Today, Microsoft presented a new hub for experiencing the 2014 World Cup, which will be played in Brazil. The hub, aptly named 'Destination Brazil', will allow gamers to see live statistics on matches, receive notifications when a match's about to start, as well as premiering Every Street United, a reality TV show produced by Microsoft Entertainment Studios.
The main app, with the live statistics, tweets, and other World Cup information, was developed by Soho Studios, who will be monitoring usage of the app to improve the experience, as he told Eurogamer.
"We don't know what you're going to be doing all of the time," he said. "We've never done this before. We don't know if it's going to be incredibly helpful and you're going to go, 'that's the most amazing thing I've ever had and I can't live without it,' or you'll go, 'yeah, it's kinda cool, but when I'm watching the game I don't want any extra information because it's a bit noisy.' Or, when I'm playing FIFA, just give me all my screen back and when something happens I'll just jump in and check it out.
Microsoft is also pushing the hub as a way to get more users to hook up their cable system to the Xbox One, as Matthew Reid, senior product marketing manager at Microsoft for Xbox sports experiences, told Polygon.
Destination Brazil will be available in Australia, Austria, Canada, France, Germany, Ireland, Italy, Mexico, New Zealand, Spain, the U.K. and the U.S. You don't need an Xbox Live subscription to use it.
If you're a soccer fan, do you plan to use the app?


The North Dakota HOSA program is an organization that provides a unique opportunity for leadership development, motivation, and recognition for secondary, postsecondary, collegiate, and adult students enrolled in health science classes. It is administered through the North Dakota Area Health Education Centers and is expanding in the state. In October, three new chapters were awarded funding through Sanford Health. The three chapters are: North Central Area Career and Technology Center in Rugby, Minot Public School, and Mandan Public School. These schools join a state membership of 303 students and advisors and 16 local North Dakota chapters.
Currently, North Dakota has 16 local HOSA chapters: Bismarck High School, Century High School, Grand Forks High School, Hettinger Public School, Killdeer Public School, Langdon High School, Legacy High School in Bismarck, Mandan High School, Minot Public School, Missouri River Area Career and Technology Center in Bismarck, North Central Area Career and Technology Center in Rugby, North Valley Career and Technology Center in Grafton, Red River High School in Fargo, Sheyenne High School in Fargo, Southeast Region Career and Technology Center in Oakes, and West Fargo High School. These schools are working with students and their future healthcare career. If you are a healthcare provider, contact your local HOSA! Get involved with the future healthcare providers!
This webinar, hosted by the North Dakota Center for Nursing, "State and Federal Resources to Build your Nursing Career Ladder: Resources and Programs for Collaboration between Health Care Facilities and Nursing Education Programs," will take place on November 9 from noon - 1:30 pm. Find the connection information online. No registration necessary.
North Dakota Area Health Education Center has funds available to healthcare provider students doing clinical rotations in rural areas. As long as the student is living in the area as part of the rotation, the student can receive funds to alleviate the cost of travel and housing. Since 2009, North Dakota AHEC has supported a total of 89 health profession students in completing their clinical rotations within the state. Clinical rotation professions have included nursing, dental, physician assistant, and all other health professions.
If you have a student that is participating in a rural clinical rotation, please have them contact Denise Andress at denise@ndahec.org or call (701) 637-0177.
The Rural Collaborative Opportunities for Occupational Learning in Health (R-COOL-Health) Scrubs Academy introduces young students to the wide range of healthcare careers and opportunities by providing hands-on learning from real healthcare professionals. The Academy takes place each summer. Connect on Facebook so you're the first to know about dates and application deadlines.
Marketplace for Kids is a national program that provides outreach and technical assistance to school districts, consortium of schools, youth organizations, and associations interested in youth entrepreneurship. Their goal is to encourage students to become a lifelong partner in building stronger communities. They provide opportunities for students to showcase their "Bright Ideas" and resources for project development. Explore their website for resources, curricula, and ideas for hands-on learning.


text:
QAnon supporters gather over theory that JFK Jr. will emerge, announce Trump to be reinstated
Marina Pitofsky
Some supporters of the QAnon conspiracy gathered in Dallas this week as a theory circulated that John F. Kennedy Jr., who has been dead for more than 20 years, would reappear and announce that former President Trump will be reinstated as president.
Kennedy, the son of former President John F. Kennedy, died in 1999 in a plane crash at the age of 38. But some believers of the QAnon conspiracy theory say that Kennedy did not die, and he is set to return as Trump's vice president, according tomultiple reports.
Although different versions of the theory have circulated, some posts appeared to state that Trump would be reinstated before stepping down. Then, Kennedy would become president and name former national security dviser Michael Flynn vice president, according to multiple reports.
QAnon supporters first gathered Monday night in Dallas before hundreds flocked to Dealey Plaza on Tuesday. Former President Kennedy was assassinated at Dealey Plaza in 1963.
Journalists and other social media users shared photos of the crowds on Twitter and questioned supporters of the conspiracy theory.
Arizona:Ron Watkins, believed to be creator of QAnon, claims he's running for Congress
2020 election:A QAnon conspiracy theory about election fraud is becoming a pro-Trump push for traceable ballots
QAnon falsely claims that there is a satanic "deep state" that supports a child sex trafficking ring. Supporters of the conspiracy theory played a prominent role in the Capitol riot on Jan. 6.
The group has previously claimed Trump won the 2020 presidential election, he will be reinstated as president, that there will be a "storm" leading to a roundup of celebrities and more.

redpajama_set_name: RedPajamaCommonCrawl


Gift cards are ubiquitous these days. People buy them for gifts, for loyalty points they provide and as an easier way to pay for goods and services without having to carry around cash. Originally you could only buy a gift card from the retailer or restaurant that would ultimately redeem the gift card. Now you can buy a gift card for any number of business from any number of different businesses which raises the question, when a business sells a gift card from a different business, should they book the revenue from that sale at the gross amount (the amount they sold it for) with the cost reflected as an expense or the net amount (the amount they sold it for less the amount they had to pay the other business) with no cost recorded since the cost was already recognized in the reduced revenue.
GAAP has specific rules on determining if a sale should be recorded gross or net. There several indicators to be evaluated two of which – who is the primary obligor and is there inventory risk – are given more prominence than the other indicators such as the ability to set the price and credit risk. Let's look at these indicators as they relate to gift cards.
It would seem the seller of the gift card has discretion in setting the price. While most retailers sell a gift card for the face value, there are some like Sam's Club that sell gift cards below face value. Really the only limit on a retailer's ability to set the price is what the customer is willing to pay and how little profit the seller wants to make. In fact a retailer could sell a gift card as a loss leader to get people in the store to buy other goods. Credit risk also seems to reside with the seller of the gift card. If the check the customer used to pay for the gift card bounces or the credit card ends up being stolen, it is the seller that is out the money, but as I said, these two indicators are not given as much weight in today's GAAP.
A more important indicator is inventory risk, but that can result in different evaluations depending on how the seller pays for the gift cards. If the seller buys the gift cards up front from the other business then they would certainly appear to have inventory risk. On the other hand, it seems many gift cards have no value until activated at the time of sale. If the seller doesn't send money to the other business until the gift card is sold, then there doesn't appear to be much inventory risk for a bunch of plastic rectangles with no value indicated on some computer server in the cloud.
The term "primary obligor" sounds intimidating, but what it really means is who does the customer see as the provider of the good or service they are buying. That's where gift cards get tricky. Does the customer see the item they are buying as the gift card itself or as the meal or electronics it can buy from the other business? Before you answer let's bring in some more thoughts. How many people buy gift cards to give as gifts? In their eyes are they buying the gift card itself? They certainly don't intend on using what the gift card can buy. They intend to use the gift card itself. I can hear those of you stuck with worthless Boarders gift cards say, but the gift card is only worth something when it can be submitted in payment to the other business. That is not entirely true. There is a vibrant market for gift cards. As the seller you won't get face value, but there clearly is a value for the gift card. So if the gift card itself has value, is it unrealistic to say the customer is buying the gift card itself and not the right to trade it for goods from some other party?
And if you think the accounting for Gift cards is fun now, wait until the new revenue standard is in effect and the indicators I discussed above are all given equal weight in evaluating whether the seller is acting as the principal or agent.
I mentioned the new Financial Reporting Framework for Small and Medium Enterprises (FRF for SMEs) in last week's blog. This week I would like to dive a little deeper into the subject and talk about how FRF for SMEs will differ from U.S. GAAP as promulgated by the FASB. The FRF for SMEs is designed to be a comprehensive basis of accounting like cash basis or tax basis so it will qualify for OCBOA (Other Comprehensive Basis of Accounting) Reporting. That means a CPA will be able to provide clients financial statements and a report (depending on the engagement agreed to with the client) and users will know exactly what they are getting.
Let's start with some simple examples of what FRF for SMEs will contain.
No impairment testing for goodwill. Instead, like in yesteryear, goodwill will be amortized. In this case the time period will 10 years or the same period that is used for federal tax purposes.
No VIE Consolidation. One of the biggest complaints of SME financial statement users is the requirement to consolidate related by irrelevant enterprises. FRF for SMEs will not require their consolidation and will allow standalone entity financial statements of the relevant entity to the user.
Lease accounting will be closely aligned with how leases are treated for tax purposes. SMEs won't have to worry about whatever the FASB and IASB decide to come up with to complicate the accounting for leases.
Simplified hedge a derivative accounting. Let's face it, most SMEs don't enter into anything strange and if they do they are usually plain vanilla currency or interest rate swaps. The accounting will coincide with the simplicity of the business operating model.
No OCI – Most SMEs don't do things that result in OCI anyway and it rarely has anything to do with real assets or cash flow so it won't be required for FRF for SMEs.
The full FRF for SMEs will be about 200 pages (that's less than the revenue recognition ED being debated currently by the FASB) and really comes down to lots of traditional things like the matching principle, conservatism and basic accrual accounting. I think one of my fellow Council members from Texas described it best when he said "It sounds a lot like GAAP before the FASB got involved." Who knows maybe all those baby boomers nearing retirement will have an opportunity for a second career teaching all of the young CPAs the basics of plain old accrual accounting!
Anyone who has been following the SEC's decision process on allowing/requiring U.S. public companies to use IFRS has heard time and again how adopting IFRS is critical to enhance the comparability of financial statements across the world. It seems likes comparability is a given – one set of global accounting standards means everyone will be accounting for the same transaction the same way – all over the world. Who can argue against the benefits of that to the investor community?
The problem is that the dream – everyone accounting for the same transaction the same way – is just that, a dream. I put forth as exhibit A, the nightmare of accounting in Europe over the value of Greek Bonds. As you know, Greece is in a little trouble and there is serious doubt about their ability to pay-off all of their debt. As a result, the level of trading in the bonds has diminished since the crisis began, but there still is trading in the bonds. That trading however indicates a price that is at a substantial discount, even lower than what some "experts" say Greece will eventually be able to pay off.
So, what should companies (mostly banks) value the Greek bonds at in their interim financial statements? Should they be valued at what they are trading for today or should they be valued at what the (experts and the) bank thinks they will eventually get back? I will be the first to tell you that there are a lot of variables in that decision, but the part that concerns me the most is that the value of the bonds seems to be determined by the country the bank is located in, not the accounting standard followed by the bank.
Yes, different banks, both using IFRS, have reported substantially different values for the bonds – and it's not because one bank lists the bonds as held to maturity and another bank lists them as available for sale. It's also not because the banks have different auditors – at least by name. Several of the banks with starkly different values appear to be clients of the same auditing firm. As a CPA with an understanding of how firms work, I know that a "firm" using the same name in different countries is really not the same firm. It is two (or more) firms – one from each country – that are bound together at some level internationally, but ultimately, each country (even office) of those firms has some, potentially significant, level of autonomy. Unfortunately, most investors don't understand the intricacies of audit firm structures. If they see two opinions signed by the firm Jones & Smith, they assume that at least those financial statements should have things accounted for consistently.
So this Greek (Bond) tragedy, besides showing cracks in various aspects of the European Union, may also be showing us that moving to IFRS is not the comparability nirvana for investors that it is touted to be. There have been a lot of good debates about U.S.GAAP vs. IFRS, but until now, those on the U.S. GAAP side did not have a good response to the comparability argument. The soft underbelly of IFRS comparability has been shown for the tough old gut it is I for one am glad we didn't rush into adopting IFRS before we had a chance to see how the supposed wonderful comparability of a single set of accounting standards really works.


