only difference is that there is a courier fee of P150.00 because it is via PoW.
Passport fee is P1,200.00
Lost and Expired fee if the passport is lost/stolen/expired will have an additional P350.00
Benefits of the Passport on Wheels
If you come to think of it, the passport on wheels is a great way of helping the society achieve what they cannot because of the proximity of some office from provinces far from it.
With the passport on wheels, people can:
Apply for a passport without going through the hassle of proceeding to a DFA satellite office;
They can attend a seminar on what they need to bring for their passport application or renewal;
If you have minors and you want them to have a passport, it's easier for you because you will not be required to travel distances just to apply for a passport; and
Total convenience especially for people who live at far edges of the country.
Read: Philippine National ID: How can you Get your Phil ID?
Other than the Passport on Wheels program, Assistant Secretary Frank Cimafranca told other projects, plans, and initiatives to meet the demand for passport processes. Recently, there were new consular offices opened in San Nicolas in Ilocos Norte, Tacloban City, and Santiago City in Isabela to somehow ease the demand of the public.
Both Parañaque City and DFA ASEANA are open on Saturdays since the early start of 2018 for passport application and renewal services.
Read Also: Who Are Exempted From DFA's Online Appointment for Passport Application
Charlene Donato says
kelan po magkakaron ng PoW sa Zambales?
lougrant aralar says
saan po merong passport on wheels s rizal
joel baguio says
paano mag parenew jan..


text:
Q: Automatically select a date in an UWP CalendarView In my UWP app, I want the current day to be automatically selected on a CalendarView, but I can't change the value of the SelectedDates property.

A: Since SelectedDates is List you can't directly assign a new value to SelectedDates. If you use SelectionMode="Single" then Clear the list and use Add.
MyCalendarView.SelectedDates.Clear();
MyCalendarView.SelectedDates.Add(DateTimeOffset.Now);

redpajama_set_name: RedPajamaStackExchange


Opportunities that resident cadets enjoy are developing their leadership skills and learning, first hand, the value of teamwork and community that results from living and working together.
Barracks inspections are conducted as necessary to insure that all concerned are meeting discipline, health, safety, security, and welfare standards. Formal inspections are conducted weekly by the Cadet Chain of Command or members of the Commandant's Staff. It is the responsibility of each resident cadet to maintain his or her barracks space to a high standard of cleanliness, neatness, and order.
Video surveillance is in place inside and outside Baugh barracks to facilitate the safety and security of our cadets.


Generous sponsors contribute amazing value packages to help generate the funds we need to produce our wonderful, action-packed festival! Please take a look at the items below, available for auction, and plan to make a bid! Bids will be managed on eBay!
Two (2) complimentary 60-minute Spa treatments of the guests' choice inclusive of taxes and service charge. Also included in this package is the use of the Spa Facilities, which include the Steam Room, Sauna, Cold Plunge Pool, Jacuzzi and Soaking Pool.
Complimentary Lunch and Spa treatments will only be honored with advance reservation.
Guests must be at least 21 years of age. This voucher is non-transferable, non-redeemable for cash, not valid with any other promotion and cannot be re-sold or re-auctioned. The complimentary Lunch and Spa treatments cannot be redeemed separately and shall be booked for the same day.
This Donation Voucher needs to be surrendered at the time of check-in to enjoy the complimentary Lunch and Spa treatments.
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text:
Pablo Alejandro Marini (* 31. Januar 1967 in Santa Fe, Provinz Santa Fe) ist ein ehemaliger argentinischer Fußballspieler auf der Position eines Stürmers, der nach dem Ende seiner aktiven Laufbahn eine Tätigkeit als Trainer begann.

Leben

Spieler
Marini begann seine Fußballerlaufbahn im Nachwuchsbereich der Newell's Old Boys. In seiner 15-jährigen Profikarriere (von 1987 bis 2002) erzielte er insgesamt 154 Tore. Einen nationalen Rekord in seinem Heimatland stellte er während seiner Zeit bei Arsenal de Sarandí auf, als er in acht aufeinander folgenden Spielen insgesamt neun  Tore erzielte. Außerdem war er zweimal Torschützenkönig der Primera B Nacional: in der Clausura 1996 mit 15 Toren und in der Spielzeit 1997/98 mit 29 Toren. Außerdem ist er mit 68 Treffern, die er für den Club Atlético San Martín erzielte, der erfolgreichste Torschütze in dessen Vereinsgeschichte.

Trainer
Seine erste Stelle als Cheftrainer bekleidete Marini 2007 bei seinem ehemaligen Verein Newell's Old Boys. Anfang Januar 2014 wurde er als Cheftrainer des abstiegsbedrohten Club Atlante verpflichtet, konnte dessen Abstieg aus der höchsten mexikanischen Spielklasse aufgrund der negativen Dreijahresbilanz der Potros aber nicht verhindern. Für die kommende Zweitliga-Saison 2014/15 unterschrieb Marini bei den neu gegründeten Mineros de Zacatecas.

Weblinks
 Spielerprofil bei BDFA

Einzelnachweise

Fußballspieler (Instituto Atlético Central Córdoba)
Fußballspieler (Club Atlético Nueva Chicago)
Fußballspieler (Arsenal de Sarandí)
Fußballspieler (CA San Martín de San Juan)
Fußballspieler (CD Arturo Fernández Vial)
Fußballtrainer (Newell's Old Boys)
Fußballtrainer (CF Atlante)
Fußballtrainer (CF Pachuca)
Fußballtrainer (Chiapas FC)
Geboren 1967
Argentinier
Mann
Fußballtrainer (Audax Italiano La Florida)

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text:
Mission Knights 7519
The online home of Knights of Columbus, Council 7519, at Mission Basilica San Juan Capistrano
Knights of Columbus, Council 7519, Monsignor Paul Martin Council at Mission Basilica San Juan Capistrano
Grand Knight: Sir Knight Leo Norton
Deputy Grand Knight: Sir Knight Ed Matthews
Financial Sect.: Sir Knight Ed Jordan
The Knights of Columbus is open to Catholic men, over the age of 18, who wish to put their faith into action. The Knights is founded upon three basic principles: Charity, Unity, and Fraternity. We follow our faith to help others; stand united with our clergy and Catholic educators; and build bonds between Catholic men.
The Knights of Columbus is also a fraternal benefit society, which means the Knights have several ways to provide financial security to members and their families, while turning premiums into charitable impact.
The Knights of Columbus was established in 1882 by Father Michael J. McGivney at St. Mary's Church in New Haven, Conn. Their intent was to bring financial aid and assistance to the sick, disabled, and needy members and their families. Today, Father McGivney is being considered for sainthood.
Our Council is named for Monsignor Paul Martin; the longtime Pastor of Mission Church. Monsignor Martin oversaw the building of the "new" church, the expansion of the school, and unprecedented growth of our parish.
Prospective Knights must complete an Admission Form and complete the Admission Ceremony. Ceremony and traditions are important to the Catholic identity and the Knights are no different. The revised ceremony is available online and, when available, the church ceremony will be open to the Knight's friends and family.
For more information, please visit our national website: https://www.kofc.org/en//index.html
Mission Knights 7519, Blog at WordPress.com.

redpajama_set_name: RedPajamaCommonCrawl


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text:
\section{Introduction}

In the seventies, systematic studies of {\it symmetries}
in nonrelativistic quantum mecha\-nics (NRQM) had already been
realized when the Schr\"odinger equation involves
time-independent potential interactions \cite{1,2,3,4}. Some of them have
considered one-dimensional~\cite{2,4}, three-dimensional~\cite{1},
 or $n$-dimensional~\cite{3} (space) systems.

Recently~\cite{5} we have added new information
by visiting higher-order symmetries of such one-dimensional
Schrodinger equations and by considering the third-order context as an effective case,
(Remember that the usual well-known symmetries of the
Schr\"odinger equation correspond to first- and second-order
operators.)

Since the event of supersymmetry in theoretical particle physics~\cite{6}
 and its implications~\cite{7} in supersymmetric
(nonrelativistic) quantum mechanics (SSQM),
 we are dealing with supersymmetric wave equations, including
time-independent superpotentials [hereafter denoted $W(x)$
in one-dimensional problems]. Such supersymmetric
equations are usually put in the following matrix form:
\begin{gather}
i \partial_t \chi(x,t)=\left[ -\frac{1}{2} \partial^2_x +
\frac{1}{2} W^2(x)+\frac{1}{2}W'(x)\sigma_3\right]\chi(x,t),
\end{gather}
where $\partial_t=\partial/\partial t$,
the prime refers to the space derivative $\partial_x \equiv
\partial/\partial x$, $\sigma_3$ is the Pauli $2 \times 2$ matrix diag$(1,-1)$, and
correlatively $\chi(x,t)$ is a two-component wave function.
For simplicity we consider systems with unit
masses and choose $\hbar=1$ in this quantum context.

In Hamiltonian form, Eq.~(1.1) contains as expected, the bosonic
part $H_b$ and the fermionic part $H_f$ given by
\begin{gather}
H_b=-\frac{1}{2} \partial^2_x+\frac{1}{2} W^2(x), \quad H_f=\frac{1}{2}W'(x)\sigma_3, \quad
H_{SS}=H_b+H_f,
\end{gather}
showing that superpotentials $W(x)$ are simply related to usual
potentials $U(x)$ by
\begin{gather}
U(x)=\frac{1}{2}W^2(x).
\end{gather}
Such supersymmetric equations (1.1) and characteristics (1.2)
have already suggested new methods and results~\cite{8,9}
by considering even and odd symmetries in connection with the so-called Lie
extended method developed in quantum physics~\cite{10}.

As a particular context that has been recently visited~\cite{8},
let us mention the case of the one-dimensional
supersymmetric harmonic oscillator corresponding to
\begin{gather}
 W(x)=\omega x\ \Leftrightarrow \ U(x)=\frac{1}{2} \omega^2 x^2.
\end{gather}

Here we want to study systematically
the supersymmetries as well as their superstructures subtended by the
SSQM-Schr\"odinger equation (1.1) for arbitrary
superpotentials $W(x)$. Such a program will appear in the
following sections where we will get a complete classification of all solvable (admissible)
interactions admitting nontrivial supersymmetries.

The contents of this paper are distributed as follows.
In Section~2 we come back on the Boyer results~\cite{3},
but for one-dimensional systems. We present the corresponding study in a particularly
convenient way for our purpose in the supersymmetric context developed in Section~3.
There we first
determine the even supersymmetries (Section~3.1), then second the odd ones (Section~3.2),
and finally we
superpose both contexts (Section 3.3) and get only four priviledged
classes of superpotentials. All the
results are quoted in three respective tables, where we mention the
largest invariance Lie (super)algebras
generated by the corresponding operators.
Remember that these extended (super)symmetries do not
necessarily close. Section 4 finally contains some comments on
isomorphic structures and some conclusions.

\setcounter{equation}{0}

\section{Going back on symmetries in NRQM}

In fact, Boyer~\cite{3} has already solved the problem
of determining all the symmetries of the Schr\"odinger
equation in n dimensions. Applied to the simplest one-dimensional context, this problem
consists in the resolution of the following invariance condition:
\begin{gather}
[\Delta, Q]= i\lambda \Delta, \quad \lambda \equiv \lambda(x,t).
\end{gather}
Here the Schr\"odinger equation defines the $\Delta$ operator on the form
\begin{gather}
\Delta \psi(x,t) \equiv \left(-i \partial_t-\frac{1}{2} \partial^2_x+U(x)\right)\psi(x,t),
\end{gather}
while we are searching for symmetry operators $Q$ of (at most)
second order with respect to space derivatives, i.e.,
\begin{gather}
Q \equiv ia(x,t) \partial_t+ib(x,t)\partial_x+ic(x,t),
\end{gather}
$a$, $b$, and $c$ being arbitrary functions.
Let us mention that higher-order symmetry operators have
recently been considered elsewhere in the same context~\cite{5}.