text:
sagc_minad September 27, 2020 October 11, 2020
San Antonio Garden Center ~
80 Years of History Worth Remembering!
NOTE: This article was written by one of the original, founding members—Annette Cavender. Annette wrote it in commemoration of Garden Center's 60th anniversary in 2000, when she was approaching her own 100th centennial birthday.
In 1940, five Garden Clubs existed in San Antonio. Among the members were two women, Mrs. R.A. Witt and Mrs. J. R. Murphy. They conceived an idea to establish a headquarters that would provide a link between organized clubs and their members, new home gardeners and the general public.
The purpose was to generate interest in horticulture, conservation, civic beautification and community projects. The women took their vision to Ellen Quillen, curator of the Witte Museum, who gave the group the use of the Weaver's House located on the grounds of the Witte.
This was the beginning of a period of intensive work by creative people who produced untold accomplishments, including promotion of the famous World War II "Victory Gardens".
San Antonio Garden Center was incorporated in 1955. It had outgrown the Weaver's House at the Witte Museum and a search was on for a new home. The City of San Antonio and the San Antonio Conservation Society approved a site at Mahncke Park. After 10 years of preparation, ground for a new building to call home was broken in 1965.
The building was constructed at a cost of $250,000 with funds raised by individual members and clubs. It was officially opened on October 26, 1966 and dedicated on May 3, 1967. A year later, an extension of 2,400 square feet was added to our building. This is now known as the Adele Frost Horticulture Hall.
The number of organized clubs grew rapidly, and by 1962 there were 65 clubs, with members totaling more than 2,000. During the ensuing years, the Garden Center contributed to many projects, including beautification of public places, planting trees at city schools, highway plantings, teaching junior gardeners and participating in the community "Litter-Bug" program. There were numerous, and intensive, garden therapy programs. However, our priority was to create a Garden for the Blind.
Even though the effort and promotion to establish a Garden for the Blind started as early as 1956, action came to fruition in 1967. Through years of hard work and a concerted effort, the Garden Center women raised $58,000 towards the project—a tremendous undertaking. Groundbreaking took place on July 21, 1976 on property adjacent to San Antonio Garden Center. Now known as The Sensory Garden, it became the cornerstone of what is now the San Antonio Botanical Garden.
Today, San Antonio Garden Center remains a centerpiece for garden clubs and plant Societies throughout the area. Supporting the The Sensory Garden is still one of our missions.


•• The world premiere of "Pitch Perfect" took place Monday, September 24th at the ArcLight Cinemas in Los Angeles, CA. Elizabeth Perkins looked absolutely perfect last night wearing a beautiful black dress with a eye-catching red belt and a black bag detail. She attended the premiere with her lovely family. Pictures from the event can be found in the photo gallery as usual. Enjoy!
New Photos of Elizabeth Perkins on Set!


This is a placeholder page for Diane Hunt, which means this person is not currently on this site. We do suggest using the tools below to find Diane Hunt.
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text:
\section{Introduction}
\noindent

The stationary  points of  any dynamical system are the ones where
velocity and acceleration  of the system simultaneously become zero.
These points,
which are important to understand the system in the first step,   are termed as fixed points (FP).
The stability of these fixed points and the motion around  them have been  studied in detail,
and can be found in any standard book on dynamical systems [Ott, 1993; Strogatz, 1994;
Jordan \& Smith, 2009; Kuznetsov, 2004; Kaushal \& Prashar 2008; Lakshmanan \& Rajasekar, 2003;
Arrosmith \& Place, 1990].

In this paper we show that, in nonlinear dynamical systems, there  also exist
a new class of  points (other than FPs) where acceleration  becomes zero while velocity remains nonzero.
These points can be  termed as {\sl perpetual points} (PP)\footnote{\label{pp} The name  ``perpetual"  is
used in analogy with
``perpetual motion" which describes a motion that continues indefinitely without any
 external driving force (acceleration) -- see {\sl  http://en.wikipedia.org/wiki/Perpetual{\_}motion}}.
These points can be traced by considering  the  higher derivative of the velocity vector of the system.
We demonstrate here that  a  study of these  perpetual points is
necessary for  understanding   several new features  of dynamical systems.
In particular,  these points can be useful for locating  the attractors, understanding the dynamics in phase space,
 and confirming whether a system is conservative or not.
To this effect, several examples of different type of dynamical systems are analyzed here:
ranging from   low to high dimension, as well as  from simple to complex ones.
We also observe that these points show the bifurcation behavior as parameters are changed.

This paper is organized as follows.
We study  the linear stability around the perpetual points
 in next section. The   distinct features   of PPs and FPs are discussed in  Sec. \ref{diff}.
This is followed by bifurcation analysis  of PPs in Sec. \ref{bif}.
The use of PPs  are discussed in Sec. \ref{appl}. The results are summarized in Sec. \ref{summ}.

\section{Perpetual points and  stability analysis}
\label{pp-lsa}

Consider a  general dynamical system specified by the equations

\begin{eqnarray}
\dot{\mathbf{X}}=\mathbf{F}(\mathbf{X},\mathbf{\alpha})
\label{eq:f}
\end{eqnarray}
\noindent
where $\mathbf{X}=(x_1,x_2,...,x_n)^T$ is $n$-dimensional vector of dynamical variables and
 $\mathbf{F}=(f_1(\mathbf{X}), f_2(\mathbf{X}), ...f_n(\mathbf{X}))^T$ specifies the
 evolution equations (velocity vector) of the system with internal
parameter $\mathbf{\alpha}$.
Here $T$ stands for transpose of the vector.
The first order Taylor expansion due to a small perturbation, $\mathbf{\bar{\delta} X}$ \footnote{\label{pert}The separate notations for
perturbations, $\mathbf{\bar{\delta} X}$ and $\mathbf{{\delta} X}$, are used for different Eqs. (\ref{eq:f}) and (\ref{gen}) respectively.} , in Eq. (\ref{eq:f}
)
 around the fixed point $\mathbf{X}_{FP}$ (where $\dot{\mathbf{X}}=0$)\footnote{Taylor expansion of a differentiable  $\mathbf{F}$ can be done at any point in phase space.} leads to
\begin{eqnarray}
 {\bar{\delta}} \dot{\mathbf{  X}}=\mathbf{F}_{\mathbf{X}^T}(\mathbf{X},\mathbf{\alpha})|_{\mathbf{X}_{FP}} \cdot \mathbf
{\bar{\delta} X}
\label{eq:df}
\end{eqnarray}
\noindent
where $\mathbf{F}_{\mathbf{X}^T}(\mathbf{X},\mathbf{\alpha})$ is  Jacobian of
size $n\times n$.
The dynamics near    the fixed points depend on the eigenvalues ($\l_i$)
and  the corresponding eigenvectors of this matrix, and the same has  been well
studied and documented in literature [Ott, 1993; Strogatz, 1994;
Jordan \& Smith, 2009; Kuznetsov, 2004; Kaushal \& Prashar 2008; Lakshmanan \& Rajasekar, 2003;
Arrowsmith \& Place, 1990].

Acceleration of  the system can be   obtained
by taking    derivative of Eq. (\ref{eq:f})  with respect to time\footnote{If the velocity
vector, $\mathbf{F}$, is differentiable.}, viz.
\begin{eqnarray}
\nonumber
\ddot{\mathbf{X}} &=&\mathbf{F}_{\mathbf{X}^T}(\mathbf{X},\mathbf{\alpha})\cdot\mathbf{F}(\mathbf{X},\mathbf{\alpha})\\
\label{gen}
                 &=&\mathbf{G}(\mathbf{X,\alpha})
\label{eq:g}
\end{eqnarray}
\noindent
where $\mathbf{G}=\mathbf{F}_{\mathbf{X}^T}(\mathbf{X},\mathbf{\alpha})\cdot\mathbf{F}(\mathbf{X},\mathbf{\alpha})$
 may be termed as acceleration vector. For convenience,  we drop $\mathbf{X}$
and $\mathbf{\alpha}$ from the arguments of $\mathbf{F}$ and $\mathbf{G}$ from now on.

For  zero acceleration of the system, we set $\ddot{\mathbf{X}}=\mathbf{G}=0$ in Eq. (\ref{eq:g}) which
gives a set of points where velocity $\dot{\mathbf{X}}$ may be either zero or a nonzero constant.
This set  includes the fixed points ($\mathbf{X}_{FP}$) with zero velocity
as well as a subset of  new points with nonzero  velocity\footnote{These are possible only in nonlinear systems.}.
These nonzero velocity  points are the perpetual points ($\mathbf{X}_{PP}$)$^{\ref{pp}}$

The linear stability analysis of Eq. (\ref{eq:g}) around the perpetual points gives
\begin{eqnarray}
\label{eq:dgen}
\delta\ddot{\mathbf{X}} &=& (\mathbf{I}\otimes {\mathbf{\delta {X}}^T})\cdot
\mathbf{F}_{\mathbf{X}\mathbf{X}^T}\cdot\mathbf{F}+\mathbf{F}_{\mathbf{X}^T}\cdot\mathbf{F}_{\mathbf{X}^T}\cdot\mathbf{\delta X}\\
&=&\mathbf{G}_{\mathbf{X}^T}|_{\mathbf{X}_{PP}}\cdot \mathbf{\delta X}
\label{eq:dg}
\end{eqnarray}
\noindent
where $\otimes$ is direct product while $\mathbf{I}$ and $\mathbf{F}_{\mathbf{X}{\mathbf{X}^T}}$ are identity and
Hessian matrices of
dimension $n\times n$ and $nn\times n$ respectively.
Note that matrix $\mathbf{G}_{\mathbf{X}^T}$
contains both the Jacobian ($\mathbf{F}_{\mathbf{X}^T}$)  and Hessian ($\mathbf{F}_{\mathbf{XX}^T}$) matrices.
For simplicity, the $ij$-element of matrix $\mathbf{G}_{\mathbf{X}^T}|_{\mathbf{X}_{PP}}$ can be written as
\begin{eqnarray}
(\mathbf{G}_{\mathbf{X}^T})_{i,j}=\sum_{k=1}^n[f_k f_{ix_kx_j}+f_{kx_j}f_{ix_k}].
\label{eq:gm}
\end{eqnarray}
\noindent
The general solution of the second order differential equation, Eq. (\ref{eq:dg})
around the perpetual  points for nonzero eigenvalues can be written as
\begin{eqnarray}
\mathbf{\delta X}&=& \sum_i^n  \mathbf{V}_i [c_{i1}\exp{(+\sqrt{\mu_i} t)}
+c_{i2}\exp{(-\sqrt{\mu_i} t)}]
\label{eq:sol}
\end{eqnarray}
\noindent
where $\mu_i$ and $\mathbf{V_i}$ are the  eigenvalues and eigenvectors respectively [Taylor, 2011].  Here
 $c_{i1}$ and $c_{i2}$ are the constants which depend on the initial position $\mathbf{X}(0)$ and
perturbation $\mathbf{\delta X}(0)$. This solution
 determines the variation of velocity around the perpetual points.
 Note that the solution of equation Eq. (\ref{eq:sol}) and Eq. (\ref{eq:df}) are not the same as acceleration vector$^{\ref{pert}}$,
 Eq. (\ref{eq:g}), may not be invertible to velocity vector, Eq. (\ref{eq:f}).
The  properties of these perpetual  points, using Eqs. (\ref{eq:gm}) and (\ref{eq:sol}),
 are demonstrated  below for some  selected systems.

\subsection{One--dimensional systems:}
In order to demonstrate the properties of perpetual points
we first consider a simple, analytically traceable, dynamical system
\begin{eqnarray}
\dot{ x}&=&x^2+\alpha.
\label{eq:1d}
\end{eqnarray}
For $\al>0$ there is no fixed point and hence system settles at infinity. The
acceleration, $\ddot{x}=2x(x^2+\alpha)$, of this system has  one perpetual point, $x_{PP}=0$.
The velocity at this point is  $\alpha$ while
 eigenvalue, corresponding to  $\mathbf{G}_{\mathbf{X}^T}|_{\mathbf{X}_{PP}=0}$, is $\mu=2\alpha$.
The general solution of Eq. (\ref{eq:dg}) for  arbitrary  initial
perturbations $\delta x(0)$ and $\delta \dot{x}(0)$  around this perpetual point is
\begin{eqnarray}
\delta x&=&c_{11} \exp(\sqrt{2\alpha} t)+c_{12}\exp(-\sqrt{2\alpha}t),
\label{eq:1d221}
\end{eqnarray}
\noindent
where $c_{11}=(\sqrt{2\al} \delta{x}(0)+\delta{\dot{x}}(0))/2\sqrt{2\al}$
and $c_{12}=(\sqrt{2\al} \delta{x}(0)-\delta{\dot{x}}(0))/2\sqrt{2\al}$.
Here, $\delta{\dot{x}}(0)=2{x}(0)\delta{{x}}(0)$
from Eq. (\ref{eq:1d}).
With  simple manipulation of this solution  and its derivative, we  get the relation
\begin{eqnarray}
2\al \delta {x}^2-\delta \dot{x}^2&=&[2\al-4x(0)^2]\delta{x}(0)^2,
\label{eq:1d1s}
\end{eqnarray}
which clearly shows that both
 $\delta x$ and $\delta \dot{x}$  decrease simultaneously as a trajectory approaches the PP
 \ie, in the neighborhood of  this type of perpetual point where $\mu>0$  system moves  slowly.
Therefore, this point is termed as slow perpetual point (SPP)\footnote{\label{fast-slow} The nomenclature  ``fast" or  ``slow" for  perpetual points is used because
system moves with ``maximum" or ``minimum" velocity at these
points.  This  nomenclature is considered in the spirit of definition  ``stationary point"
 where velocity is zero.}.
The magnitude of  velocity, $|\dot{x}|$, is shown in Fig. \ref{fig:1d}(a) while direction of motion in phase-space
is indicated in (b).
Here the size of the arrows indicate the magnitude of velocity.
Note that the trajectory passes through the PP, in contrast to the FP where
 trajectories never cross.

\begin{figure}[h]
\begin{center}
\vskip.4cm
\includegraphics [scale=0.6]{figure1.eps}
\end{center}
\caption{Plots in top  row show the magnitude of velocity
while bottom row show the schematic motion in phase-space of Eq. (\ref{eq:1d}).
Left and right panels correspond to the parameter values
 $\alpha=2$ and $\alpha=-2$, respectively.}
\label{fig:1d}
\end{figure}

However for $\al<0$, Eq. (\ref{eq:1d}) has  two fixed points, $x_{FP}=-\sqrt{|\al|}$ and $\sqrt{|\al|}$,
which are respectively stable and unstable \ie, initial conditions $x(0)<\sqrt{|\al|}$ lead to
$x_{FP}=-\sqrt{|\al|}$ otherwise settle at  infinity.
The perpetual point for this case is
$x_{PP}=0$ where velocity and eigenvalue are  $-|\alpha|$ and $\mu=-2|\alpha|$ respectively.
The general solution of Eq. (\ref{eq:dg})   around this  PP  is
\begin{eqnarray}
 \delta x=c_{11}\cos( \sqrt{2|\al|} t)+c_{12} \sin(\sqrt{2|\al|} t)
\label{eq:1d22s}
\end{eqnarray}
\noindent

where $c_{11}=\delta{x}(0)$ and $c_{12}=\delta \dot{x}(0)/\sqrt{2|\al|}=2x(0)\delta x(0)/\sqrt{2|\al|}$,
which along with its derivatives give the relation
\begin{eqnarray}
2{\lvert\al\rvert } \delta {x}^2+\delta \dot{x}^2&=&[2|\al|+4x(0)^2]\delta{x}(0)^2.
\label{eq:1d2s}
\end{eqnarray}
This indicates that as $\delta x$ decreases \ie, trajectory reaches to $x_{PP}=0$,
  $\delta \dot{x}$ increases as shown in Figs. \ref{fig:1d}(c) and \ref{fig:1d}(d).
 This suggests that as the system reaches  PP, its  velocity becomes higher and higher, and hence it moves
 faster. Therefore this type of PP, where $\mu<0$, is termed as faster perpetual point (FPP)$^{\ref{fast-slow}}$.

 For special cases when  eigenvalues are zero, Eq. (\ref{eq:sol}) can be written as
 $\mathbf{\delta X}=  \mathbf{V}_i [c_{i1} +c_{i2} t]$ where
$\mathbf{V}_i$ is eigenvector corresponding to the zero eigenvalue. For an example,
consider system $\dot{x}=(x-1)^3-\alpha, \alpha>0$ which  has one unstable fixed point,
 $x_{FP}=1+\alpha^{1/3}$, with $\lambda=3\alpha^{2/3}$ and one perpetual point, $x_{PP}=1$, with  $\mu=0$.
Since $\mu=0$ therefore there is no extremum in velocity. However the trajectory starting from
$1<x(0)<2$ approaches  $x=1$ with high velocity and then becomes constant at PP. Once it passes through PP,
velocity increases again. This can be seen as an inflection point in velocity-distance plot, or also
from the solution $\delta x=\delta x(0)+t\delta \dot{x}$.

We observed similar results for other one-dimensional systems also -- see Eq. (\ref{eq:bif}).
The formalism, (Eq. (5)),  which is  verified here for  1D-systems,
now can be  extended  to  higher dimensional systems, as given below.

\subsection{Two--dimensional systems:}
Here we   consider the  celebrated Duffing oscillator [Ott, 1993]
\begin{eqnarray}
 \ddot{x}+\beta \dot{x}-\alpha x+x^3=0.
\label{eq:2da}
\end{eqnarray}
\noindent
It has three fixed points at $x_{FP}= 0$ and $\pm \sqrt{\alpha}$ for $\alpha>0$. The first  point is unstable
while the last two are stable, which are shown in Fig. \ref{fig:2d}(a) in ($x_1=x, x_2=\dot{x}$) plane with
open and filled circles.
The perpetual points of this system are
$(-\sqrt{\al/3}, -\frac{2\al}{3\beta}\sqrt{\al/3})$ and $(\sqrt{\al/3},
 \frac{2\al}{3\beta}\sqrt{\al/3})$\footnote{Here  PPs are in fact
the   inflection points of the potential $x^4/4-\alpha x^2/2$,  Eq. (\ref{eq:2da}).}. The stability analysis  suggests that
 eigenvalues for both  the  PPs are  $\mu=(\beta^2\pm\sqrt{\beta^4+16\alpha^2/3})/2$.
Since the largest eigenvalue  is positive for these PPs   the velocities
should be  slower. This is confirmed in Fig. \ref{fig:2d}(b) where the magnitude of  velocity,
 $|F|=\sqrt{\dot{x}_1{^2}+\dot{x}_2^2}$, along the velocity vector, $(1,0)^T$ at one
PP is  plotted. This clearly shows that the velocity is minimum at this PP.

\begin{figure}
\begin{center}
\includegraphics [scale=0.5] {figure2.eps}
\end{center}
\caption{The (a) dynamical behavior around the  fixed and perpetual points,
(b) the magnitude of  velocity as a function of $x_1$ along
 the vector $(1,0)^T$ near  one of the PPs of Eq. (\ref{eq:2da}) for $\alpha=1$ and $\beta=1$.
(c) The orbits and loci of fixed and perpetual points respectively of Eq. (\ref{eq:2db})-see
 text for details.  Arrows show the directions of flow.}
\label{fig:2d}
\end{figure}

In another example of two-dimensional system we consider
a system having  coexisting attractors, a stable fixed point and a limit cycle,
\begin{eqnarray}
\nonumber
\dot{r}&=&r(r-1)(2-r)\\
\dot{\theta}&=&\omega.
\label{eq:2db}
\end{eqnarray}
\noindent
Here $r=\sqrt{x_1^2+x_2^2}$ and $\theta=\tan^{-1}{x_2/x_1}$ correspond to the radius
 and the phase of the system with frequency $\omega$.
The fixed point analysis of this system gives  two coexisting attractors at
$r=0$ (stable fixed point) and $r=2$ (limit cycle), and  one unstable periodic
orbit (UPO) at $r=1$.  These, stable and unstable features,  are shown in Fig. \ref{fig:2d}(c) with
solid  and dotted  lines respectively. The  perpetual points of this system are,  $r_{PP}=1\pm1/\sqrt{3}$
which form  closed loci,  shown in Fig. \ref{fig:2d}(c)
with red-dashed lines. The eigenvalues at perpetual points are
$\mu=-6r_{PP}(1-r_{PP})^2(2-r_{PP})$. Since $r_{PP}<2$, therefore $\mu<0$,  which implies
that velocities have maxima at these points. The other two-dimensional systems are also considered in Sec. \ref{appl-cons}.