The above problem leads to a set of partial differential equations
giving rise to $x$-independent functions
$a_0$, $b_0$, and $c_0$
and to the following first-order partial differential equation on $U(x)$:
\begin{gather}
\left(\frac{1}{2}\dot a_0 x+b_0\right)U'(x)+\dot a_0U(x)
=-\frac{1}{4}\mathop{a}\limits^{\ldots}\!{}_0 x^2-\ddot b_0x-i
 \dot c_0+\frac{i}{4}\ddot a_0,
 \end{gather}
where the overdots evidently refer to time derivatives. The
general solution of Eq.~(2.4) appears as the sum of the general
solution $U_0(x)$ of the homogeneous equation and of a particular
solution $U_1(x)$ of the inhomogeneous equation. Due to the at most
quadratic dependence on $x$ in the inhomogeneous part of Eq.
(2.4), Boyer has proposed to search for the general solution~\cite{3}
\begin{gather}
U(x)=U_0(x)+U_1(x),
\end{gather}
with
\begin{gather}
U_1(x)=\frac{1}{2}\alpha x^2+\beta x+\gamma,
\quad \alpha, \beta, \gamma =\mbox{arbitrary constants},
\end{gather}
and to distinguish three cases according to $\alpha= 0$,
$\alpha=\omega^2 > 0$, or $\alpha=-\omega^2 < 0$.

If the whole discussion takes place in Boyer's work~\cite{3}, let us
notice here the following results and properties in order to
exploit them in the supersymmetric context.

In the free case, i.e., $U=0$ $(U_0 = 0 = U_1)$, as already obtained by Niederer~\cite{1},
we get at most six symmetries whose
commutation relations lead to the largest invariance algebra seen as a semidirect
sum $(\Box)$ of the so-called
``conformal'' algebra so$(2,1)$ and the Heisenberg algebra $h(2)$.

In the interacting case but when $U_0=0$,
we want to point out a new result, i.e., the potential
\begin{gather}
U(x)=U_1(x)
\end{gather}
leads to isomorphic structures so$(2,1) \Box h(2)$ a
s in the free case $(\alpha=\beta=\gamma=0)$
whatever are the constants $\alpha$, $\beta$, and $\gamma$.
As particular cases, the harmonic oscillator
corresponds to $U_0=0$, $\alpha=\omega^2$,
$\beta=\gamma=0$ [see Eqs. (1.3) and (2.7)] while the linear
potential to $U_0=0$, $\alpha=0$, i.e.,
\begin{gather}
U(x)=\beta x+\gamma.
\end{gather}
Consequently, these cases also admit six symmetries
and there exist changes of variables connecting all the equations
including the potential forms (2.7) for arbitrary $\alpha$, $\beta$ and~$\gamma$,
with the free Schr\"odinger equation. Let us just quote
as an example some formulas corresponding to the
change of variables between the case $\alpha = \omega^2>0$
and the free case $(\alpha=\beta=\gamma= 0)$.
It can be shown that the relations
\begin{gather}
t_1=(1/\omega) \tan^{-1} \omega t_2, \quad
x_1=(1+\omega^2t^2_2)^{-1/2}(x+\beta /\omega^2)-\beta/\omega^2
\end{gather}
correspond to a well-defined change
of variables between the above interacting case (indices 1) and the free
case (indices 2) implying a modification in the
corresponding Schr\"odinger wave functions according to
\begin{gather}
\Psi_1(x_1,t_1)=(1+\omega^2t^2_2)^{1/4} \exp \left[\left(
\frac{i\beta^2}{2\omega^3}-\frac{i\gamma}{\omega}
\right)\tan^{-1}\omega t_2-\frac{i\beta^2}{2\omega^3}\frac{t_2}{1+\omega^2t^2_2}\right]\nonumber\\
\phantom{\Psi_1(x_1,t_1)=}{}\times
\exp \left[-\frac{it_2x}{2(1+\omega^2t^2_2)}(2\beta+\omega^2x) \right] \Psi_2(x_2,t_2).
\end{gather}
As a more particular case included in this comment, i.e., the harmonic oscillator case with
$\alpha = \omega^2$, $\beta= \gamma= 0$, we immediately recover the Niederer result~\cite{1}:
\begin{gather}
\Psi_1(x_1,t_1)=(1+\omega^2t^2_2)^{1/4} \exp
\left[-\frac{it_2\omega^2x^2}{2(1+\omega^2t^2_2)}\right]
\Psi_2(x_2, t_2).
\end{gather}

When nontrivial potentials $U_0(x)\not=0$ are considered, only two cases have to be mentioned:
either $U_0$ is arbitrary, then all the potentials
\begin{gather}
U(x)=U_0+\frac{1}{2}\alpha x^2+\beta x+\gamma
\end{gather}
lead   to at least two  symmetries (the corresponding Hamiltonian
and the identity operator); or $U_0$
takes the nonzero form
\begin{gather}
U_0(x)=\delta/(\mu x+\epsilon)^2, \quad \mu \not =0,
\end{gather}
then all the potentials
\begin{gather}
U(x)=\delta/(\mu x+\epsilon)^2+\frac{1}{2} \alpha x^2+\beta x+ \gamma,\quad
[(\mu,\epsilon)=(\alpha,\beta) \ \mbox{if} \ \alpha \not=0],
\end{gather}
lead to four symmetries generating the direct sum ${\rm so}(2,1) \oplus I$.

Such properties are of special interest for the following
discussion of the supersymmetries of Eq.~(1.1) in particular.

\setcounter{equation}{0}

\section{Going to supersymmetries in SSQM}

Already considered \cite{8,9}
for only one-dimensional supersymmetric harmonic oscillators characterized by
interacting terms given in Eq. (1.4),
the search for the largest number(s) of one-parameter Lie algebras can
be extended to arbitrary (one-dimensional) systems. This asks for considering
the problem (2.1) but with an operator ASS defined by the
supersymmetric equation (1.1) and with symmetry
operators $Q$ containing even $(\vec 0)$ and odd (1) parts~\cite{8} according to
\begin{gather}
Q=Q_0+Q_1,
\end{gather}
refering to the expected graduation in the supercontext.
Consequently, let us decompose our program in three steps: first
to study the even supersymmetries (Section 3.1) by exploiting the
results contained in Section~2 on symmetries; second to develop
the new odd context and to get the corresponding supersymmetries
(Section~3.2); and, third, to superpose the two sets of results
(Section~3.3) in order to obtain the complete classification of
solvable interactions in SSQM.

Let us just notice here that, in connection with Eq. (1.1), we
understand that even and odd considerations are directly
connected with $2\times 2$ Pauli matrices or more correctly with the
Clifford algebra $Cl_2\equiv \{\sigma_0\equiv I_2, \sigma_1, \sigma_2, \sigma_3\}$,
where we easily
distinguish the even matrices $(\sigma_0,\sigma_3)$
and the odd ones $(\sigma_1, \sigma_2)$
the usual fundamental representation~\cite{11}.
Such a remark directly enlightens Sections 3.1 and 3.2.

\subsection{Even supersymmetries in SSQM}

The invariance condition (2.1) is replaced here by
\begin{gather}
[\Delta_{SS}, Q_0]=i\lambda_0\Delta_{SS}, \quad \lambda_0=\lambda_0(x,t),
\end{gather}
where
\begin{gather}
\Delta_{SS}=\left(\!\! \begin{array}{cc}
-i\partial_t-\frac{1}{2}\partial^2_x+\frac{1}{2}W^2(x)+\frac{1}{2}W'(x) &  0 \vspace{2mm}\\
 0  & -i\partial_t-\frac{1}{2}\partial^2_x+\frac{1}{2}W^2(x)-\frac{1}{2}W'(x)\end{array}\!\!
  \right)\!\!
  \end{gather}
and
\begin{gather} Q_{0}=\left( \begin{array}{@{}c@{}c@{}}
\begin{array}{@{}c@{}}
-i(a_0+a_3)\partial_t+i(b_0+b_3)\partial_x\\ {} +i(c_0+c_3)\end{array} &  0 \vspace{2mm}\\
 0  & \begin{array}{@{}c@{}} i(a_0-a_3)\partial_t+i(b_0-b_3)\partial_x\\
 {}+i(c_0-c_3)\end{array} \end{array}
 \right) \end{gather}
due to the explicit forms of the even matrices $\sigma_0$ and $\sigma_3$.
Such a problem is equivalent to a set of two
distinct ones in NRQM, as discussed in Section~2.
Indeed we get the two invariance conditions
\begin{subequations}
\begin{gather}
\left[-i\partial_t-\frac{1}{2}\partial^2_x+V_1(x), i(A_1\partial_t+B_1\partial_x+C_1)\right]=i\Lambda_1
\left(-i \partial_t-\frac{1}{2}\partial^2_x+V_1(x)\right)
\end{gather}
and
\begin{gather}
\left[-i\partial_t-\frac{1}{2}\partial^2_x+V_2(x), i(A_2\partial_t+B_2\partial_x+C_2)\right]=i\Lambda_2
\left(-i \partial_t-\frac{1}{2}\partial^2_x+V_2(x)\right),
\end{gather}
\end{subequations}
where the arbitrary functions $A_i$, $B_i$, $C_i$ and $\Lambda_i$ $(i= 1,2)$ are
evidently simply related to the above $a_0, a_3, \ldots$, while we have defined
\begin{subequations}
\begin{gather}
V_1(x)=\frac{1}{2}W^2(x)+\frac{1}{2}W'(x)
\end{gather}
and
\begin{gather}
V_2(x)=\frac{1}{2}W^2(x)-\frac{1}{2}W'(x),
\end{gather}
\end{subequations}
these functions being nothing else than the potentials associated with superpartners~\cite{12}.

\newpage

\begin{center}
\footnotesize

{\bf Table 1.}\\[2mm]
\begin{tabular}{@{}c@{}c@{}c@{}c@{}c@{}}
\hline
$\begin{array}{@{}c@{}} \mbox{Clas-}\\
\mbox{ses}\end{array}$ &
$\begin{array}{@{}c@{}} \mathcal{E} \ \mbox{Super-} \\
\mbox{symmetries and}\\
\mbox{their Lie algebras}\end{array}$ &
$\begin{array}{c@{}} \mbox{Number of}\\
\mathcal{E} \ \mbox{super-}\\
\mbox{symmetries}\end{array}$
   & $\begin{array}{c@{}} \mbox{Explicit forms of associated}\\
\mbox{superpotentials}\end{array}$  & Characteristics \\
\hline
$1$ & $\begin{array}{@{}c@{}}[{\rm so}(2,1)\Box h(2)] \\
\oplus\,[{\rm so}(2,1)\Box h(2)]\end{array}$& $12$
& $W(x)=ax+b$            & $\begin{array}{@{}c@{}} \mbox{Free case}\\
\mbox{Linear case} \\ \mbox{Harmonic} \\ \mbox{oscillator~\cite{9}} \end{array}$ \\
$2$ & $\begin{array}{@{}c@{}}[{\rm so}(2,1)\Box h(2)]\\
\oplus\, [{\rm so}(2,1)\Box {\rm gl}(1)]\end{array}$ & $10$
& $W(x)=\pm 1/(x+c)$     & Coulomb $(c=0)$ \\
$3$ &                             &      & $W(x)=ax\pm 1/x$      & Calogero $(a=\omega)$ \\
$4$ & $\begin{array}{@{}c@{}}[{\rm so}(2,1)\oplus {\rm gl}(1)]\\
\oplus\, [{\rm so}(2,1)\oplus {\rm gl}(1)]\end{array}$
 & $8$  & $W(x)=ax+c/x$             & $a\not=0$, $c\not=\pm 1$ \\
$5$ &                               &      & $W(x)=(fx+g)/(cx^2+dx+h)$ &
$\begin{array}{@{}c@{}} f\not=0,\ c\not=0, \\
f\not= \pm c, \ c \not=0 \end{array}$ \\
$6$ & $\begin{array}{@{}c@{}}[{\rm so}(2,1)\Box h(2)]\\
\oplus\,[{\rm so}(2)\oplus {\rm gl}(1)]\end{array}$
& $8$ & $W(x)=ax+b+ \frac{ce^{\mp ax^2 \mp 2bx}}{d+cfe^{\mp ax^2 \mp 2bx}dx}$
& $\begin{array}{@{}c@{}} (a,b)\not=(0,0) \\
d \not=0, \ c\not=0\end{array}$ \\
$7$  &&& $W(x)=\frac{c}{dx+f}+\frac{g}{h(dx+f)^{\pm 2c/d}\pm [g/(d\mp 2c)](dx+f)}$ &
$\begin{array}{@{}c@{}} d\not= \pm 2c \\
g \not=0, \ c \not=0\end{array}$ \\
 $8$ & $\begin{array}{@{}c@{}}[{\rm so}(2,1)\oplus {\rm gl}(1)]\\
\oplus\,[{\rm so}(2)\oplus {\rm gl}(1)]\end{array} $ & $6$ & $W(x)=\frac{c}{\pm 2cx+d}+
\frac{f}{(\pm 2 cx+d)(g+(f/2c)\ln |\pm 2cx+d|)}$ & $\begin{array}{@{}c@{}} f \not=0, \
a \not=0,\\
d\not=0\end{array} $\\
$9$  &&& $W(x)=ax+b+\frac{c}{dx+f}+\frac{g(dx+f)^{\mp 2c/d} e^{\mp ax^2\mp 2bx}}
{h\pm gfe^{\mp ax^2\mp 2bx}(dx+f)^{\mp 2c/d}dx}\!$ & $ c \not=0, \pm 1$ \\
$10$  & $\begin{array}{@{}c@{}} [{\rm so}(2)\oplus {\rm gl}(1)]\\
\oplus\,[{\rm so}(2)\oplus {\rm gl}(1)]\end{array}$
 & $4$ & $W(x)\not= \ \mbox{above  forms} $ & $\cdots $ \\
\hline
\end{tabular}
\end{center}

By combining and superposing the potentials (2.6), (2.7), (2.12),
and (2.14) in known NRQM, we immediately deduce the
cases leading to (at most) 12 even supersymmetries
or to 10, 8, 6, and (at least) 4 of them. The (six) associated
invariance Lie algebras are also easily determined (see Table~1): the largest
one is seen as the direct sum $[{\rm so}(2,1)\Box h(2)]\oplus [{\rm so}(2,1)\Box h(2)]$
and the smallest one as $[{\rm so}(2)\oplus {\rm gl}(1)]\oplus [{\rm so}(2)\oplus {\rm gl}(l)]$.
Such direct sums evidently come from
the superposition of both projections by $P_\pm =\frac{1}{2}(\sigma_0 \pm \sigma_3)$
of the ordinary symmetries
obtained in NRQM. Moreover, by exploiting the explicit forms
obtained for $V_1$, and $V_2$ in NRQM, it is possible
through Eqs. (3.6) to get the correspon\-ding superpotentials $W(x)$ entering in Eq.~(1.1).
Let us, for example, treat the case leading to the maximal number of even
supersymmetries, i.e., let us consider
\begin{gather}
V_1(x)=\frac{1}{2}\alpha_1 x^2+\beta_1 x+\gamma_1
\end{gather}
and
\[
V_2(x)=\frac{1}{2}\alpha_2 x^2+\beta_2 x+\gamma_2.
\]
Through Eqs. (3.6) we readily get the linear superpotential
\begin{gather}
W(x)=ax+ b, \quad a,b =  \mbox{const},
\end{gather}
which also corresponds to the free case $(a= b= 0)$ as well as to
the one-dimensional harmonic oscillator $(a =\omega$, $b= 0)$. Here are
associated 12 even Supersymmetries, an old result quoted in the even notations~\cite{9},
\begin{gather}
[(H_B, C_{\pm}, I, P_{\pm})\sigma_0] \quad \mbox{and} \quad
  [(H_B, C_{\pm}, I, P_{\pm}) \sigma_3].
   \end{gather}

The general discussion leads to specific families of supcrpotentials
given in Table~1 simultaneously with their
associated invariance Lie algebras
and their dimensions. Let us point out the Coulomb-like and
Calogero-like forms admitting ten even supersymmetries.

\subsection{Odd supersymmetries in SSQM}

With the operator $\Delta_{SS} \equiv (3.3)$
we have now to exploit the invariance condition
\begin{gather}
[\Delta_{SS}, Q_1]=i\lambda_1\Delta_{SS},
\quad \lambda_1=\lambda_1(x,t),
\end{gather}
where
\begin{gather}
  Q_{1}=\left(\begin{array}{@{}c@{}c@{}}
   0  &  \begin{array}{@{}c@{}} (ia_1+a_2)\partial_t+(ib_1+b_2)\partial_x\\
   {} +ic_1+c_2 \end{array} \\
 \begin{array}{@{}c@{}}(ia_1-a_2)\partial_t+(ib_1-b_2)\partial_x\\
 {}+ic_1-c_2\end{array} & 0  \end{array} \right)
\end{gather}
due to the explicit forms of the odd matrices $\sigma_1$ and $\sigma_2$. Such a
problem leads to a set of two third-order equations, which take the following forms,
where the
functions $\alpha_i$, $\beta_i$, and $\gamma_i$, are the $x$-independent parts of
$a_i$, $b_i$, and $c_i$ $(i=1,2)$, respectively:
\begin{subequations}
\begin{gather}
\frac{i}{8}\alpha_2W^{'''}-\frac{3i}{4}\alpha_2 W^2W'-\frac{i}{4}\ddot \alpha_2 x^2W'
-i \dot \beta_2 x W'
-\frac{1}{4}\dot \alpha_2W'+\gamma_2W'\nonumber\\
\qquad {}-\frac{i}{4}\dot \alpha_1 W^2-\frac{i}{2}\ddot \alpha_2 xW-i\dot \beta_2W
 -\frac{i}{4} \mathop{\alpha}\limits^{\ldots}\!{}_1x^2-i \ddot \beta_1x
 -\frac{1}{4}\ddot \alpha_1+\dot \gamma_1=0
\end{gather}
and
\begin{gather}
-\frac{i}{8}\alpha_1W^{'''}+\frac{3i}{4}\alpha_1 W^2W'+\frac{i}{4}
\ddot \alpha_1 x^2W'+i \dot \beta_1 x W'
+\frac{1}{4}\dot \alpha_1W'-\gamma_1W'\nonumber\\
\qquad{}-\frac{i}{4}\dot \alpha_2 W^2+\frac{i}{2}\ddot \alpha_1 xW+i\dot \beta_1W
 -\frac{i}{4} \mathop{\alpha}\limits^{\ldots}\!{}_2x^2-i \ddot \beta_2 x
 -\frac{1}{4}\ddot \alpha_2+\dot \gamma_2=0.
 \end{gather}
\end{subequations}
These inhomogeneous nonlinear equations simultaneously
admit the particular solution (3.8), so that
we can in this supersymmetric context search for the general solution
\begin{gather}
W(x)=W_0(x)+W_1(x),
\end{gather}
where we accept
\begin{gather}
W_1(x)=ax+b, \quad a,b=\mbox{const},
\end{gather}
and where we have to discuss the two cases $W_0=0$
or $W_0\not =0$. Such a discussion is analogous to the one
developed in NRQM through Eqs. (2.5), (2.7), and (2.12).

Let us (first) consider $W_0(x)=0$, so that
\begin{gather}
W(x)=W_1(x)=ax+ b.
\end{gather}
Here again we can distinguish $a=0$ and $a\not=0$. Both cases lead to
12 (odd) supersymmetries. In particular, if $a=\omega$, $b= 0$,
this context coincides with the supersymmetric
harmonic oscillator already visited and
characterized by this maximal number of odd supersymmetries~\cite{9}.

Then let us (second) take $W_0\not=0$ and insert the value (3.13) in
Eqs. (3.12). For arbitrary $W_0$, it is once again interesting to
distinguish between the two cases $a=0$ and $a\not=0$. Such a
discussion leads to at least two odd super-symmetries, which appear
on the forms
\begin{gather}
Q_1^{(1)}=i\sigma_1\partial_x-\sigma_2W(x) \quad  \mbox{and} \quad
Q_1^{(2)}=i\sigma_2 \partial_x+\sigma_1W(x).
\end{gather}
We also point out that they generate the simplest $N=2$ superalgebra
sqm(2) initially introduced by Witten~\cite{7}. We effectively have
\begin{gather}
\{Q_1^{(1)}, Q^{(1)}_1\}= \{Q_1^{(2)},
Q^{(2)}_1\}=-2\partial^2_x+2W^2(x)+2\sigma_3W'(x) =4H_{SS}= 4i \partial_t, \nonumber\\
 \{Q_1^{(1)}, Q^{(2)}_1\}=0, \quad  [Q_1^{(i)}H_{SS}]=0, \quad i
= 1,2.
\end{gather}