\vskip.2cm
\noindent
\subsection{Three--dimensional systems:}
\label{3d}
The  self-excited attractors, whose  basins  intersect with the neighborhood of
the fixed points (\eg~ Lorenz, Rossler, Chua, \etc)  have been studied in
detail [Ott, 1993; Strogatz, 1994;
Jordan \& Smith, 2009; Kuznetsov, 2004; Kaushal \& Prashar 2008; Lakshmanan \& Rajasekar, 2003;
Arrowsmith \& Place, 1990]. Very recently, a new type of attractors called
hidden attractors, that don't intersect with the neighborhood of  any FP
have been reported [Kuznetsov \etl~ 2010; Leonov \etl~ 2011a; Leonov \etl~ 2011b;
 Leonov \etl~ 2013].
Due to the absence of unstable FP in its
neighborhood these type of attractors are less tractable.
Therefore, it is  also difficult to understand their characteristic
behavior [Kuznetsov \etl~ 2010; Kuznetsov \etl~ 2011;
 Leonov \etl~ 2010; Leonov and Kuznetsov 2011;
Leonov \etl~ 2011a, Leonov \etl~ 2011b;   Leonov \etl~ 2011c;  Chaudhuri \& Prasad 2014].
  As an example, we  consider such a system that has no fixed point
 and  provides  hidden attractor [Wang \&  Chen, 2013],
\begin{eqnarray}
\nonumber
\dot{x}_1&=&x_2 \\
\nonumber
\dot{x}_2&=&x_3 \\
\dot{x}_3&=&-x_2+3x_2^2-x_1^2-x_1x_3+\alpha.
\label{eq:3d}
\end{eqnarray}
\noindent
This system doesn't have any fixed point for parameter $\alpha<0$.
A typical chaotic hidden attractor is shown in Fig. \ref{fig:3d}(a)
for $\alpha=-0.05$.  Because there is no fixed point in this system
at this value of parameter,  this attractor is termed as  hidden one.

\begin{figure}
\begin{center}
\includegraphics [scale=0.5]{figure3.eps}
\end{center}
\caption{ (a) A hidden chaotic attractor and
 (b) the magnitude of  velocities, along the velocity vectors passing through
 the perpetual points.}
\label{fig:3d}
\end{figure}

The perpetual points for this systems are $(0, x_{2PP\pm},0)$ where $x_{2PP\pm}
=(1\pm\sqrt{1-12\alpha})/6$. These  are shown  in
Fig. \ref{fig:3d}(a) with  red-circles. The
largest eigenvalues $\mu_i$, corresponding to the matrix $\mathbf{G}_{\mathbf{X}^T}$,   at these PPs
are $6x_{2PP\pm}-1$ and $[5x_{2PP\pm}-1\pm\sqrt{13x_{2PP\pm}^2-14x_{2PP\pm}-4\alpha+1}]/2$
which are  $+$ve  for the both points\footnote{The eigenvalues, $\mu_i$ at $x_{2PP+}$ and $x_{2PP-}$ are
($1.2649, 0.4437\pm i 0.7470$)  and ($0.0684,-1.2649, -1.2892$) respectively.}.  Therefore the velocities
at these points should be slower, which is confirmed in Fig. \ref{fig:3d}(b) where
the magnitude of velocities are plotted along the velocity vectors at these points\footnote{\label{para} The velocity vectors  at PP $(0,x_{2PP\pm},0)$ are
 $(x_{2PP\pm},0,-x_{2PP\pm}+x_{2PP\pm}^2-\alpha)^T$.
The velocities are calculated along  the lines which are estimated using
the   parametric ($p$) form of the equation of a
 line passing through these PPs:
 $x_1=px_{2PP\pm}$, $x_2= x_{2PP\pm}$ and $x_3=p(-x_{2PP\pm}+x_{2PP\pm}^2+\alpha)$ which
give as relation $x_3=x_1 (-x_{2PP\pm}+x_{2PP\pm}^2+\alpha)/x_{2PP\pm} $.}.
An another system with no fixed point is also considered  in Sec. \ref{appl-hid}.

\section{Perpetual Points vs. Fixed Points}
\label{diff}

\begin{center}
\begin{table}
\tbl{Comparative properties of FP and PP. Here, $\mu_m$ is the largest nonzero
eigenvalue among $\mu_i$.}
{    \begin{tabular}{| c | c | c |}
    \hline
~&Fixed Point& Perpetual Point\\
\hline
Velocity, $|F|$ & $|F|=0$ &$|F|\ne0 $ \\
~&~ & Extremum if $\mu_m \lessgtr 0$\\
~&~ & Inflection if  $\mu_i=0~~ \forall i$ \\
\hline
Acceleration & $0$ & $0$\\
\hline
$\l_i$  & $+, -, 0$ & At least one of $\l_i=0 $\\
$ $ [Eq. (\ref{eq:df})] &  & \\
\hline
$\mu_i$  & $\mu_i=\lambda_i^2$  & $ +, -, 0$\\
$ $ [Eq. (\ref{eq:dg})] &  & $ $\\
\hline
Motion  & Stable or unstable & Closed locus\\
 of points & periodic orbits&   \\
\hline
Trajectory & Moves towards  & Passes through \\
~ & or Moves away  & ~ \\
\hline
  \end{tabular}}
\end{table}
\end{center}

In this section we present the  comparative properties of PPs and FPs, as  summarized in Table I: ({\sl i})
The  velocity at the perpetual points  is  either maximum or minimum or of inflection behavior
while zero for fixed points. However, as per definition, acceleration is zero at both  the PPs and FPs.
({\sl ii}) The eigen values, $\lambda_i$, corresponding to Eq. (2) are either negative or positive or zero at
 fixed points. However  one of $\l_i$ must be zero at PPs. Its reason can be explained as follows.
In general, if $\mathbf{F}_{\mathbf{X}^T}\cdot\mathbf{F}=0 $ then there is either
a trivial solution $\mathbf{F}=0$ or infinite number of  solutions. Since  $\mathbf{F}\ne 0$ at the perpetual points
 therefore a finite number of solutions exists if and only if $\mathbf{F}_{\mathbf{X}^T}$ admits at least
one  zero eigenvalue corresponding to the eigenvector  $\mathbf{F}$.
({\sl iii}) Here, as we have observed in previous section,  the value of $\mu_i$ could be either positive or negative or zero at PP.
 At FPs, first term in Eqs. (\ref{eq:g}) becomes zero due to $\mathbf{F=0}$,
and hence $\mu_i$ is related to $\l_i$  as $\mu_i=\l_i^2$.
({\sl iv }) A trajectory   passes through a PP whereas  it either moves  away or settles on a fixed point.
Note that  in some cases, for example Eq. (\ref{eq:2db}), PP forms a closed
 locus as shown in Fig. \ref{fig:2d}(c) whereas  FP forms either stable or unstable periodic orbits.

\section{Bifurcations}
\label{bif}
In order to explore the possibilities of
occurrence of bifurcations of perpetual points as a function of parameters, say $\alpha$,
we first consider system Eq. (\ref{eq:1d}). Shown in  Fig. \ref{fig:bif}(a)  are the filled and open circles for
stable and unstable fixed points along with the solid-blue and dashed-red line for fast and slow PPs respectively.
This shows that below $\alpha=0$ there are two fixed points (stable and unstable) and one
 fast perpetual point at $x=0$\footnote{\label{bifnote}In one-dimensional systems there must be at least
one fast perpetual point in between two fixed  points.}.
As parameter $\alpha$ passes through  $\alpha=0$  there is no fixed point but
the  fast perpetual point becomes slower one \ie~ there is change in magnitude  of velocity from maximum to minimum
 across $\alpha=0$.  Therefore this  change in  dynamics  may be termed as bifurcation of PP ($x_{PP}=0$).

In another example, we construct a system,
\begin{eqnarray}
\dot{x}&=&x^3-3\alpha x-1.
\label{eq:bif}
\end{eqnarray}
 \noindent
Depending on the parameter, $\alpha$, this system has either one or three  fixed points  which are
 shown in bifurcation diagram, Fig. \ref{fig:bif}(b). The  open  and filled circles
correspond to the stable and unstable fixed points (denoted as SFP and UFP respectively).
This system has two perpetual points,  $x_{PP}=\pm\sqrt{\alpha}$, which are
 shown in Fig. \ref{fig:bif}(b)  with solid and dashed
lines. At $\alpha=0$, the fast ($\mu=6(-2\alpha^2-\sqrt{\alpha})$) and
the slow ($\mu=6(-2\alpha^2+\sqrt{\alpha})$) perpetual points
(shown as solid and dashed lines respectively) are created.
 As parameter $\alpha$ is increased
further,  slow perpetual point becomes fast at $\alpha\sim 0.62$ where
saddle-node bifurcation$^{\ref{bifnote}}$ for fixed points occurs.
 We observe similar bifurcations in  other systems (from Ref. [Strogatz, 1994]) also,
which confirm that the perpetual points do show  bifurcations behavior in parameters space.

\begin{figure}
\begin{center}
\includegraphics [scale=0.55]{figure4.eps}
\end{center}
\caption{ The bifurcation diagrams of systems (a) Eq. (\ref{eq:1d}) and (b) Eq. (\ref{eq:bif}) as a function of
 parameter $\alpha$. Arrows show the bifurcation points. Filled and open circles
are the stable and unstable FPs while Solid-blue and dashed-red lines are FPP and SPP respectively.}
 \label{fig:bif}
\end{figure}

\section{Applications}
\label{appl}

\subsection{Conservative vs. Dissipative}
\label{appl-cons}

Checking a system whether it is  conservative or not is an important problem in nonlinear dynamics.
 There are various ways to confirm whether a system is conservative or
not [Strogatz, 1994; Ott, 1993]. In this work we show that this can be checked
in a simple way by searching the perpetual points.
Let us consider an autonomous Hamiltonian system
 $H=H(q,p)$ of one-degree of freedom (the following results can be extended for
the systems with $n-$degrees of freedom  also).
Here $q$ and $p$ are the generalized co-ordinate and the momentum respectively.
The  equations of motion are

\begin{eqnarray}
\nonumber
\dot{q}&=&\frac{\partial H}{\partial p}, \\
\dot{p}&=&-\frac{\partial H}{\partial q}.
\label{eq:h1}
\end{eqnarray}

\noindent
The next  higher order derivatives of these equations are given as

\begin{eqnarray}
\nonumber
\ddot{q}&=& \frac{\partial^2 H}{\partial p \partial q }\dot{q}+
 \frac{\partial^2 H}{\partial p\partial p }\dot{p} \\
\ddot{p}&=&- \frac{\partial^2 H}{\partial q \partial q }\dot{q}-
\frac{\partial^2 H}{\partial p\partial q }\dot{p},
\label{eq:h2}
\end{eqnarray}

\noindent
which can be recast in the matrix form as
\begin{eqnarray}
\nonumber
& &\\
\begin{bmatrix}
\ddot{q}\\
\ddot{p}
\end{bmatrix}
&=&
\begin{bmatrix}
\frac{\partial^2 H}{\partial p \partial q } & \frac{\partial^2 H}{\partial p^2 }\\
-\frac{\partial^2 H}{\partial q^2} &-\frac{\partial^2 H}{\partial p \partial q}
\end{bmatrix}
\begin{bmatrix}
\dot{q}\\
\dot{p}
\end{bmatrix}\\
\Rrightarrow \ddot{\mathbf{X}}&=& \mathbf{F}_{\mathbf{X}^T}\cdot\mathbf{F} \mbox{~~~~~[cf. Eq. (\ref{gen})]}
\end{eqnarray}

\noindent
where $\mathbf{X}=(q,p)^T$.
For getting perpetual points we must have $\ddot{\mathbf{X}}=0$. However,
if $\mathbf{F}_{\mathbf{X}^T}\cdot\mathbf{F}=0 $ then there is either
the trivial solution $\mathbf{F}=0$ or there are infinite number of  solutions.
Since  $\mathbf{F}\ne 0$ at the perpetual points,
the finite solution exists if and only if $\mathbf{F}_{\mathbf{X}^T}$ admits at least
one  zero eigenvalue corresponding to the eigenvector  $\mathbf{F}$.
However, due to the special structure of the Hamiltonian, the trace of $\mathbf{F}_{\mathbf{X}^T}$ is zero.
This means that the determinant of $\mathbf{F}_{\mathbf{X}^T}$ should  also be zero.
But $\mathbf{F}_{\mathbf{X}^T}=0$ is possible
 only at the fixed point,  hence the  existence of  PP is ruled out. This suggests that the existence of
PP can confirm   dissipation in the systems.  This is demonstrated in the following examples.

\vskip.2cm
\noindent
{\sl Duffing systems:} We first consider the  Duffing system, Eq. (\ref{eq:2da}), which has two
 perpetual points
$(-\sqrt{\al/3}, -\frac{2\al}{3\beta}\sqrt{\al/3})$ and $(\sqrt{\al/3},
 \frac{2\al}{3\beta}\sqrt{\al/3})$.
These points are shown in Fig. \ref{fig:cons}(a) with squares. This clearly indicates  that for zero   strength of
dissipation, $\beta \to 0$,  the PP goes to infinity \ie~  there is no PP in the conservative limit,
and hence at $\beta \to 0$ system is conservative.

\vskip.2cm
\noindent
{\sl Plane pendulum}: Consider the  equation of  a plane pendulum
\begin{eqnarray}
\ddot{q}+\beta\dot{q}+\alpha \sin{q}&=&0
\label{eq:pen}
\end{eqnarray}
\noindent
where $\alpha$ and $\beta$ are the system parameters. For $\beta=0$, system
is conservative and Hamiltonian (total energy) is constant of motion.  Its  equations of motion can be written
 as
\begin{eqnarray}
\nonumber
\dot{q}&=& p\\
\dot{p}&=&\beta p -\alpha \sin{q}.
\end{eqnarray}

\noindent
The fixed points of this system are $(\pm k\pi, 0)$ where $k=\pm1, \pm2 ...$
The perpetual points for this system are $(\pm (n+1/2) \pi, \pm \alpha/\beta$). These points, FPs (circles) and
PPs (squares) are shown in Fig. \ref{fig:cons}(b). The color represents the acceleration
 $\sqrt{\ddot{q}^2+\ddot{p}^2}$.
Similar to the Duffing system, it clearly indicates that as strength of dissipation, $\beta \to 0$
 the PP goes to infinity \ie~
there is no PP in the conservative limit. Here also  in strong dissipation, \ie~ $\beta\to\infty$,  ${\dot{p}}_{_{\tiny PP}}\to 0$.
 Note that these PPs are at the inflection  point of the potential of the Hamiltonian.

\vskip.2cm
\noindent
{\sl Lotka-Volterra system:} We consider another celebrated system which is not in the Hamiltonian form.
 The governing equations of  this system [Lotka, 1920] are
\begin{eqnarray}
\nonumber
\dot{x}&=& x(a-by)\\
\dot{y}&=&y(cx-d)
\label{eq:lv}
\end{eqnarray}

\noindent
where $x$ and $y$ are prey and predator populations respectively while $a,b,c,$ and $d$ are
the system's parameters. Note that this system is quite different in structure   as compared to the
Duffing and Pendulum systems. However, after certain transformation [Lotka, 1920] it can be shown
 that this system has one invariant $I=d\log{x}-cx+a\log{y}-by$,  suggesting that the system is conservative.
For checking the existence  of PP in this system, we examine the acceleration vector
$$
\begin{bmatrix}
G(X)
\end{bmatrix}
=
\begin{bmatrix}
x(a-by)^2-bxy(cx-d)\\
cxy(a-by)+y(cx-d)^2
\end{bmatrix}.
$$
\noindent
The fact is that  $G(X)\ne0$ for positive parameters. This implies that  there are no perpetual points,
 and hence it is a conservative system.
All these examples suggest that, in a system,  if there   exists a PP   then it is
 dissipative otherwise  conservative.

\begin{figure}
\begin{center}
\includegraphics [scale=0.95]{figure5a.eps}\\
\includegraphics [scale=0.95]{figure5b.eps}
\end{center}
\caption{Acceleration in $x-\dot{x}$ plane for (a) Duffing system, Eq. (\ref{eq:2da}), and (b) plane
 pendulum, Eq. (\ref{eq:pen}), at parameters $\alpha=1~\&~\beta=3$ and  $\alpha=2~\&~\beta=1$ respectively.}
 \label{fig:cons}
\end{figure}

\subsection{Locating hidden and coexisting attractors}
\label{appl-hid}
The understanding of hidden attractors (cf. Sec. \ref{3d}), as compared to the excitable ones, is
difficult due to the absence of fixed points.  Even to locate the  hidden attractors
in a given system, one requires proper search method consisting of analytical and numerical
techniques [Leonov \etl~ 2010; Leonov \etl~ 2011b; Bragin \etl~ 2011].
In this work we show  that  we can use perpetual points to locate such hidden attractors.

Consider the system, described by Eq. (\ref{eq:3d}),  which has no fixed point but has one chaotic hidden attractor as shown in
 Fig. \ref{fig:3d}(a) (see Sec. 2).  It has two  perpetual points,
 $(0,x_{2PP+},0)$ and  $(0,x_{2PP-},0)$ as shown in Fig. \ref{fig:hd}(a) with red-circles.
The transient trajectories starting from these PPs  are shown in Fig. \ref{fig:hd}(a). It clearly shows that
the trajectories starting from the former one goes to the  hidden attractor (Fig. \ref{fig:3d}(a))
where as the  later one goes to infinity [Chaudhuri \& Prasad 2014].
This confirms that the perpetual point,  $(0,x_{2PP+},0)$, is useful to locate the
hidden attractor.

\begin{figure}
\begin{center}
\includegraphics [scale=0.55]{figure6.eps}
\end{center}
\caption{The transient trajectories starting from perpetual points (red circles) for systems
(a) Eq. (\ref{eq:3d}) and (b) Eq. (\ref{eq:nh}).}
 \label{fig:hd}
\end{figure}

We consider  another example, the Nose-Hoover system  [Jafari \etl~ 2013]
\begin{eqnarray}
\nonumber
\dot{x}_1&=&x_2\\
\nonumber
 \dot{x}_2&=&-x_1-x_2x_3\\
\dot{x}_3&=&x_2^2-\alpha.
\label{eq:nh}
\end{eqnarray}

\noindent
This system doesn't have any FP but shows  chaotic motion ($\alpha=1$), as shown in Fig. \ref{fig:hd} (b).
This system has one PP which is $(0,0,0)$. The trajectory starting from
the perpetual point  leads to the chaotic attractor.
As in  other similar systems (from Ref. [Jafari \etl~ 2013]) without FP,  but having oscillations can
also be located. These examples   confirm that  hidden attractor can be located with PP.
These numerical results  also indicate that hidden attractors (oscillating ones) also have
 reference point similar to the fixed points of self-excited oscillations. However, a detailed
connection between the perpetual points and the hidden attractors needs to be
established. Perhaps there is a need to develop a  manifold type of theory  for perpetual points as exists for
 fixed points [Kuznetsov 2004].

We  observed that the coexisting attractors can  also be located using perpetual points. We can easily see
in Fig. \ref{fig:2d}(a) that the trajectories starting from different perpetual points
go to different  stable FPs, either $(0,-\sqrt{\al})$  or $(0,\sqrt{\al})$.
  The trajectories passing through the perpetual points
 are shown in Fig. \ref{fig:2d}(a) by black and blue lines.
The conclusion that the PPs can be used to locate the coexisting  attractors
can also be drawn form Fig. \ref{fig:2d}(c) for limit cycle cases where initial
conditions starting from the perpetual points $r_{PP}=1-1/\sqrt{3}$ and $r_{PP}=1+1/\sqrt{3}$ lead to the
stable fixed point ($r_{FP}=0$) and stable limit cycle ($r_{FP}=2$) respectively.
These examples suggest that  the knowledge of  perpetual points is useful for locating   the  hidden and coexisting
attractors\footnote{The multi-stable
attractors [Pisarchik, \& Feudel, 2014] where number of attractors are very large \eg~ in conservative
limit, are yet to be studied.}.

\subsection{Transients}
In phase space the velocity or the acceleration of a system doesn't remain constant
(except for circular motion).
The accelerations in the  $x-\dot{x}$ plane for the systems described in Eqs. (\ref{eq:2da}) and (\ref{eq:pen})
are shown in Fig. \ref{fig:cons} (color).
The accelerations are different in different regions
of phase space. Particularly at the PPs,
accelerations are zero while velocities are extremum (Fig. \ref{fig:cons}).
Therefore, as a  trajectory moves in phase space
the durations of travel for the equal distances are different. The variation of velocity also  effects the transient
time\footnote{Transient time is defined as the duration in which a system, starting from an initial condition,
reaches to the asymptotic attractor.} \eg~ If we start the system from an initial condition
for which the trajectory passes through the neighborhood of  perpetual points, where velocity is extremum (Fig. \ref{fig:cons}),
then it requires either longer or shorter time (corresponding to SPP or FPP respectively)
 to reach the attractor.
Therefore,  in many applications where understanding of transients is  important
[Hastings, 2001; Ovaskainen \& Hanski, 2002], location of PPs  in phase space (Fig. \ref{fig:cons})
 is useful.

\section{Summary}
\label{summ}

{\sl Summary:} A new set of  points, termed as {\sl perpetual points} where
velocity remains nonzero while acceleration becomes zero, are observed.
At  these points the velocity can be  either maximum or minimum or of inflection behavior.
The  properties of perpetual points, along with the fixed points, are
summarized in Table I (Sec. \ref{diff}).

The perpetual points, each having its extremum value of velocity, influence the transient dynamics.
Therefore, the study of PPs is essential to understand   many
natural phenomena, \eg,  experiments where transients
persist for   longer time, neural processing [Hastings, 2001; Ovaskainen \& Hanski, 2002],
transient chaos, and in ecology  where the transient dynamics play an important role.
Using these perpetual points one can also locate
the presence of co-exiting  as well as hidden attractors.
The existence of PPs in a system  can be used to confirm whether the system is conservative or not.

It  is easier to examine the magnitude of the velocities in lower dimensions
(particularly one and two dimensional systems).
In case of  high dimensional systems  it is  difficult to visualize  the extrema of the velocities in phase space.
Here, the  presented generalized formulation (cf. Eqs. (\ref{eq:dgen}) and (\ref{eq:gm})) can  easily be applied
to any (lower or higher) dimensional systems.
This work also shows that it may be useful to consider
the higher derivatives  (without any additional initial conditions) of the velocity vector for
better understanding of  nonlinear dynamical systems\footnote{The  higher-order derivatives of a nonlinear system
 may give either FPs/PPs only or an entirely  new set of points.
The physical meaning of the higher derivatives and the  corresponding  new points need
to be explored.}.
Here  we have demonstrated  the analysis  for several different type of systems, which
suggest that the presented results  are quite general.