In order to complete our classification of admissible interactions
characterized by odd supersymmetries, we now want to determine the
impact due to each symmetry on the superpotentials $W_0(x)$ left
arbitrary in Eq. (3.13). This can be studied by quoting the general
forms of our arbitrary functions $\alpha_i$, $\beta_i$,  and
$\gamma_i$ (depending only on~$t$) appearing in Eq.~(3.12). When
$a=0$, these functions are obtained in terms of the 12 arbitrary
constants $A_{(0)}$, $B_{(0)}$, $C_{(0)}$, $D_{(0)}$, $E_{(0)}$, $F_{(0)}$,
$G_{(0)}$, $H_{(0)}$, $K_{(0)}$, $L_{(0)}$, $M_{(0)}$, and $N_{(0)}$ (the
subscript refers to this $a=0$ case) as follows:
\begin{gather}
\alpha_1(t)=\frac{1}{2} A_{(0)}t^2+B_{(0)}t+C_{(0)}, \nonumber\\
\alpha_2(t)=\frac{1}{2} D_{(0)}t^2+ E_{(0)}t+ F_{(0)}, \nonumber\\
 \beta_1(t)=- \frac{1}{4}b D_{(0)}t^2+ G_{(0)}t+ H_{(0)},\nonumber\\
 \beta_2(t)= \frac{1}{4}b A_{(0)}t^2+ K_{(0)}t+ L_{(0)},\nonumber\\
\gamma_1(t)=\frac{1}{4}A_{(0)}t\left(1+\frac{3i}{2}b^2t\right)
+\frac{i}{4}B_{(0)}b^2t+iK_{(0)}bt+M_{(0)},\nonumber\\
\gamma_2(t)=\frac{1}{4}D_{(0)}t\left(1+\frac{3i}{2}b^2t\right)
+\frac{i}{4}E_{(0)}b^2t-iG_{(0)}bt+N_{(0)},
\end{gather}
while, when $a\not=0$, they are given by
\begin{gather}
\alpha_1(t)=A \exp
(iat)+B\exp(-iat)+iC \exp(3iat)-iD\exp(-3iat),\nonumber\\
\alpha_2(t)=E \exp (iat)+F\exp(-iat)+C \exp(3iat) + D\exp(-3iat),\nonumber\\
\beta_1(t)=\frac{i}{2} b[A\exp(iat)-B \exp(-iat)]+i[K \exp(2iat)-L
\exp(-2iat)]\nonumber\\
\phantom{\beta_1(t)=}{}
-\frac{3}{2}b[C\exp(3iat)-D\exp(-3iat)]+M,\nonumber\\
\beta_2(t)=\frac{1}{2}b[E \exp(iat)-F
\exp(-iat)]+K\exp(2iat)+L\exp(-2iat)\nonumber\\
\phantom{\beta_2(t)=}{}+\frac{3i}{2}b [C \exp(3iat) - D \exp(-3iat)]+ G,\nonumber\\
\gamma_1(t)=\exp(iat)\left(iP+\frac{1}{4}aE+\frac{1}{4}b^2E+\frac{i}{4}aA+\frac{i}{4}b^2A
\right)\nonumber\\
\phantom{\gamma_1(t)=}{}-\exp(-iat)
\left(iQ-\frac{1}{4}aF+\frac{1}{4}b^2F+\frac{i}{4}aB-\frac{i}{4}b^2B
\right)\nonumber\\
\phantom{\gamma_1(t)=}{}
+2ib[K \exp(2iat)+L\exp(-2iat)]-C
\exp(3iat)\left(\frac{3}{4}a+\frac{9}{4}b^2\right)\nonumber\\
\phantom{\gamma_1(t)=}{}
-D\exp(-3iat)\left(\frac{3}{4}a-\frac{9}{4}b^2\right),\nonumber\\
\gamma_2(t)=P\exp(iat)+Q\exp(-iat)+2b
[K\exp(2iat)-L\exp(-2iat)]\nonumber\\
\phantom{\gamma_2(t)=}{}
+\frac{3i}{4}C\exp(3iat)
(3b^2+a)+\frac{3i}{4}D\exp(-3iat)(3b^2-a),
\end{gather}
showing once again 12 arbitrary constants.

As an example, let us introduce (3.13) and (3.14) in Eqs. (3.12)
when $a=0$, i.e., when $W(x)=W_0(x) + b$. By exploiting the
relations (3.18) when only the constant $A_{(0)}$ is nonzero, we
finally obtain three time-independent conditions on $W_0(x)$, which
are
\begin{gather*}
W^{'''}_0-6W_0(W_0+2b)W'_0=0,
\\
2bxW'_0+W_0(W_0+4b)=0,
\\
x(xW'_0+2W_0)=0.
\end{gather*}
They are easily handled for getting the unique solution $W_0(x)=0$.
This $A_{(0)}$ context leads to the symmetry operator
\begin{gather}
Q_1^{A(0)}=\sigma_1\left(\frac{i}{2}t^2\partial_t+ \frac{i}{2}tx\partial_x+
\frac{1}{4}x+ \frac{1}{4}bt^2W-\frac{1}{8}t^2W^2 +\frac{i}{4}
t-\frac{3}{8}b^2t^2\right)\nonumber\\
\phantom{Q_1^{A(0)}=}{}+
\sigma_2\left(
\frac{i}{4}bt^2\partial_x+\frac{1}{2}btx+\frac{i}{8}t^2W'-\frac{i}{4}t^2W\partial_x-\frac{1}{2}txW\right).
\end{gather}
By collecting all the similar information for the whole set of odd
(super)symmetries associated with the case $a=0$, we finally
determine besides the maximal (12) and minimal~(2) numbers of odd
supersymmetries already obtained that only three intermediate cases
can occur: either $W(x)=\pm 1/x$ admits ten (odd) symmetries; or
$W(x)=\pm c/x$ admits four (odd) symmetries if $c \not=\pm 1$; or
$W(x) = b + W_0(x)$ admits four (odd) symmetries if we take account
of an extradependence in terms of Legendre functions.

When $a\not=0$, the developments are more elaborate but the complete
results can once again be obtained through the resolution of
relatively complicated nonlinear differential equations. Just as an
example with
\begin{gather}
W(x)=W_0(x)+ax+b, \quad a\not=0,
\end{gather}
let us use Eqs. (3.12), (3.13), (3.14) and insert Eq. (3.19) when
only the arbitrary constant $C$ is nonzero. This case is then
characterized by the functions
 \begin{gather}
 \alpha_1(t)=iC \exp(3iat), \quad
\alpha_2(t)=C \exp(3iat),\nonumber\\
\beta_1(t)=-\frac{3}{2}bC \exp(3iat), \quad \beta_2(t)=\frac{3i}{2}bC
\exp(3iat),\nonumber\\
\gamma_1(t)=-\frac{3}{4}aC \exp(3iat)-\frac{9}{4}b^2C \exp(3iat),
\nonumber\\
\gamma_2(t)=\frac{9i}{4}b^2C \exp(3iat)+\frac{3i}{4}aC \exp(3iat).
\end{gather}
Thus we get the following third-order (nonlinear) differential
equation on $W_0(x)$:
\begin{gather}
W^{'''}_0=6W^2_0W'_0-12(ax+b)^2W'_0+12(ax+b)W_0W'_0-36a(ax+b)W_0,
\end{gather}
or, in terms of $W(x)\equiv (3.21)$,
\begin{gather}
W^{'''}=6W^2W'-18(ax+b)^2W'-6aW^2-36a(ax+b)W+ 54a(ax+b^2).
\end{gather}
Such an equation has already been quoted and solved in the
literature~\cite{13}: it corresponds to the derivative of a Painlev\'e
IV-type equation and leads to the solution~\cite{13}
\begin{gather}
W(x)=\epsilon\frac{dP_4}{dx}(0,\delta; x)+\frac{\epsilon}{\mu}
\left(x+\frac{b}{a}\right).
\end{gather}

Now, by collecting all the corresponding information for the whole
set of odd (super) symmetries associated with the case $a \not=0$,
we see that only five intermediate cases can occur: Either $W(x)=\pm
1/(ax+ b) + ax + b$ admits ten (odd) symmetries; or $W(x)=c/(ax+b)+
ax+b$ admits four (odd) symmetries if $c\not=\pm 1$; or $W(x) =
W_0(x)+ax+b$ admits four (odd) symmetries if $W_0$ is a solution of
Eq. (3.23); or
\[
W(x)=\frac{d \exp(\pm ax^2)}{d\mp c \int \exp(\pm ax^2)dx}+ax
\]
admits three (odd) symmetries; or
\[
W(x)=\frac{c \exp(\frac{1}{2}b^2x^2 \mp 2bx)}{d\pm c \int \exp(
\frac{1}{2}b^2x^2\mp 2bx)dx} \mp \frac{1}{2}b^2x+b
\]
admits three (odd) symmetries.

Consequently, we can summarize in Table~2 the specific families of
superpotentials admitting odd supersymmetries.

Already mentioned in the even context, we notice once again that the
free case, the linear case, and the harmonic oscillator case are
also involved within the same class $1'$ and that their 12 odd
supersymmetries can be quoted [in correspondence with (3.9)] in the
forms
\begin{gather} [(H_B, C_{\pm}, I, P_{\pm})\sigma_1] \quad \mbox{and} \quad [(H_B,
C_{\pm}, I, P_{\pm}) \sigma_2]
\end{gather}
according to old notations~\cite{9} and remembering that $\sigma_1$ and
$\sigma_2$ are the two odd matrices of $Cl_2$.

\begin{center}
\footnotesize

{\bf Table 2.}\\[2mm]
\begin{tabular}{@{}c@{}c@{}c@{}c@{}}
\hline
Classes &   $\begin{array}{c@{}} \mbox{Number of}\\
\mathcal{E} \ \mbox{super-} \\ \mbox{symmetries}\end{array}$
   & $\begin{array}{c@{}} \mbox{Explicit forms of} \\
   \mbox{associated superpotentials}\end{array}$  & Characteristics \\
\hline
$1'$ &  $12$        & $W(x)=ax+b$      & $\begin{array}{c@{}} \mbox{Free case}\\
\mbox{Linear case} \\ \mbox{Harmonic oscillator \cite{9}}\end{array}$   \\
$2'$ &  $10$        & $W(x)=c/x$       &  $c=\pm 1$ \\
$3'$ &  $10$        & $W(x)=ax+b+c/(x+b/a)$       &  $a\not=0, \ c=\pm 1$ \\
$4'$ &   $4$            & $W(x)=ax+b+c/(x+b/a)$       &  $a\not=0, \ c\not=\pm 1$ \\
$5'$ &          & $W(x)=c/x$       &  $c\not=\pm 1$ \\
$6'$ &   $4$       & $\begin{array}{c@{}} W(x)=b+W_0(x) \\
\mbox{if} \ W^{'''}_0-6W^2_0W'-12bW_0W'_0-6b^2W'_0=0 \end{array}$   &  $a=0$ \\
$7'$ &          & $\begin{array}{c@{}} W(x)=ax+b+W_0(x)\\
\mbox{if} \ W^{'''}_0-6W^2_0W'-12(ax+b)W_0W'_0\\
{} +12(ax+b)^2W'_0+36a(ax+b)W_0=0\end{array}$
 &  $a\not=0$   \\
$8'$ & $3$ & $W(x)=ax+ \frac{c\exp(\pm ax^2)}{d\mp c \int \exp(\pm
ax^2)dx}$   &
$a\not=0, \ c\not=0$ \\
$9'$  &   & $W(x)=\mp
\frac{1}{2}b^2x+b+\frac{c\exp(\frac{1}{2}b^2x^2\mp 2bx)} {d\pm c
\int \exp (\frac{1}{2}b^2x^2\mp 2bx)dx}$ & $b\not=0, \ c\not=0$ \\
$10'$ &  $2$         & $W(x)=W_0(x)+ax+b, \ W_0\not=\mbox{above \ forms} $     & $\cdots$    \\
 \hline
\end{tabular}
\end{center}

\subsection{Supersymmetries and invariance superalgebras in SSQM}

We can now superpose the results on even and odd supersymmetries
collected in Tables~1 and~2, respectively. If such a superposition
is relatively direct for superpotentials belon\-ging to the classes
$1$, $2$, $3$, $4$ and $1'$, $2'$, $3'$, $4'$ due to their similar forms, it is
evident that the superposition of all other information becomes
relatively tedious and that it is not interesting to insist on the
corresponding properties.

Besides the information on the maximal number $24$ $(=12+12)$ of
supersymmetries associated with the classes 1 and $1'$, as well as
on the minimal number $6$ $(=4+2)$ associated with the classes 10 and
$10'$, we can distinguish what are the superstructures generated by
some subsets of operators. We have determined that only three
(closed) invariance Lie superalgebras can be pointed out. We have
summarized these structures and their associated properties in Table~3.
We evidently recover the expected results~\cite{9} for the
supersymmetric harmonic oscillator but also find new ones for the
Coulomb and the Calogero problems.

We notice that only a few cases are priviledged in this
supersymmetric context when we require invariance su
perstructures.