\nonumsection{Acknowledgments} \noindent
Author  thanks B. Biswal, R. S. Kaushal, M. D. Shrimali and R. Ramaswamy for critical comments on this manuscript.
  The financial supports from the DST, Govt. of India  and DU-DST PURSE  are also acknowledged.

redpajama_set_name: RedPajamaArXiv


text:
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My favourite film of 2022 was probably Living, staring Bill Nighy as an ageing civil servant, Mr. Williams. The actor has received an Oscar nomination for the role. His character's life is stuck on hold in a bureaucratic machine. County Hall where he works seems to operate with the sole purpose of stopping anything happening that would improve the lot of 1950's Londoners. No capes are donned. No skyscrapers crumble, but the movie packs a powerful punch. Mr. Williams receives the devastating news that he is terminally ill. His first response is to try and live it up a bit with a trip to the seaside. But escapism fails to satisfy his desire to live out his days well, rather than just existing for the drudgery of the office.
Although what does it for Mr Williams is returning to work. He unites his team in a project that will actually do something for the ordinary people of London, a city that has not yet been rebuilt following the Blitz. The message of the film is that we find purpose in life by doing things that make a difference for others. The final scenes are almost unbearably poignant.
Jesus said, 'I have come that they might have life, and have it abundantly'. That's why he died for his people on the cross and rose from the dead. But Jesus' vision of abundant life isn't an endless round of parties, glitz and glamour. He called upon his followers to love their neighbour as themselves, to care for the sick and feed the poor. Life to the full is for those who believe in the Lord Jesus, die to self and give their lives in the service of others. That's living alright.
* For the February 2023 edition of various local magazines
Labels: Christian faith, Film Review
Deity & Decree, by Samuel D. Renihan
Published in the UK by Broken Warfe, 2021, 134pp.
Evangelicals rightly demand theological precision and accuracy when it comes to the doctrine of Scripture, or justification by faith alone. Any drift from biblical inerrancy is detected and rejected in short order. Similarly when it comes to including works in justification. 'By faith alone, by grace alone', we insist. The same theological care isn't necessarily displayed when attention turns to the doctrine of God. Some contemporary Evangelical theologians suggest that belief in divine impassibility makes seem God cold and remote. Others have argued that the Son stands in a eternal relationship of submission and authority to the Father.
Part of the problem is that Evangelicalism contents itself with brief statements of belief, as opposed to elaborate confessions of faith. Compare the Doctrinal Basis of the Fellowship of Independent Evangelical Churches with the Second London Baptist Confession of Faith, 1689. Point 1 of the FIEC Doctrinal Basis has a 54 word statement on 'God'. What it says is perfectly fine and good. But by way of contrast, the 2LBCF Chapter 2 devotes three paragraphs totalling 408 words to 'Of God and the Trinity'. The older confession self-consciously echoes the creedal heritage of the church and gives expression to what is sometimes called the 'classic doctrine of God', 'The Lord our God is a... most pure spirit, invisible, without body, parts, or passions'. Renihan wants to recover the older emphasis of the confession.
If the doctrine of God is 'first theology' and of primary importance, we need to ensure that what we say of God is biblically accurate and informed by the theological reflection of the past. That is where Deity & Decree comes in. With impressive clarity and brevity Renihan gives attention to God's Unity, Triunity and Decree.
God's Unity: God is self existent, with life in himself. He is uncaused cause of all things. God's attributes such as his omnipotence, holiness and love are not the bits of which his being is composed. God is simple, having no component parts. All that is in God is essential to God, because all that is in God is God. That is why he cannot change. An unchanging God is not susceptible to suffering. There is nothing within the being of the ever blessed God that could cause him to suffer. Suffering cannot be imposed upon him from without, as that would give the created order an advantage over him, compromising his omnipotence and immutability. The impassible God is not cold, or remote, however, for God is love, full of self-generated compassion and mercy towards lost sinners. The move towards attributing suffering to God's being risks compromising the uniqueness of the incarnation of the Son of God. In Christ as man God did what is impossible for him to do as God namely, to suffer and die for sinners.
God's Trinity: The Bible reveals that in the one God there are three persons, or subsistences: Father, Son and Holy Spirit. All three persons are equally and fully God, yet the Three are not interchangeable. The Father is unbegotten, the Son is eternally begotten of the Father, and the Holy Spirit proceeds from the Father and the Son. It is these personal properties alone that distinguish the persons. We may not ascribe an attribute such as authority to the Father and submission to the Son in terms of their eternal relations. The Son has the same power and authority as the Father because he is of the same essence as the Father. But there is an order in the Trinity and the missions of the three persons in the world of time reflect the eternal relations. The Father sent the Son into the world at his incarnation. The Father and Son poured out the Holy Spirit upon the church on the Day of Pentecost. Getting the Trinity right isn't theological hair splitting. As the Second London Baptist Confession states, "which doctrine of the Trinity is the foundation of all our communion with God, and comfortable dependence on Him." (2:3).
God's Decree: The decree is a simple, eternal and sovereign act of God's being. The Almighty's unchangeable decree, however, does not reduce creatures to the status of puppets in his hands. As the confession makes clear, "nor is violence offered to the will of the creature, nor yet is the liberty or contingency of second causes taken away, but rather established; in which appears His wisdom in disposing all things, and power and faithfulness in accomplishing His decree." (3:1). The decree does not make God the author sin, which he willingly permits for his own ends. Neither does it deprive human beings of responsibility to God for their actions. God decreed the salvation of his people not because of anything in them, but because of his own free grace given them in Christ before the foundation of the world. Those not elected to salvation are passed by according to God's decree. The cause of the damnation of the wicked is not the divine will per se, but their own sin, which rightly deserves eternal punishment.
In line with the Reformed Catholic tradition Renihan insists that God's decree is the expression of his will which is a property of the divine being, not the persons of the Trinity. This cuts across the idea proposed by some contemporary Evangelicals that the Son's will was eternally subordinate to that of the Father. The divine will is common to all three persons of the Trinity in the being of God. The Son, as well as the Father and the Holy Spirit was therefore party to the decree of salvation. The Son's submission to the Father in the economy of redemption cannot be read back into the eternal relations of the Trinity.
Renihan handles the biblical materials underlying God's Unity, Trinity and Decree with insight and care. His treatment of these topics is enriched by the Great Tradition of Christian thought, especially writers of the Reformation and Puritan periods. The author's prose is limpid and precise, yet his tone tone is meditative and devotional. A fine work of 'first theology' that demands a response of joyful doxology of the reader:
Glory be to God the Father. Glory be to God the Son. Glory be to God the Holy Spirit.
Glory be to the only, living, true, and triune God.
Labels: Creeds Confessions, Samuel D Renihan, Theology, Trinity
'Glory to the New-born King'
So says the chorus of a favourite carol, Hark! the Herald Angels Sing. But why should glory be ascribed to the new-born Jesus? After all, he would have looked much like every other baby. Cute, yes, but worthy of the angels' praise? I know artists often portray the infant in the manger as if he glowed in the dark with heavenly splendour, but that has no basis in fact. If anything, the Bible stresses how ordinary looking was Jesus. He 'took the form of a servant, being born in the likeness of men' wrote the apostle Paul. As with any other baby, Jesus was weak and totally helpless, 'tears and smiles like us he knew'.
Yet Christians believe that he who as an infant was cradled in his mother Mary's arms, was also the eternal Word of God who upheld the universe by his divine power. He is fully God, the Father's only Son as well as fully human. That is why angels worshipped the new-born King. They recognised him as their Maker made flesh. Another reason for worship is what Jesus was sent into the world to do. As the angel of the Lord explained to startled shepherds keeping watch over their flock by night, 'Fear not, for behold, I bring you good news of great joy that will be for all the people. For unto you is born this day in the city of David a Saviour, who is Christ the Lord.'
God became man in Jesus because we needed a Saviour. That tells us something about the human condition. The Bible tells us, 'all have sinned and fallen short of the glory of God'. We are incapable of saving ourselves from sin, otherwise God would have left us to get on with it. Jesus came to live a life of perfect obedience to God on our behalf. He then laid down his life as a sacrifice for sin. His death was sufficient to rescue the world from sin. That's because it was the Son of God in human form who suffered in our place at the cross.
Jesus is the King of love. He was born in the royal city of David. He was crucified as 'King of the Jews' to win us a place in God's eternal kingdom. He rose from the dead and was exalted to the right hand of the Father, where he reigns as King of kings and Lord of lords. He is able to save completely those who put their trust in him. Will you join the angels in singing, 'glory to the new-born King!'?
Christmas Services at Providence & Ebenezer.
* For the Christmas/New Year editions of several parish magazines
Labels: Christian faith, Christmas
History on Fast Forward
I'm old enough to remember life before music could be downloaded or streamed. I can even remember when CDs were a novelty, rather than old hat. Apart from a few cassettes most of my teenage music purchases were on vinyl and had to be played on a record player. Records had two sizes and speeds. Albums had to be played on 33rpm, singles on 45rpm. If you forgot to flip the switch from 45rpm when listening to an album it would play at high speed and at a higher pitch than was intended. You could produce the same effect by pressing the 'play' and 'fast forward' buttons at the same time on a cassette player. That was our idea of fun in the 1970's and 80s. We didn't have TikTok and stuff back then.
Right now it seems like the album of history is being played at 45rpm. It's a pain if you have to submit a monthly article like this one, which sometimes includes comment on current affairs. As I write this just before the deadline, Kwasi Kwarteng has been sacked as Chancellor and Jeremy Hunt has been appointed in his place. Prime Minister Liz Truss has vowed to carry on, but who knows who'll be PM by the time you read this in November? In September Boris Johnson stood down, Liz Truss took over and then the Queen died. Now we're all having to get used to singing, 'God save our gracious King'. It's all happening too fast.
It's much better when history proceeds at a glacial pace and nothing much seems to be going on. But time is hurtling by at a dizzying speed. The key thing is to have the wisdom to know what do to with the brief span allotted to us. We live in a day of great gospel opportunity. God has sent his Son the Lord Jesus to die for our sins and rise again from the dead. Jesus now calls us to put our faith in him that we may be forgiven and have the hope of eternal life. History seems to be stuck on fast forward. In the words of the old hymn, 'swift to its close ebbs out life's little day'. So, hurry up and wait for what's worth waiting for. Seek the Lord while he may be found; call upon him while he is near.
*For November edition of various parish mags
Labels: Christian faith
An unexpected visit to the National Gallery
The car started to make a funny noise as we travelled to London for a family visit. The idea was that we would stay in London from Thursday to Saturday and then set off to Eastbourne for a two week break.
But as we turned off the M4 we noticed the car sounded a bit odd. Like our old school unleaded guzzling Ford Focus had transitioned into a whining elecric job. Freaky. On arriving at our destination a peek under the bonnet revealed a fluid leak. Not engine oil, but whatever it was, there was quite a bit of it. Too much to risk proceeding with our journey without getting it looked at.
A visit to a garage on Saturday morning revealed that the power steering pipe needed replacing. Couldn't be done until Monday at the earliest. We were stuck. In London. Where there's always stuff to see and do.
Like arty stuff in an air conned gallery during yet another summer 2022 hot spell. And so we braved the sweltering Bakerloo line and headed for the effortlessly cool National Gallery.
We hadn't visited for years, so it was like bumping into old friend after old friend as we wandered through the various exhibition rooms. There's Rembrandt as a young man and then as an oldie. The greatest self-portraits ever? And his epic Belshazzar's Feast.
I wanted to see Turner's The Fighting Temeraire. There it was. Like, wow. The ghostly old ship being towed to the breaker's yard by the fiery, modern tug boat. That sunset. On the way we saw Gainsborough's portraits of gentry couples proudly posing on their estates, shooting a confident gaze at their viewers. Placed next to tenderly intimate depictions of the painter's young daughters.
Then the Monets and Reniors. Not to mention Van Gogh's Sunflowers, Chair and Wheat Field. It was the visual eqivalent of playing a setlist of all your favorite songs, with some welcome surprises thrown in. And this was a rushed 2 hour visit in which we sampled only some of the artworks on display in the grandeur of the National Gallery. All for free. To think, we could have been travelling to Eastbourne.
Posted by Guy Davies at 10:28 pm No comments:
An Introduction to John Owen: A Christian Vision for Every Stage of Life, by Crawford Gribben
Crossway, 2020, 190pp
Crawford Gribben has written a full scale biography of John Owen entitled, John Owen and English Puritanism: Experiences of Defeat. This is something different. Here Owen's story is interwoven with his teachings on how the Christian faith casts light on every stage of life, from childhood to death and eternal life. Novices will find this a useful way of getting into Owen and will be stimulated to dive deeper. Seasoned Owen readers will discover fresh insights into some of his key writings.
John Owen was a particular favourite among early Particular Baptists such as Nehemiah Cox. They valued his account of the relationship between the old and new covenants, which they saw as tending in a Baptist direction. Owen was an Independent and a paedobaptist, however. He wrote in defence of infant baptism, but he had a cordial relationship with the Particular Baptists. Unlike other contemporaries he did not accuse them of being schismatic Donatists because they insisted on baptising believers who had been 'baptised' as babies.
Owen's advocacy of infant baptism made for tensions in his ecclesiology. He acknowledged that in the apostolic church "all baptized initiated persons, ingrafted into the church" were recognised as "sanctified persons" (p. 57). Further, "the proper subjects of baptism" are "professed believers... and their infant seed" (p. 58). But this did not mean children of believers should be admitted to church membership, at least not until they had made a credible profession of faith. Admitting unconverted people into the church would have compromised the Independent's vision of churches as a gatherings of visible saints. 'Well, quite', Owen's Baptist friends may have been tempted to say.
Issues of baptism aside, Owen firmly believed that the children of believers needed careful instruction in the faith. To that end he penned The Primer and The Principles of the Doctrine of Christ, Unfolded in Two Short Catechisms. These texts were intended to supplement the teaching children will have received in church meetings.
The rise of William Laud not only made church life difficult for Puritan-minded types. It also made things rather challenging for godly students at Oxford and Cambridge. Certainly for Owen, whose dreams of pursuing an academic career at Oxford were dashed.
Owen's university days had given him a good grounding in theology, but it was through the ministry of an unknown preacher in London that he was converted. Now he had an experiential knowledge of the truths he had studied so diligently at Oxford.
Owen returned to the city in 1651, where he was appointed dean of Christ Church and then vice-chancellor of the university. He took the opportunity to preach to the young people in his charge. Knowing the danger of having only an intellectual knowledge of the truth, the laid great emphasis on practical godliness. John Locke was among Owen's students, but he didn't take kindly to the Puritan's attempts at fostering reformation among the student body.