\setcounter{equation}{0}

\section{Comments and conclusions}

As already noticed (and expected), the free case leads to the
largest number (24) of Supersymmetries and to the largest
(13-dimensional) kinematical invariance superalgebra. These results are
also valid for the linear case and the harmonic oscillator context,
which, both, are isomorphic to the free case as it is true in NRQM.
In fact, let us point out that for those three cases we are dealing
with the superpotential given by (see Table~3):
\begin{gather}
W(x)=ax+b,
\end{gather}
so that the corresponding supersymmetric Hamiltonian (1.2) is
\begin{gather}
H_{SS}=\frac 12 p^2 +\frac 12 (a^2 x^2 +2abx+b^2)+\frac 12 a\sigma_3.
\end{gather}
Then, by using the unitary transformation
\begin{gather}
U=\exp[(i/2)at\sigma_3],
\end{gather}
immediately gel for the operator $\Delta_{SS}\equiv (3.3)$, i.e.,
\begin{gather}
\Delta_{SS}\equiv -i\partial_t+H_{SS},
\end{gather}
that
\begin{gather}
U\Delta_{SS}U^{-1}=\left[-i\partial_t-\frac 12 \partial_x^2 +\frac 12(a^2 x^2+2abx+b^2)\right] I_2.
\end{gather}
This expression corresponds to the NRQM context characterized by the
potential (2.6), but amplified by the identity matrix $I_2$
belonging to the Clifford algebra $Cl_2$. We thus recover the six
symmetries obtained by Niederer~\cite{1} multiplied here (four times) by the
ele\-ments of $Cl_2$ leading to $12\mathcal {E}+12\mathcal{O}$, i.e., to 24
supersymmetries~\cite{9} characterized in Eqs.~(3.9) and (3.26). Among them
only 13 close and lead to the largest kinematical invariance
superalgebra ${\rm osp}(2/2)\Box \,{\rm sh}(2/2)$~\cite{14}. Associated with these
comments are changes of variables easily determined from the
formulas (2.9)--(2.11) and directly connected with other results
\cite{1,15} when, for example, $a=\omega$ and $b=0$.

Let us also insist on the specific interest of the simplest Witten
superalgebra sqm(2) considered in Eqs.~(3.17) and recovered as a
part of the minimal closed superstructure found in Table~3. We
immediately notice that
\begin{gather}
{\rm osp}(2/2) \supset {\rm osp}(2/1) \supset {\rm sqm}(2),
\end{gather}
a physical chain of particular interest.

Besides the general conclusions that can be drawn from the tables
and more particularly from Table~3, let us recall that different
types of superpotentials have already been studied in SSQM (see more
particularly the reviews of D'Hoker et al~\cite{16} and of Lahiri et
al~\cite{17}). All these superpotentials fall into one of the classes 1--4
contained in Table~3, as well as those we have considered as
partner potentials in parasupersymmetric quantum mechanics~\cite{18}.

\subsection*{Acknowledgment}

We want to thank Dr. J. Lombet for interesting information
concerning nonlinear differential equations.

\newpage

\begin{center}
\scriptsize

{\bf Table 3.}\\[2mm]
\begin{tabular}{@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}}
\hline
&& \multicolumn{3}{@{}c@{}}{Number of supersymmetries} &
\multicolumn{2}{@{}c@{}}{Invariance Lie superalgebras} & \\
 \hline
& &&&&&&  \\[-3mm]
&  Superpotentials & $\mathcal{E}$  &  $\mathcal{O} $  & $N=\mathcal{E}+\mathcal{O}\; $ &
Dimension ($d$) &
Superstructure  & Characteristics \\
$1$ & $W(x)=ax+b$ & $12$ & $12$ &  $24$ & $d=13$ & ${\rm osp}(2/2)\Box
\,{\rm sh}(2/2)$ & $\begin{array}{@{}c@{}} \mbox{Free case}\\ \mbox{Linear case} \\
\mbox{Harmonic} \\ \mbox{oscillator \cite{9}}\end{array}$ \\
$2$ & $W(x)=c/x \left|\begin{array}{@{\,}l@{}} c=\pm 1, \\ c\not= \pm 1, \ c\not=0
\end{array} \right. $ & $\begin{array}{@{}c@{}} 10 \\ 8 \end{array}$  &
$\begin{array}{@{}c@{}} 10 \\ 4 \end{array}$  &
$\begin{array}{@{}c@{}} 20 \\ 12 \end{array}$  &
$\begin{array}{@{}c@{}} d=7 \\ {} \end{array}$  &
 $\begin{array}{@{}c@{}} [{\rm osp}(2/1)\Box \, {\rm so}(2)]\oplus {\rm gl}(1) \\ {}
 \end{array}$ & $\begin{array}{@{}c@{}} \mbox{Coulomb} \\
\mbox{Calogero}\end{array}$ \\
$3$ & $\; W(x)=ax+c/x \left| \begin{array}{@{\,}l@{}}  c=\pm 1, \\ c\not= \pm 1, \ c\not=0
\end{array} \right. $ &
$\begin{array}{@{}c@{}} 10 \\ 8 \end{array}$  &
$\begin{array}{@{}c@{}} 10 \\ 4 \end{array}$  &
$\begin{array}{@{}c@{}} 20 \\ 12 \end{array}$  &
& &  \\
$4$ & $W(x)\not= \mbox{above \ forms} $ & $8,6, \mbox{or} \ 4\;\;$
& $4,3, \mbox{or} \ 2\;\;$ & $12 \leq N \leq 6$
& $d=5$ & $[{\rm sqm}(2)\Box \,{\rm so}(2)]\oplus {\rm gl}(1)$ &$\cdots$  \\
 \hline
\end{tabular}
\end{center}

redpajama_set_name: RedPajamaArXiv


text:
Preparing for Prosperity
April 20, 2021 China Report ASEAN Development Leave a comment
Xinjiang residents develop skills to thrive in the future
Kucha City is known for amazingly distinctive scenes of China's western regions, but also for its peace and tranquility. Its senior residents enjoy chatting in the sun. Children and young people on electric bicycles wave as they pass.
Kucha is situated where the ancient kingdom of Qiuci was located. Qiuci occupied a strategic location north of the Taklamakan Desert along the ancient Silk Road. Its grotto art is even older than that of the Mogao Caves in Dunhuang, Gansu Province. Kucha is now under the jurisdiction of Aksu Prefecture, Xinjiang Uygur Autonomous Region, and remains home to various ethnic groups including Uygur, Han, Hui, and Mongolian.
Fashion Dream
Barely 50 square meters large, the workshop of Adila Clothing Co., Ltd. in Kucha is bustling at most hours. Founder Adila frequently shuttles between the sewing machines and the exhibition area for colorful ready-towear clothes. The company is a comprehensive garment manufacturer that integrates design, tailoring and sewing. It produces school uniforms, security uniforms, curtains, dresses, and travel products.
"I designed this qipao [a traditional Chinese dress] using Atlas silk with Uygur characteristics," she revealed. "I also tried to add elements of Qiuci culture into the design, which many people like." Adila plans to leverage her strength in design to build her own brand of garments.
Employees of Adila Clothing Co., Ltd at work. They are all local women.
After graduating from Xinjiang Medical University, Adila decided not to become a doctor. Instead, she headed to Beijing Institute of Fashion Technology (BIFT) to study clothing and apparel design to satiate her ambitions in fashion design. After graduating from BIFT, she was hired as design director for a garment company in Hebei Province at a high salary. However, Adila ultimately decided to return to her hometown. "When I went back to visit my family, I realized that many women in my hometown lacked jobs or professional skills to make a living," she recounted. "All they could do was stay home and take care of their children. So, I decided to quit my job in Hebei and come back to Kucha to start a business. I wanted to use what I learned to help local women earn money."
Adila received considerable support from the local government, which provided her a work space and equipment and helped her hire local women. In August 2018, Adila Clothing Co., Ltd. was established. The new and small company didn't have many orders at first, but thanks to the local government support and her own efforts, the business volume grew steadily soon. Now, the fastgrowing company is capable of producing four to five thousand pieces of clothes a month. In 2019, Adila's sales reached 400,000 yuan (US$ 62,000).
Although the business is growing, Adila remains modest. "I'm not just the boss," she said. "I am also one of the tailors, and I work every day. Most importantly, a lot of women are encouraged by working alongside me. I believe we are all embracing a better future."
In the future, Adila plans to adopt the model of "company+households" to expand her business and create another 100 jobs in her hometown while building her own brand. "I want a brand from Xinjiang to become popular across China and even around the world."
Highway to a Better Life
Kangcun Village of Age Township, Kucha City, is located at the start of the famous Duku Highway connecting Dushanzi District and Kucha City on China's National Highway 217.
Blocked by mountains, Age Township used to be the only community in extreme poverty in all of Kucha. Villagers continued subsisting by planting crops, raising animals, and doing odd jobs until recently. Construction of Duku Highway enabled Age Town and Kangcun Village to regain vitality. New industries like tourism developed quickly thanks to support from the local government. New houses are rising, and villagers are earning more money through technical jobs and tourism services.
Muhammad is a villager from Kangcun. He has witnessed the rapid development of the village and benefited greatly from it. Only five years ago, Muhammad and his wife lived on temporary jobs because they lacked education and skills. The family could barely cover daily expenses.
To help villagers find jobs, the local government offered free training classes on working skills and standard Chinese. Muhammad and his wife participated and got hired at a local coal cleaning plant. Jobs in the plant are more secure and reliable, and the yearly income of Muhammad's family has jumped to nearly 100,000 yuan (US$15,500).
"In the past we lived in shanty houses with dirt floors, and all the roads were unsurfaced," he said. "But now we live in new and beautiful houses and have asphalt roads. It has been dramatic." Muhammad smiled when recounting the changes in his hometown. "Since Duku Highway opened, our life has changed tremendously. Villagers opened restaurants and shops and started engaging in tourism and transportation industry. My family income is only at a medium level in the village."
After embracing a better life, Muhammad started making plans for the future. He did not get much schooling in his younger years, so he is keen on investing in his daughter's education so she can make greater contributions to the country and society. Starting a business is part of Muhammad's plans.
"Our village has many coal mines, and demand for coal transportation is big," he said. "I want to get a driver's license and then buy a large trailer to transport goods. The work may earn me tens of thousands of yuan each month."
Muhammad is also planning to travel to other places in China with his wife and daughter. "I have seen a lot of pictures of cities in different parts of the country," he said. "The scenes were impressive, and I look forward to visiting such places. We might join a tour group to the southern coastal city of Sanya. I want my daughter to see the sea."
By Pan Zheng, Ran Shanchuan
Previous Post: Like Seeds of a Pomegranate
Next Post: A Big Job


Akhashmaas is a garden world with an environment conductive to most sophonts. The system has a population between 10,000 and 100,000, lacking the population to be an agricultural supplier. This world is a satellite of a gas giant or another planet in the system. This is a temperate world, with a climate of average temperatures. It is a member of Third Imperium in the Kuriishe Subsector of Dagudashaag Sector and in the Domain of Vland. Akhashmaas, as a member world of the Third Imperium, holds the estate of an Imperial knight and a baronet. Both are members of the Imperial Nobility charged with overseeing the world. During the Long Night this world was named Uushkhaa.
The world is the first satellite of the double ringed small gas giant Aakaii, the second planet of the star system. There are a further two gas giants further out from the Aaakaii. The only other notable astrographic feature is a small rocky planet in the inner orbit, a baked, barren world with little to recommend it to the traveller.
Akhashmaas is some 150 million kilometres out from the G1 V star, but is surprisingly earth-like. The sky is dominated by Aakaii, visible even in the daylight. Perhaps the only reason that this planet has not been settled extensively (only having a population of 45,000) is that the atmospheric pressure is twice Terran normal.
Despite abundant natural resources it wasn't heavily exploited, probably as a result of the easier profits to be made investing in the previously settled systems in the cluster, or on the Sylean Main. The first serious investment came during the Second Imperium, when a mining facility was built to support limited operations in the two asteroid belts which dominate the second and third orbits out. However, extensive operations were never developed, and the facility was closed down some hundred years before the onset of the Long Night.
Originally designated Station Seven by the Imperium to enable them to covertly spy on the Kuriishe Eraki, the planet was abandoned by 40.
Initial surveys by the IISS showed that the two belts had limited deposits of some rare earth materials, and a colonisation programme was instigated during the late 200s.
Akhashmaas was subsequently settled by a team lead by a retired Vilani scout under an Imperial Charter, who named the world after one of the legendary heroes who fought against the Ancient's war machines on Vland. Following many years of service, Irka Laparkikumiin was looking for a world to settle down away from the pressures of the Imperial expansion, and the almost constant warfare of the early Third Imperium.
This page was last modified on 14 July 2017, at 00:17.


I am an assistant professor in the Department of Electrical and Computer Engineering (ECE) at the University of Florida (UF). My research interests include design automation of System-on-Chips and energy-efficient systems, formal verification, hardware security validation, and post-silicon validation and debug. I received my Ph.D. from the Department of Computer and Information Science and Engineering (CISE) at the University of Florida, 2018. I received my B.Sc. and M.Sc from the Department of Computer Engineering at the University of Tehran, Tehran, Iran in 2010 and 2013 respectively. For more information, please refer to research and publication pages.
I am looking for highly motivated and hardworking students with a solid background in computer engineering, electronics, and mathematics. If you are interested, please send me a copy of your CV as well as a summary of your relevant research experiences.


text:
HAM is een historisch Nederlands merk van auto's en motorfietsen dat gevoerd werd van 1902 tot 1907.

De bedrijfsnaam was: Haarlemsche Automobiel- en Motorrijwiel Fabriek, Heemstede-Haarlem (H.A.& M.F). Deze onderneming was een voortzetting van motorfiets- en automobielbouwer Altena. Het merk HAM kwam voort uit het merk Altena waaronder het bedrijf eerder handelde. H.A.& M.F bouwde in 1906 de eerste Nederlandse gemotoriseerde ambulance.

Het bedrijf moest in 1907 wegens faillissement zijn deuren sluiten in een periode dat Nederland getroffen werd door een economische depressie die bijvoorbeeld ook Spyker ten onder deed gaan.

Nederlands automerk
Nederlands historisch motorfietsmerk


text:
Manafinder
Manafinder Review: Classic JRPG with a Twist
Manafinder pits itself as a classic JRPG-style game but it ends up being something different. While managing to riff off classic JRPGs Manafinder finds its own identity by having only one character and streamlined gameplay and storytelling. While having its pitfalls the game carries itself through as a fun time.
Srinivasa 2022-11-29
Manafinder pits itself as a classic JRPG-style game, with turn-based combat that is reminiscent of the early Final Fantasy games. But Manafinder is very different from those games in many ways. For example, whereas all the Japanese-style turn-based RPGs have a team of main characters, Manafinder only has one character to play as. It means that there are not multiple kinds of character classes to play as. But it rather implies that there is only one kind of playstyle that one can pursue with each playthrough. The game is way more straightforward than most of the classic JRPG games.
On the whole, Manafinder is a way more streamlined game version of a JRPG. This is streamlining with only one character changes a lot about how enemies are designed and how the game plays. Storytelling is also handled interestingly. Manafinder does end up doing its own thing from the classic JRPGs. Here are some changes which work and some which do not.
Manafinder is available on steam for $13.99.
Manafinder - Official Game Trailer HD
1) Story – Interestingly Deep
1.1) Lambda and the Manafinders
1.2) Conflicts of the Setting
1.3) Storytelling and Making Choices
2) Gameplay – Simple and Fun
3) Graphics and Sounds – Meeting the Homage
Story – Interestingly Deep
We play as Lambda; we meet her as she is in jail, being humiliated. It is never sure what crimes Lambda has committed. And she, along with all the other prisoners, is judged by the King to be banished from the city. Through various conversations, it shows how dogmatic the town is. The King is seemingly worshipped as a god. It is apparent at the start that people who are banished are as good as dead because the city, aka the Manacity, is the only safe space in the world.
Banished from Manacity
The city is guarded by a safety shield, and once outside, all the prisoners including Lambda are just terrified. We also meet up with the other prisoners and it is odd. Because people we meet do not seem like criminals but rather just normal people. There are weak families, kids and many others in the group. Lambda is unsure but on the whole, is sympathetic to a mother and child. The people do get end up ambushed by some monsters. This causes chaos and the group is dispersed and killed by the lot. Lamba barely makes it out alive, unsure about the fate of the rest of the companions.
Lambda and the Manafinders
Here is where Lambda is rescued by the titular "Manfinders". Manafinders are explained to be the people who extract Mana from the world and use it for magic. The world of the game is named Aevi, and all the magic and the world stems from Mana. Mana is found across the world in the form of Mana gems. Manafinders are trained to harness this strength. Even the shield of the city from the start is powered through Mana Gems. The city has almost an unlimited supply of Mana as they literally reside on a hill made up of Mana Gems. Whereas people outside have to scavenge and use the gems for survival.
Finding Mana Gems in Manafinder
We as Lamba end up joining the Manafinders in a refugee camp. And Lambda slowly but surely grows through their ranks. Here it becomes a normal hero story with Lambda realizing that she is really good as a Manafinder. As she movies through the places in and around the camp with various quests, it is a pretty standard hero's journey. We meet many quirky characters to interact with in the camp.
It is fine but not the most important part of the story. Sadly Lambda is one of the blandest characters I have ever played as. It is like a homage to FF1 where the main character has almost no personality. I understand the homage but it seems like a missed opportunity, not really developing the main character. She does have a fun distinct look to her which is good. But that is not the most important or interesting part of the story.
Conflicts of the Setting
So here is where the central conflict of the story comes in. The people who live outside the Manacity have their own mana shield to protect themselves. Manafinders try to find the Mana to keep the shield up. This inadvertently leads them to be very much reliant on it. The world outside is not just in the refugee camp, though. A set of people believe that the over-reliance on Mana is horrible and that everyone must go back to a world with no Mana. These people are known in-game as barbarians.
Barbarians in Manafinder
They live outside and are brutal to a point. They do make sense in a way. Even the gods of the land reflect this divide. The Barbarians do make many good points with the Manafinders. Showing how brutal and uncaring the people of the city have become. With no one questioning the king. There are four gods of the land out of which three of them are really supportive of the Mana and its usage. At the same time, the fourth goddess is very adamant against using it. We interact with these gods a lot and their internal bickering and conflict are fun to watch. They are fun and slowly give a lot of revelations about the story, something that I won't be mentioning in the review. Do go experience them first-hand.
Storytelling and Making Choices
As seen from the pictures and the trailer the story is told mostly with the character and text boxes, but there are some really well-animated cutscenes which do help the visual flair of the story. Nut other than that the whole game relies on its retro style and characters talking to Lambda as she does not respond directly. It is like they are talking to a namely protagonist. Most of the world-building is actually optional but I think it is necessary to pay attention.
There are choices to make which to end up causing different endings to the story. They are not obvious yes or no choices but rather small ones which you chose as you go along. But this kinda taking up different endings has a few problems. Near the end, when the story pivots into a choice, many threads which were set in the quests before are just left behind. This is because they do not directly contribute to the present storyline anymore. Many plot threads are left dangling. I understand the pivot, but it does feel empty like those stories ceased to exist because you went another way. But on the whole, the endings do feel justified. With almost 15 hours to reach an ending, it is good, but the side quests do get annoying as one goes.
Gameplay – Simple and Fun
As mentioned, the gameplay is very much streamlined. if one knows how to play a JRPG, then you are in. It is simple and actually way easier than most the JRPGs. For most of the same, all you have is Lambda and her Dog. Lamba is the only real fighter. the dog is a great help, too but Lambda is the only one the combat with any real depth. She has her basic movies and many weapons which can use to counter different types of enemies. there are also different elements of power which are as obvious as they sound. It is fun and breezy while being hard when it needs to be.
Combat in Manafinder
The other part of this game is exploring the world and fighting enemies to collect spirit dust. Every time you collect enough spirit dust and rest Lambda levels up. When levelling up Lambda can contact the gods and buy upgrades for her. There are also different Manashards which grant new magical abilities. Along with all these the character slows does. It is a fun loop and works pretty well.
Upgrading the stats
Graphics and Sounds – Meeting the Homage
The retro style of the game is really charming and works a lot. The sprites are great and creative. It is really a blast to look at. The menu is a bit clunky to navigate but nothing too complicated. It is functional and not too obtrusive. Almost all the details of the game are in the menu alongside the chapters and play time of the game. The Sprite of Scar (the dog) is also really damn cute so it helps.
Menu Screen in-game
The Music, while it did not stick with me was good. it really matches the tone and feel of the rest of the game while not being abrasive at all. The graphics and sound honestly are what one would need to expect to form a retro throwback JRPG game. and I am glad it did not falter here at all.
King of the Mana city
Sidequest
Cutscenes before boss fight
Navigation and exploring
The Key for Manfinder was provided by Jorge Blanco.
Manafinder pits itself as a classic JRPG-style game but it ends up being something different. While managing to riff off classic JRPGs Manafinder finds its footing in its interesting world, Streamlined combat. But it is not all perfect as it also loses some of the fun complexity of JRPGs.
Fun and streamlined Gameplay
Interesting Story
Beautiful art and visuals
Boring main charecter
Side quests inconsistency
Assassin's Creed's mythology: The twist history needed
Nebuchadnezzar Review: A Return to Classic City Building
Star Ocean: The Divine Force Review – A JRPG Out of This World (PC)
Asdivine Cross Review: Closer to a Classic (XB1)
Barbarian Review– An Instant Classic that Subverts Expectations
Super Smash Bros. Franchise Quiz: Get Ready for Classic Mode
Srinivasa
Srinivasa is Passionate about Games, Movies and art in general, mostly playing games on PC. He loves to discuss and debate about all them until it gets toxic.


Staining products listed in this catalogue are usually kept in stock. Dyes and stains not included within this catalogue may also be available upon inquiry.
All staining and accessory solutions will be sold in glass or plastic bottles corresponding to 2-oz., 4-oz., 8-oz., pint, quart and gallon. Follow label and procedural instructions for bring concentrates or dry gram weights to the correct dilution. All # products required special poison packaging. A fee of $18.00 will be charged for each poison package.
FOB Danvers, MA 01923, net 30 days. Prices are subject to change without notice. There is a $15.00 minimum purchase requirement. Quotations can be made for the purchase of large quantities.
When ordering particular reagents, specify product number, name and reagent(s) and desired quantity. Mail orders to Rowley Biochemical, Danvers Industrial Park, 10 Electronics Ave., Danvers, Massachusetts, 01923 or call (978) 739-4883.
Purchase orders must contain complete shipping instructions, including marking and routing. Chemicals which cannot be sent via UPS/RPS will be shipped Air Freight or with various truck firms.
Although complete instructions are provided with our in vitro diagnostic products, the staining results cannot be guaranteed, inasmuch as sample preparation, skill and technique of the user are the determining factors.
Many of the in vitro diagnostics contain hazardous materials. The burden of safe use of our laboratory products rests entirely with the user.
Returns may be made, if authorized, following the issuance of appropriate shipping instructions. Poisons and hazardous material must be shipped in accordance with Department of Transportation's requirements for handling hazardous materials. We reserve the right to refuse the return of certain items such as those with a limited shelf-life, custom orders or other items which, in our judgment, have limited resale potential, unless the request for return is due to an error on our part. Authorized returns may be subject to a restocking charge when the return is due to customer error.
All orders will be accompanied by a Safety Data Sheet for each and every item.
RT – Store at room temperature, 15°-30°C (59°F – 86°F).
LS – Light Sensitive; protect from exposure to sunlight.
4°C – Store in the refrigerator.
0°C – Store in the freezer.