Two of Owen's sermon series preached to students at Oxford later became the basis of some of his most celebrated works, On the Mortification of Sin and Of Communion with God. In the second title, Owen sought to show how the believer may enjoy distinct communion with each person of the Holy Trinity. He wanted his students not only to have a clear understanding of orthodox theology, but also to deep delight in the one God who is Father, Son and Holy Spirit.
The Restoration of the monarchy in 1660 spelled the end of Owen's role as a prominent public figure. He was dismissed from Oxford and had to keep a low profile, giving himself to pastoral ministry among Independent congregations. Owen now had to plead with the authorities to grant toleration to Puritans who would not conform to the Church of England. He argued that Nonconformists were law abiding citizens who sought to contribute to the common good of England. They were no threat to the established order and should therefore be accorded liberty to practice their faith free from persecution. Owen's ideas were later taken up by his old student, John Locke, in An Essay Concerning Toleration, which is often regarded as a key text in the development of classic liberalism.
For Owen, middle age involved an experience of painful defeat that followed the collapse of Oliver Cromwell's Commonwealth. But if this world often meant suffering for the godly, Owen consoled himself, "It is but yet a little while before it will be no grief of heart unto us for to have done or suffered any thing for the name of the Lord Jesus." (p. 116).
Death and Eternal Life
John Owen looked forward to better days for Christ's 'peaceable kingdom' on earth. Jesus would not, he believed, "leave the world in this state, and set up his kingdom on a molehill." (p. 128). But in later life he lost confidence in his ability to understand what God was doing in history. Gone was the old certainty that the Lord was on the side of Parliament, showing his approval by granting the Ironsides victory over the Royalists at Naseby and Marston Moor. After all, the Charles II was now King, and those identified with the Good Old Cause found themselves on the losing side. He reflected, "I do not know... a greater rebuke, in the whole course of my ministry, than that I have been labouring in the fire to discover the causes of God's withdrawing from us without any success." (p. 130).
John Owen died on 24 August 1683. He knew that death is not a kindly friend, but an unnatural rending of body and soul due to sin. But death could be welcomed, none the less. For the believer death means the end of a lifelong struggle with sin and a departure from this world to be with Christ. Despite the disappointments and reversals he experienced of his earthly life, Owen did not die a broken, disillusioned man. One of his final works was Meditations and Discourses on the Glory of Christ, in which he sought to set forth his view of the supreme glory of the Lord Jesus. The believing soul, which has glimpsed the glory of Christ by faith will at last see him by sight. "the sight of God in Christ, which is intellectual, not corporeal; finite, not absolutely comprehensive of the divine essence, is the sum of our future blessedness." (p. 139).
In his conclusion the author reflects on Owen's lasting impact on society and the the church. The old Puritan's ideas on religious toleration helped to sow the seeds of classic liberalism. His theological writings are the subject of renewed attention in the contemporary Evangelical world.
Crawford Gribben has ably opened up John Owen's Christian vision for every stage of life. An excellent read.
* I am grateful to the author for kindly sending me a free copy.
Posted by Guy Davies at 8:00 am 1 comment:
A tough question
With Boris Johnson announcing that he is standing down as Prime Minister various candidates have been vying for his job. Now the list has been whittled down to the final two, Rishi Sunak and Liz Truss. It is up to Conservative party members to decide who will be the next occupant of 10 Downing Street. You would expect journalists to quiz the candidates on what they would do about the cost of living crisis if they gained power, would they cut taxes and so on. But these days it seems than no media interview or hustings event is complete without politicians being asked: 'What is a woman?' Tough question.
The dictionary definition is 'adult human female'. No surprises there. But giving that answer could get a politician into hot water with those who believe that anyone who says they are a woman is a woman. Even if their anatomy suggests otherwise. Debates over the 'trans' issue have become a highly contested aspect of today's 'culture wars'. Everyday words are changed to reflect this. In guidelines produced by one NHS trust 'mothers' are renamed 'birthing parents', 'fathers' as 'second biological parent'. There is great concern over the number of children being referred to the NHS Gender Identity Development Service because they believe they were born in the wrong body. The vast majority of children seeking help are girls. It was recently announced that the Tavistock child gender identity clinic is due to close, following criticism the quality of care provided in an independent review.
Of course, people suffering from gender dysphoria should be treated with respect and given all the help they need. But there is no escaping biological reality. Each cell in our bodies either has two X chromosomes (female) or one X and one Y chromosome (male). That cannot be changed. It is the way God made us, "So God created mankind in his own image, male and female he created them." The Bible honours the created differences between men and women, but also insists that male and female are of equal value and worth before God.
Jesus counted women as well as men among his early followers. According to the gospel accounts it was women who first discovered that Jesus' tomb was empty and saw him risen from the dead. At the time of the early church society was deeply divided between ethnic groups, salves and masters, men and women. Yet the Christian message was one that brought people together. It teaches us that we are all sinners, but through Jesus we can be forgiven and be put right with God. To believe in him is to belong to his people, where there is "neither Jew nor Gentile, neither slave nor free, nor is there male and female, for you are all one in Christ Jesus."
*For the August edition of various parish magazines
Particular Baptists and Calvinistic Methodists on the Covenant of Grace
John Eilas (1744-1841)
Hanserd Knollys (1599-1691)
Chapter VII of the Westminster Confession of Faith (1646) and the Savoy Declaration (1658) is devoted to 'God's Covenant with Man' (see this tabular comparison). The two confessions are not identical at this point. The wording is different here and there. Savoy omits quite a bit of Westminster's paragraph 5 and the whole of paragraph 6. But they have quite a lot in common. Both both the Presbyterians and Congregationalists were Paedobaptists, holding that the children of believers should be baptised. An essential element of Paedobaptist theology is that just as Abraham's offspring were to be circumcised, so the children of believers should not be denied the new covenant sign of baptism.
That is why Westminster and Savoy say that the covenant of grace was 'differently administered' during the era of the law to what is now the case under the gospel (VII:5). In other words, the Abrahamic and Sinai covenants were administrations of the covenant of grace, as is the new covenant. Under all the various administrations the children of covenant members were to receive the sign of the covenant and either be circumcised (under the law) or baptised (under the gospel).
The trouble with that is under the Abrahamic and Sinai covenants, simply being a descendant of Abraham according to the flesh did not make a person a true believer in the coming Messiah. Paul says as much in Romans 9:6-13. How, then could the Abrahamic and Sinai covenants be administrations of the covenant of grace, when, according to both Westminster and Savoy, the covenant of grace was between God and the elect, who would most certainly be saved?
the Covenant of Grace; wherein he freely offereth unto sinners life and salvation by Jesus Christ, requiring of them faith in him that they may be saved, and promising to give unto all those that are ordained unto life, his Holy Spirit, to make them willing and able to believe. (VII:3).
The framers of the Second London Baptist Confession (1689) denied that the Abrahamic and Sinai covenants were administrations of the covenant of grace. Rather, they were 'steps' under which the covenant promise of salvation was revealed until it was fully made known under the new covenant.
This covenant [of grace] is revealed in the gospel; first of all to Adam in the promise of salvation by the seed of the woman, and afterwards by farther steps, until the full discovery thereof was completed in the New Testament (VII:3).
Accordingly, baptism is only for those who were ordained unto life and have been savingly engrafted into Christ, the evidence of which is their profession of repentance towards God and faith in the Lord Jesus Christ (Chapter XXIX 2LBCF).
Now, eyebrows might be raised at the idea of 'Calvinistic Methodism', thinking that Methodists were Arminians like John Wesley. But George Whitefield was both a Calvinist and a Methodist. So too were his Welsh counterparts, Daniel Rowland and William Williams. Second generation Welsh Calvinistic Methodists left the Church of England and formed their own church grouping. Their leaders such as John Elias and Thomas Charles were very much Calvinist in doctrine and Methodist in spiritual vibrancy. Their confession of faith reflects that.
What I want to highlight here is how the Confession of Faith of the Calvinistic Methodists (1823) resembles the Second London Baptist Confession more than it does Westminster or Savoy in its treatment of covenant theology. Chapter 13 is entitled, 'Of the Eternal Covenant of Grace'. The confession says that the promises of the covenant of grace are given to 'Christ and his seed' and under this covenant this 'seed' will receive eternal life. That could not be said of all Abraham's natural descendants and regretfully, neither is it true of all children of new covenant believers. The final paragraph of Chapter 13 says,
God in his own time reveals this covenant through the gospel to all his people, and, by bringing them to approve and embrace it, brings them into the bond of the covenant, and into actual possession in their own persons of its grace, gifts, and privileges. The covenant of grace was revealed by degrees, and under various dispensations; but the gospel dispensation is the last and most glorious. This covenant is free, sure, holy, advantageous, and eternal.
Note the way in which the penultimate sentence seems to echo the emphasis of the Second London Baptist Confession. Contrary to Westminster and Savoy, the covenant of grace is not said to be 'differently administered' over time, but 'revealed by degrees, and under various dispensations: but the gospel dispensation is the last and most glorious'. That is more or less the equivalent of the 2LBC's 'revealed... by farther steps, until the full discovery thereof was completed in the New Testament'. Quite how on this basis the Calvinistic Methodist fathers still went on to affirm infant baptism in Chapter 37 of the confession, I am at a loss to know.
My point is that few would doubt that the early Welsh Calvinistic Methodist churches were part of the Reformed family. Their confession placed them in the mainstream of Presbyterian and Reformed thought. Particular Baptist teaching on the covenant of grace sprang up from within the Reformed churches, especially the Independents in the seventeenth century. But they saw with greater clarity that the Abrahamic and Sinai covenants could not simply be identified with the covenant of grace. They were 'covenants of promise' (Ephesians 2:12) in which the covenant of grace was progressively disclosed.
All agree that the covenant of grace is with God and his elect people in Christ and made effective by the Spirit. The genius of the Particular Baptists was to follow the biblical logic of that position to say that baptism should therefore only be administered to believers on profession of faith, who are then admitted to the membership of a local church. Doctrinally speaking, we are indeed Reformed Baptists. But that in itself is not sufficient, we also need something of the life and fire of the old Calvinistic Methodists.
Labels: Baptists, Creeds Confessions, Second London Baptist Confession
The cost of living (Jesus' Way)
Here's where I embarrass myself by writing an article on what the government needs to do to fix the cost of living crisis. Basically, they have to make sure that stuff is cheaper, and that people have enough money to pay for the stuff they need. I think that just about covers it. Agreed?
Whether Liz Truss or Rishi Sunack wins the Conservative leadership election, their success as Prime Minister will rest on coming up with policies that address the cost of living crisis. Especially when it comes to fuel and food. It can't be right that some people in our society will have to choose between heating and eating come the chilly winter months.
Jesus spoke about the cost of living too. According to the economics of the kingdom of God the gift of eternal life can't be bought, but it will cost you everything. It can't be bought because salvation is by God's free grace, not our efforts. That's why he sent Jesus to die for our sins so that all who believe in him may be forgiven and have the hope of glory to come.
While grace is free, it is not cheap. People may quite like the idea of eternal life, but strictly on their own terms. Well, no. Jesus wants disciples who will follow him, not consumers who just want what he has to give. The Lord Jesus challenged his would-be followers, "Whoever does not bear his own cross and come after me cannot be my disciple." He urged people to count the cost of discipleship saying, "any one of you who does not renounce all that he has cannot be my disciple." If we would truly live, we must die to self and follow Jesus. That's the cost of living his way.
*For the July edition of local parish magazines.
Pastors, bodily training is of some value
In one of the Bible's Horrible Histories moments Eglon the tubby tyrant is put to the sword by Ehud the left-handed judge. See Judges 3:12-30 for the lowdown. When Ehud stabbed the King of Moab in the guts with his sneakily concealed blade we are told, "And the hilt also went in after the blade, and the fat closed over the blade, for he did not pull the sword out of his belly; and the excrement came out." (Judges 3:22). Nice.
Now, I don't think this episode is in the Bible first and foremost to shame us into keeping ourselves in trim. But it does seem that mention of Eglon's weight is meant to tell us something about his character. Similarly, when Eli fell backwards off his chair on hearing the Philistines had captured the ark of the covenant, we are told, "his neck was broken and he died, for the man was old and heavy." (1 Samuel 4:18). Eli and his sons had previously been accused of, "fattening yourselves on the choice parts of every offering made by my people Israel?'" (1 Samuel 2:29).
Gluttony is condemned in Proverbs 23:20-21, 28:7. According to Paul a distinguishing mark of "enemies of the cross of Christ" is that, "their god is their belly" (Philippians 3:19). Meanwhile, among the fruit of the Spirit is "self control" Galatians 5:23). While Paul urged Timothy to "train yourself for godliness", he also admitted, "bodily training is of some value" (1 Timothy 4:7-8). Too right.
A recent government report revealed that around three quarters of those aged 45-74 in the United Kingdom are overweight or obese. Being overweight leads to a range of other serious health problems. According to a report in thebmj, "Covid-19 death rates are 10 times higher in countries where more than half of the adult population is classified as overweight".
The answer to question 73 of The Baptist Catechism on the sixth commandment ("you shall not kill") spells out what is required in that commandment, "The sixth commandment requireth all lawful endeavours to preserve our own life (Eph. 5:28,29) and the life of others". That's why self control in diet, plus regular bodily exercise aren't optional lifestyle choices for followers of Jesus, but a matter of obedience to the Lord.
Now, the reasons why people become overweight are complex. Physical exercise isn't a possibility for people with debilitating illnesses that severely limit their movement. We know that. But in general terms regulating weight is about eating sensibly and taking regular exercise. Elders/overseers should model a life characterised by self control (1 Timothy 3:2, Titus 1:8). How can we preach to others on that virtue (Titus 2:2, 5, 6, 12) when self control is conspicuously lacking in us?
Perhaps all this is easy for me to say as I've never had to battle with being overweight. My teenage nickname was 'Ribs the Mod' because I was skinny and a mod. Shortly after getting married in my mid 20's I went up a waist size from 32" to 34", but I've remained that size until now (mid 50's). If I did one of those 'before and after' photos, all you'd notice is I now have less hair than 10 years previously. In fact few things bring out the Pharisaic 'older brother' in me than the hearty congratulations elicited by 'after diet' snaps, "'Look! All these years I've been slaving [slimming] for you and never disobeyed your orders [rarely ate biscuits]. Yet you never gave me even a young goat so I could celebrate with my friends.'" (Luke 15:29).
You want to know the secret of the 'Davies Diet & Exercise Regime'? Sorry to keep you in suspense until the end of the post. Here it is. Eat less stuff as you get older and your metabolism slows down. Rarely eat between meals. Spurn biscuits. Mostly. Enjoy a balanced diet with plenty of fruit and veg. Have a bit of a workout with some reps & a spin on an exercise bike most days. Go for a decent walk with your wife on your day off. Climb a mountain every now and again. Because bodily training is of some value.
Labels: Christian Life, Pastoral ministry