Habitat for Humanity of Greater Centre County is a nonprofit, nondemoninational housing ministry. Habitat welcomes all people -- regardless of race, religion, ethnicity or any other difference -- to build simple, decent, affordable houses with those who lack adequate shelter.
We construct quality houses that are sold to homebuyer families through no-profit, no-interest loans. Homebuyers complete 350 sweat-equity hours and other requirements, pay for their homes and all upkeep, and maintain current payments on their properties.
Additional information for ReStore can be found by clicking here.


One thing that keeps people tied to the same clothing and the same style year after year is the fear of change. Years ago you may have discovered a formula that works for you and rather than try new looks you stick with the old look because you got a compliment on it 10 years ago. All the while, change is constantly happening all around you. Your career changes, your body changes and your lifestyle changes. Life is constantly throwing you curve balls, egging you on to change. Your style must keep pace with you and shift with the changes in your life.
Occasionally I encounter someone whose style is 10 – 20 years behind. An interesting question to ask this person is when was the last time you felt really good about how you look? The answer often reveals they felt their best 10 – 20 years ago! You can't hold onto your 'glory days' simply by holding onto the clothing from that time. That time has passed, and staying in the old clothes denies the person you have become since then. New glory days are happening and your new style is waiting to be discovered. See me if you don't know where to start!
I am the first to admit I am extremely averse to change and trying new things. I understand the hesitation and the fear. I stayed in a corporate job for 15-1/2 years, a job I did not love, because I didn't know what else to do. I thought if I kept doing the same thing, it would be okay. It wasn't. I was miserable. I loved my company and my co-workers, but I was never able to find satisfaction in my job. Change was begging to happen and I kept putting it off.
Don't put off accepting change as long as I did. Whether it's a new job, a new style or a new city you seek, embrace the change and the adventure. If you need an illustration of how silly it is to think you can avoid change, consider the change happening right under your nose this very second. Our earth rotates on its axis at a speed of about 1,000 miles per hour while rotating around the sun at a speed of 67,000 miles per hour. We are rotating around the center of our Milky Way galaxy at a speed of 490,000 miles per hour while our galaxy is speeding through the universe at a rate of over 2.2 million miles per hour.
Do you really think change isn't going to find you? Change is real, and change is constant. Step out and seize it before it seizes you!
Previous You Can Learn A Lot About Yourself By Cleaning Out Your Closet!


Last month, we began to feel a shift in astral gear, from languid and laidback to full throttle ahead as Mars entered Aries. This spirit of renewal and initiation continues into March as more of the personal planets take their turn to ingress into Aries. Get ready for plenty of action from the get-go, starting with a series of spectacular aspects between the benefics and Uranus in Aries on the 3rd and 4th, bringing about some unexpectedly positive developments, and culminating in a solar eclipse at the spring equinox, which ushers in a brand new six month cycle for our planet. The new astrological year sets everyone off with a bang!
The urge to spring clean your life could loom large at the Virgo Full Moon on the 5th. Coming just a day after a series of remarkable transits between Venus, Jupiter and Uranus, at 18h05 GMT (13h05 EST/20h05 SAST) during which new and rather startling developments could force you to make some important decisions in a very short space of time, this Full Moon could see you letting go of aspects of your life that are no longer working. Reinforcing the theme of catharsis and transition is a trine between the Moon and Pluto, the planet associated with dramatic shifts, purging and elimination. Like a snake shedding its skin, you could find yourself casting off emotionally-driven patterns of behaviour, routines or habits that disempower you, hold you back or make you ill. Surgery is a powerful theme now, as is detoxing and dietary changes. At this time, you'll feel more confident about letting go of relationships or situations that have had their day than you have in a long time; as well as capable of exercising more discernment about who you give your time and energy to. No bad thing – the more you streamline your life now and face whatever is haunting you psychologically, the more ready you'll be to welcome in the exciting changes and new developments that arise at the New Moon solar eclipse on March the 20th.
If the Full Moon on the 5th is about letting go of what is not ideal for you, then this New Moon Solar Eclipse is all about embracing a new way of life and being that allows us to become who we feel we were meant to be. This eclipse comes at an interesting time –at the start of a new lunar cycle and at the Spring Equinox and the beginning of a new astrological year – and at an interesting place in the zodiac – in the last degrees of Pisces, just prior to the Sun's ingress into Aries. As such, I think it should be interpreted as a sort of sacred space between the ideal (Pisces) and the realised (Aries), between imagination and action. In other words, in terms of energy and themes, I think that we can expect the next six months to be very much about trying to realise ideals, put ideas into action and turn dreams into reality. Astrologically, there has never been a better time to begin anew. If you aspire to live a more authentic and spiritually attuned life, then use this energy to begin your journey – carpe diem!
For a more in-depth forecast, visit my March-April 2015 eclipse predictions.
This year, the Sun will ingress into action-oriented and independent Aries on the 20th at 22h45 GMT (17h45 EST/00h45 SAST). Marking as it does in the northern hemisphere the Spring Equinox and the start of a brand new astrological year, this is an important seed moment – a time of renewal and vibrancy, of beginnings and of hope, like sunshine after a rainstorm.
Coming as it does in the wake of a solar eclipse in the final degrees of Pisces, this ingress is infused with a spiritual and creative energy that inspires us to realise our individual potential whilst also working towards the greater good, combining self-fulfillment with a spirit of higher intentionality.
Midmonth, Saturn will station in time for its annual six month long retrograde spell. Between now and early August, you'll feel less restrictions in terms of judgement from yourself or others if you don't get things right first time. With the pressure off, you can feel more freedom to experiment, test out your beliefs against everyday experience and expand your knowledge base, especially when it comes to travel, philosophy, religion and the law. Learning from well-respected teachers, gurus or perhaps through books about other cultures, philosophies or religions are all good ways to open your mind and explore new intellectual horizons.
The only thing you'll want to watch out for is Saturn's re-entry into Scorpio in mid-June, signalling a 3 month period lasting until 1 October when you may need to tie up a few loose ends left over from the last two years. For a recap of what this could mean for you, visit my January 2015 Skylights page and navigate to 'Saturn back into Sagittarius'.
A month after Mercury ended its first retrograde spell, the planet of learning, communicating, travelling, politics and commerce re-enters Pisces on March the 13th. Traditionally, Mercury is not very happy in this sign, mainly because logical thought and the ability to transmit ideas relies on precision, structure and clarity – qualities that subtle but nebulous Pisces is not renowned for. Still, this could be a creative time when your ability to tune into other ways of thinking and other forms of consciousness comes much easier. Meditation, philosophical contemplation and cultivating an active imagination are all possible expressions of Mercury in Pisces. If you are easily confused or have a problem with boundaries, then you may want to take extra time and care in preparing your accounts, or any company contracts or memos because it'll be easy to get muddled up now. Ideally, save tasks such as editing, reviewing or critiques until April when Mercury's ingress into Aries should help to sharpen up your mental faculties again.
After her early celebrations with Jupiter and Uranus, Venus will settle down into a more stable and more established routine when she glides into earthy Taurus on the 17th. Traditionally, Venus is exalted here, no doubt because of the fertility and abundance of this particular sign, which chimes so well with the planet of love's voluptuous and sensual nature. The next few weeks should be about the pleasure of the senses – taking the time to smell the spring blossoms, eat delicious food in good company and generally enjoy the return of nature's beauty and lush bounty to our immediate surroundings. If you enjoyed some passionate encounters or creative peaks when Venus was in Aries, then this could be a time when you consolidate your gains and assess what your next month should be.
Preparing for the next Venus-Jupiter encounter is one way to do so – after her encounter with Jupiter in early March, she will reunite with her fellow benefic in late April when she ingresses into Gemini– a golden period you'll want to take advantage of, especially if you are in the media, communications, education, travel or fashion business. For a recap of key Venus-Jupiter transits during 2015, visit my 2015 Skylights page.
Below are some astrological highlights you won't want to miss during March.
If you thought the Venus-Mars conjunction last week-end was exciting, you'll want to think again. Over the next two days, the two benefics team up with unpredictable and dynamic Uranus in Aries to rock your world – in a big way! Get ready for change – possibly of the unexpected, but certainly of the positive kind. If you've been hankering for adventure or been keen to expand your creative or romantic horizons, then consider this a golden opportunity to live a more authentic life, find a stimulating and thrilling partner to share your life with, or alternatively, carve out more space and autonomy for yourself within existing relationships.
If you want to make a difference in the world, then you could find doors suddenly opening for you around this time. One thing you will not tolerate at this time is restriction of any kind, whether this be social rules or traditional conventions. The words 'no', 'can't' or 'impossible' are not likely to be part of your vocabulary now, and anyone who uses them is likely to find themselves politely dismissed or ignored – and rightly so! Belief in miracles is essential if they are to happen, and right now, anything is possible. The sky's the limit, so don't be afraid to reach for the stars!
The good vibes continue well into March as Mars, planet of action, motivation and physical vitality moves to trine jovial Jupiter. If you've been feeling a bit lacklustre, bored or generally lacking in confidence of late, then get ready for a turbo-charged boost of motivation, verve and joie de vivre! This auspicious aspect is likely to give you back your mojo. Under this transit, you could rekindle a passion for learning, philosophy or travelling, regain your health or rediscover your sense of fun and playfulness. Most importantly, you'll have the energy and enthusiasm necessary to achieve some major milestones politically or socially. This could be a real high point in terms of your social, religious, educational or cultural life. Get ready to shine!
With any highs also come lows and sadly, today we reach another chapter in the story that is Uranus-Pluto as these two planetary heavyweights prepare to do battle once again after wreaking havoc with a spate of brutal beheadings and fatal road and aviation accidents between mid-November and early January. Once again, we are asked to confront the growing gap between the haves and have-nots in society, between the idealism and rebellion of youth and the cynicism and conservativism of old age, and between the violence of revolution and the tyranny of those who want to hold onto power.
As I have watched this aspect surface again and again in relation to violent events such as wars, riots and terrorism, I am struck by the recurring themes of social alienation and injustice that seems to have become an anthem for our times. As the economic and political chasm widens between those in a position of power and privilege, on one hand; and the masses, on the other, many of whom are feeling increasingly exploited and disenfranchised by what they perceive to be a social and economic system that is firmly rigged in favour of the wealthy few, I think that the potential for civil unrest will continue to grow. Sadly, then I expect this aspect to coincide with fresh headlines about brutality in Syria and Iraq, war in Ukraine, and riots and mass killings, especially in those countries affected by the Arab Spring.
On a more personal note, the next few weeks could bring up the shadow side of change, whether this be via dramatic circumstances that force change upon you, or through encountering people who are angry, disruptive or oppressively controlling. Such encounters are most likely to occur if you keep resisting change, even though you know it needs to happen, or are somehow trying to hold other people back, perhaps because you are afraid of losing them. If so, then things could reach a climax of sorts now, perhaps via an emergency or urgent crisis that demands your full attention. My advice: however painful or dire things may seem, try not to hold on or resist what is happening – it'll only make matters worse. Acceptance and adaptation are the two qualities you'll need to survive now, so cultivate them and then let go. The sooner you face up to what needs to happen, the sooner you can make the transition into a new, more authentic way of being that will ultimately benefit everyone.
For more predictions and insights into the astrological weather for March, be sure to 'Like' my Facebook page, or follow me on Twitter, where you'll get access to FREE daily Astro-Insights, news about exclusive special offers on astro-reports and lots, lots more.