* Holiday Jazz Chants is a collection of 50 songs and chants celebrating major holidays in the United States. * Organized according to the calendar year, the provides four to five thematic songs or chants for each month from January through December. * Holidays include Valentine s Day, Mother s Day, Thanksgiving and many more. * The chants and songs teach vocabulary, expressions, and language functions associated with each holiday, as well as interesting cultural traditions.


[Activity gallery] YVC opened a promotion hall in Gangnam Tourist Information Center.
YVC opened a promotion hall in the Gangnam Medical Tour Center.
It provides professional counseling to foreign tourists visiting the Medical Tour Center.
YVC's specialized voice surgeries were publicized.


A smash hit for Flo Ziegfeld in 1928 on Broadway and again in 1930 for Samuel Goldwyn, Whoopee! made Eddie Cantor an even bigger star than he already was and gave the world two of the greatest songs of the first half of the 20th century, "Makin' Whoopee" and "Love Me Or Leave Me". A thoroughly goofy story of rivalry, car (and horse) chases, threatened violence, and true love, Whoopee! is a gem of a show that is a lot like 1930 Bolton/McGowan/Gershwin beaut Girl Crazy only with a whole lot of hypochondria thrown in! William Anthony McGuire's book is a gas, and Gus Kahn and Walter Donaldson's songs are an outright hoot in classic, saucy 1920s musical comedy style. We're not talking deep here, but man are we having fun!
Bob Wells, the sheriff of Mission Rest, Arizona, the scene of our story, is preparing to marry local beauty Sally Morgan from the Bar M Ranch, but she loves her childhood friend Wanenis, the Dartmouth-educated son of the chief of a local tribe of native Americans. Since Sheriff Bob has made it clear that he'll kill her love if he comes anywhere near town, Sally flees the wedding with hypochondriac Henry Williams (who has come out West to die) leaves a note saying they've eloped! Chasing them are jilted Bob, Henry's nurse Mary (who's totally in love with him and knows he isn't dying) and plenty of others. All, of course, works out for the best in this best of all musical comedy worlds!


Over one third of high school students don't know basic civics. Here is an exciting way to teach them America's system of justice. Susan Kuklin gives readers the inside story of a dynamic contemporary court case and uses exclusive interviews with all the participants to explain what happened. Kuklin had unparalleled access to the prosecution, the defense, the judge, and even, after the case, the jury in a dramatic case involving a kidnapping ring in New York's Chinatown.


Across the country there are band programs that locally have a big following and get lots of recognition, but nationally don't typically get the love and attention they deserve.
One of those bands is the UMASS Minuteman Marching Band. These guys will blow you away!
We were able to visit with their staff this past summer and we can tell you first hand that they can march into any stadium and absolutely take over. Like the Jacksonville State Marching Southerners, this is a band that immediately draws the attention of everyone in the crowd with their size and monster sound. Let's just say they you better put your best show on the field that day or else they will blow you out of your own stadium.
Under the direction of Dr. Tim Anderson this band will continue to be the king of the northeast and we can't wait to see what they do next.
Enjoy this monster postgame performance from their recent game against Appalachian State.
Crazy good! And all the singers were in band! They are amazing!!


Although the childhood aggression literature is well developed, there is relatively little research examining longitudinal relations between early childhood parenting and peer interaction and later aggressive behavior in children. Relationships with parents affect how future relationships are approached, and receiving sensitivity from and having a secure relationship with one's parents are related to less child aggression. Additionally, peer relationships contribute to the development of aggression. The current study examines how characteristics of parental quality (maternal sensitivity, conflict, and closeness) and interactions with peers (prosocial, aggression, and positive and negative contributions to play) at 54-months are associated with children's aggressive behavior, as reported by multiple informants, in 3rd grade through 6th grade (N = 1,364; 52.4% female; 85.4% White). Data came from the SECCYD, and I tested these associations with structural equation modeling using Mplus version 6. Maternal, teacher, and self reports of aggressive behavior in grades 3-6 were examined. In the maternal report model, I report stability in aggression behaviors overtime and that maternal relationships in early childhood are related to general and relational aggression, but generally unrelated to changes in child general and relational aggression across grades 3-6. I also did not find much of a relation between friendships in early childhood and later aggression. Further, only the maternal report yielded significant findings. I conclude that maternal relationships could be predictive of maternal views of their children's initial aggressive behavior, both relationally and in general, but not predictive of changes in aggression. Overall, these findings suggest that prevention and intervention efforts should be focused prior to third grade.