This game was nothing like any other game I had ever played before, I never got into Magic for instance. Its structure and mechanics were just so different that it took me several games before I could play coherently. Once I reached that point however strategy as I had never seen before unfolded. The game is played out with two players engaging in conflict in an attempt to gain control of story cards which are placed in the middle; first to three wins. Every turn player will summon characters, support cards (items and places) and events to use in their attempt at the stories. They pay for these cards with domains which gradually grow to larger and larger values, they can drain all of their domains once each turn. The player then commits characters to story(s). Their opponent opposes them with characters of their own. Four struggles are resolved, Madness, Combat, Arcane and Investigation, the player's characters tally their icons and they are compared to determine the winners at the stories. The winner of the madness struggle drives an opposing character insane. The winner of the combat struggle wounds an opposing character. The winner of the arcane struggle may ready an exhausted character. The winner of the Investigation struggle places a success token on the story. After all of the struggles have been resolved, the total skill of remaining characters is calculated for both sides and the attacker achieves success only if their skill is higher than the defender's. Once a player has won three stories, they are victorious.
The game's cards are very visually pleasing and well designed, they have great illustrations. The board is just the right size and also features nice illustration. The Cthulhu domain markers are, to say the least, extremely cool. Although unpainted they look and work just fine.
The base set itself is reasonably priced (around $35-$40) and the expansions while more costly if you get a lot of them aren't that bad either ($7-$10 each). One of the features of this game is that you only have to buy one of each expansion to have all of the cards, no random buying.
This game has a very high replay value, the multiple factions to choose from combined with the deck building aspect make every game different. For me at least this game never gets old.
Unfortunately the learning curve for this game is quite steep, someone who has never played a game of this type will usually take multiple games to be able to start fully grasping the strategy.
While it does incur a significant amount of luck of the draw, due to the deck building aspect, even if a player draws badly, that doesn't lose them the game.
Overall, I loved this game it is fun and very engaging. The replay value is high and I hope to play it many more times.
When using the 'Ritual of Summoning' Silver Twilight Lodge card, keep in mind that it does not require you to summon a character of a specific faction. It can be quite effective to stick a few ancient ones from other factions in your deck to summon as a nasty surprise for your opponent.
I know at least one, possibly more people have put forwards strategies for the chapel, and I mostly agree with them, however, I think that you should be more liberal with it. In my experience the best strategy is to buy one on the first or second turn. When you draw it, trash ALL other starting cards (copper/estates) in your hand, make sure you get silver when you do not draw it in your hand so you don't get stuck moneyless. It will only be a few turns before you have a very sleek deck from which to build something deadly.
Unless (a) the game is nearing its close or (b) you really need to win a race for a specific route, do not use your wilds as part of a normal set. Wild cards are powerful for completing a last minute play, for crossing those confounded canals that require them and for insurance when attempting tunnels; have patience and don't waste them.
When you are playing your trains, and you don't have all of the cards you need to complete your route(s) yet, it's generally a good idea to play on the routes that are confined to a single color first. All too many times you play on that grey route then get stuck drawing the color you just used up.
One player (defender) drafts their army (point value is up to you), the other (attacker) then drafts from remaining units. Initially, the attacker is weaker (with respect to points and terrain), but after each defeat, increase the points available for their draft until they overwhelm the defender (who uses the same army for each fight, it's up to you if they recover losses in between battles), see how many waves the defender can defeat.
Sometimes its it can be more helpful to you, overall, to take an action that is essential to another player, even if it's not the most profitable action with respect to yourself.
Example: you see that Player 1 only has 1 food of the 6 they need, and it is a harvest round. You also see that they have a clay oven and plenty of wheat. you should probably take the bake bread space to make trouble for them (assuming you will be able to meet your own feeding needs regardless).
Don't get me wrong, this game is really fun with just the core set, I played a long time before I bought any expansions. Personally however, I think that the added variation that even just 1 or 2 expansions provide is a great bonus.
Some characters (such as 'The Thing Behind You' (not core set)) let you make some sort of payment other than the normal resource cost. Put one of these cards in a deck of a different faction and give the enemy a nasty surprise.
Interrogation center is a location support card that prevents all neutral characters from committing to stories. Old Sea Dog is a character whose ability lets you exhaust him to make any character lose their faction affiliation (i.e. become neutral). Once you have put interrogation center into play, Old Sea Dog(s) can exhaust to prevent opposing characters of your choice to be unable to commit that turn.
Like a Moth allows you to reduce a character's skill to 0 until the end of the phase. Tear gas is attached to a character, that character gets -1 skill and is immediately destroyed if their skill is ever reduced to 0. This combination also allows you to destroy any character by attaching tear gas to them, then Playing Like a Moth on them, reducing their skill to 0 which causes tear gas to kill them.
Note: This one seems not as powerful as the previous combination because, rather than use an attachment then gain a character, you use an attachment then lose an event.
Strange Delusions is attached to a character and allows you to change their faction temporarily, Emerging deep one requires that you destroy a cthulhu faction character when you bring it out. This combination lets you choose and destroy ANY character your opponent has in play. simply use Strange Delusions to make them Cthulhu faction then play Emerging deep one and destroy them instead of one of your own characters.
When building your deck, smaller is better, get as close to the 50 card minimum as you can. Think of it this way, the less cards you have, the more likely you are to draw the cards that you really need.
With this house rule, when a player declares an attack, before the dice are rolled, the defender may choose to retreat all of their remaining units into an adjacent territory that they control.
At the beginning of a game, look carefully at what cards are being used, and how they might work together. One thing in particular that I always note is: are there any cards that give more than one action? (i.e. Village and Festival) If there are not, then cards that give you lots of draws but no actions (i.e. Smithy and Council Room), should not be sought after, (generally only get one or two at most). Since these cards give no additional action, if they have no support from Village/Festivals, then they end your action playing, often drawing more actions that you are unable to play.
There are many powerful combinations in this game, but one that is pretty easy to use is to stock up on Smithies and Villages more heavily than other types of actions. This will let you (often, not always) lead with a village from your hand, then play a Smithy. This leaves 1 extra action to use if you pick up another action card in the three draws from the Smithy.
When you are playing as Mr. jack, be careful who you choose, if Jack is a weak character, Watson for instance, you choosing him over a strong character, Holmes for instance, will be very suspicious.
When playing Mr. Jack, wins by escaping are much less common, (especially against an experienced player). It is easier to keep characters in the light than in the dark, even in the end, try to keep suspects grouped with other characters to avoid discovery.
Getting a good tray that fits in Agricola's box and has compartments for all of the resources saves lots of set up/clean up time, it also makes a bank that is easy to pass around between players.
Make sure to get rid of your square and square+1 parts before the board gets too crowded, they are some of the harder bits to play late in the game.
Think long and hard before playing a set, whoever plays last has the advantage. On the flip side, don't horde yourself to death.
When in doubt, such as when you don't know the judge very well, always play something funny rather than realistic, most people judge based on comedy value (in my experience anyway).
We all know the feeling, there lies a face up wild, take it or not? If it is early in the game, it is almost never a smart play to take it, you will most likely use every color at some point, and thus ANY two cards are better than one, even if it is wild. Late in the game when time and remaining trains are concerns, sometimes taking the wild is a good play.
1) Is a route 'key'? How long will a detour take you?
2) Is the route colored or wild? If possible, wait to play on wild (grey) roots, claim routes that are confined to one color first.
3) Are there cards you need face up in the draw area? If there are, take them, they are more likely to be taken by other players than the route you might otherwise play on.
Of course, each of these things has to be taken one case at a time, but generally they are sound.
Make sure to keep family growth in mind, even though it costs you more food, a new family member's benefits far outweigh the negative effects, not to mention the points they are worth at the end.
Make sure not to underestimate the power of farmers, they're often the deciding factor when determining the winner. On the flip side, don't commit too many meeples to farming early on or you will be playing at a disadvantage for the rest of the game.
Make sure the players coordinate their character choices so as to have a wide range of abilities, try to avoid having multiple people with very similar characters.
A fun variation (if you have enough expansions for it) is to play with only attack cards, especially ones that give curses, it makes for a very drawn out, low-scoring game, but it can be quite entertaining.
In the beginning, make sure to buy some silver (and gold if possible). In fact, it is often a good idea to buy silvers on both of your first two turns, this guarantees you 5 money in at least one of the two following hands, with a fair chance of 6 (for a gold).
In my (and everyone I play with as well) opinion, the game is much more enjoyable when you disregard the rule that prevents you from trashing a field containing only one bean.
It can be fun to play with the added option of 'promising' someone a card that you don't have when trading. As soon as you receive the type of bean that you owe someone, you immediately give it to them to be planted, no matter whose turn or what phase it is (a player may forgive a debt, in which case, they are not given the bean).
While definitely not recommended for every battle, it can be quite fun to: instead of playing to the usual victory banner conditions, fight to the last man. Whichever side totally eliminates all of the other side's units first is victorious.
My friends and I have a set of noises associated with different actions (i.e. ready to flip over chosen cards, or when you build a card).
It may sound silly, but it's actually quite entertaining and helpful, an easy way to keep track of what's happening and stay in sync.
I love just about all games (all euro-games at least), but currently my favorites are '7 Wonders' and 'Dominion'.


Will it slide? - I Can Teach My Child!
Today we embark on a brand new thematic unit–Penguins! To start us off, we read my favorite penguin book, Tacky the Penguin. Next, we talked about how penguins like to slide on ice.
After that, we decided to try our very own experiment to see which toys slide on ice and which don't.
Here's what you'll need to conduct your own experiment: a shallow pan, water, and 5 (more or less) items to test. You'll also want a pen and paper to make a table showing the results.
1. Add water to a shallow pan and then let it freeze. We just stuck ours outside overnight.
2. Make a recording sheet on paper (or a markerboard). In the meantime, let your little one choose 5 small toys to test to see whether they'll slide or not. I'm sorry I couldn't get the picture to rotate!
3. Put a bowl underneath the pan to create a small angle.
4. Let your little one start testing out their objects! Prior to each, have your child make a prediction about whether that specific object will slide or not.
Afterwards, we talked about whether more objects slid or didn't slide. We then counted how many in each column. This was a super easy "science experiment" that we both enjoyed!
Tacky is an odd bird. He doesn't march in a straight line or dive gracefully into the water like the other penguins. At first, his friends don't appreciate his uniqueness…but after a run-in with some trappers, they come to appreciate Tacky for who he is! Not only is this a fun penguin book, it's also a great way to start a discussion about accepting individual differences in others.
Great idea. I have posted a link from my science blog to this experiment.


The american singer Gwen Stefani is on the cover of the fashion magazine Elle UK for the month of April 2011.
This romantic photoshoot is made by Matthias Vriens McGrath.
The April issue is available on 9 March 2011.


We are crazy for xMangaves here at Peacock Horticultural Nursery. xMangaves are a cross between an Agave and a Manfreda. xMangaves tend to grow much faster than Agaves, and they are polycarpic, so they will flower and set seeds many times before dying. We have many of the new crosses available here @ Peacock Horticultural Nursery, including xMangave 'Moonglow' in the photo. As well as many more, including: xMangave 'Inkblot, xMangave 'Jaguar', xMangave 'Spotty Dotty' and xMangave 'Man of Steel'. And, more new varieties will be available soon. xMangave, like their parents, do not like wet feet in winter, so best planted in a well draining raised bed, or also will do great in pots.