OpenLLM-France/wikimedia huggingface dataset:
# Knowing Someone/Conversation Topics/Conversation catalysts

Conversation catalysts are personal and revealing without being intrusive. Here are some suggestions:
* Who taught you to tie your shoes?
* What’s the first meal you learned to cook?
* What was your favorite childhood book or story?
* Who gave you your first piece of advice that really stuck with you?
* What was your favorite activity to do after school when you were a kid?
* What’s a tradition or habit your family had that you still follow today?
* When was the first time you felt truly independent?
* Who was your first role model growing up?
* What’s a small, seemingly insignificant thing from your childhood that you remember vividly?
* What was the first big decision you made for yourself?
* What’s a skill you learned as a child that you still use today?
* What was your favorite thing to do during summer vacations as a kid?
* What’s a piece of advice you received from a grandparent or older family member?
* What was the first job you ever had, and what did you learn from it?
* Who taught you to ride a bike, and how did that experience go?
* What’s a memorable birthday or holiday gift you received as a child?
* Do you remember the first time you traveled somewhere far from home?
* What’s the first movie or TV show that really made an impact on you?
* What’s a hobby or interest you picked up from a family member or friend?
* Was there a specific place or space that made you feel most at home growing up?
* Who was the first teacher that really influenced or inspired you?
* What’s the first song or album you remember loving?
* What was the first pet you ever had, and what was its name?
* What’s a lesson you learned from a mistake you made early in life?
* What’s the first thing you remember saving money for?
* Who was the first person outside your family who really believed in you?
* What’s a tradition or custom from your childhood that you still find meaningful today?
* Do you remember the first time you stood up for something you believed in?
* What’s a favorite childhood game you used to play with friends or family?
* Who taught you how to drive, and how did it go?
* What’s a family recipe or dish that brings back memories?
These prompts encourage reflection on formative experiences, offering insights into personal history and values, while remaining light and open. They tap into personal memories, offering opportunities for meaningful connections without feeling too direct or invasive.
# Knowing Someone/Big Talk

In contrast to small talk, "Big talk" conversations delve into deeper, more substantial topics that go beyond the surface. These discussions often involve personal beliefs, values, and experiences. Here's a list of topics that can spark meaningful and thought-provoking "big talk" conversations:
* Your Story:
** Tell me your story. Where did you grow up? Tell me about school. Tell me about work. Tell me about living. What is your brand?
** I noticed … and was wondering …
* Life Goals and Aspirations:
** "What are your long-term goals, and what steps are you taking to achieve them?"
* Philosophy of Life:
** "What guiding principles or philosophies shape your approach to life?"
* Meaningful Experiences:
** "Can you share a significant experience that has had a profound impact on your life?"
* Passions and Dreams:
** "What are you truly passionate about, and do you have any dreams you're working towards?"
* Personal Values:
** "What values are most important to you, and how do they influence your decisions?"
* Moral Dilemmas:
** "Are there any ethical dilemmas or moral questions that you find particularly interesting or challenging?"
* Books or Articles That Impacted You:
** "Can you recommend a book or article that significantly influenced your perspective?"
* Social or Environmental Causes:
** "Are there social or environmental causes that you're deeply passionate about?"
* Challenges and Overcoming Adversity:
** "What challenges have you faced, and how have they shaped who you are today?"
* Personal Growth and Development:
** "In what ways do you strive for personal growth, and how do you handle self-improvement?"
* Cultural Perspectives:
** "How has your cultural background influenced your worldview?"
* Travel Experiences:
** "What is the most impactful or eye-opening place you've visited, and why?"
* Creativity and Expression:
** "How do you express your creativity, and why is it important to you?"
* Health and Well-being:
** "How do you prioritize and maintain your physical and mental well-being?"
* Relationship Dynamics:
** "What do you believe contributes to healthy and meaningful relationships?"
* Educational Pursuits:
** "Are there subjects or areas of study that you find particularly fascinating or challenging?"
* Hobbies and Personal Projects:
** "Do you have any hobbies or personal projects that bring you a sense of fulfillment?"
* Global Issues:
** "What global issues concern you the most, and how do you think they should be addressed?"
* Mindfulness and Reflection:
** "How do you practice mindfulness or reflection in your daily life?"
* Legacy and Impact:
** "When you think about your legacy, what kind of impact do you hope to leave?"
Remember to approach these topics with sensitivity, and be prepared for varying levels of comfort with personal disclosure. "Big talk" is about fostering deeper connections and understanding, so it's important to create a space where both individuals feel comfortable sharing their thoughts and experiences.
# Knowing How You Know/template
## Template

How do you decide what to believe?
Your theory of knowledge provides answers to the important questions: “How do you know?”, “How do you know?”, and “How do you know?”
Develop your own Theory of Knowledge by answering these questions.
It may be helpful to study the annotated version of this template to gain insight into the various questions posed here.
Please make a copy of this template for your use before answering the questions so this copy is ready for the next student.
* How do you assess the reliability, objectivity, and relevance of an information source?
* How do you evaluate the credibility, reliability, objectivity, and relevance of an expert or authority?
* How do you assess the relevance of evidence?
** How do you assess the relevancy of anecdotal evidence compared to systematic evidence?
** How do you assess the credibility, reliability, objectivity, and relevance of information based on statistics?
** When empirical evidence contradicts a firmly held ideology, how do you resolve the conflict?
* When do you find expert testimony more or less compelling than direct examination of evidence?
* How do you maintain your objectivity when subjected to various forms of influence?
** Sources of influence include direct observation, listening, dialogue, suggestion, recommendation, advice, opinion, education, previous experience, existing beliefs, ideology, reading, advertisements, indoctrination, propaganda, censorship, counseling, peer pressure, attachment, and habits.
* How do you maintain your objectivity when subjected to various forms of power?
** Power may be present in the form of
*** Dominance—The ability to inflict harm, also known as aggressive coercion, or
*** Stature—The ability to provide help, also known as leverage, or
*** Influence—altering people's beliefs.
* When do you examine your beliefs from a variety of reference frames?
** What happens when you drill down to a much smaller and more detailed scale of time or space?
** What happens when you frame up to a larger and more comprehensive scale of time or space?
** What happens to your beliefs when you adopt a global perspective?
** When and how might you change your beliefs if they are contradicted when examined from a particular reference frame, such as those mentioned above?
* How do you maintain your objectivity when a compelling narrative depends on incredible beliefs?
* How do you assess nonfalsifiable claims?
* When are you comfortable describing your assessment of a belief as “unsure” rather than as strictly true or false?
* What does it take for you to change your mind?
* How do you distinguish well-founded beliefs from assumptions, rumors, myths, and opinions?
You may wish to study examples from this gallery of Theories of Knowledge.
# Forcing equation/Plane/Monomial parameter situation/Example

Let $X$ denote a plane (like $K^{2},\mathbb {R} ^{2},{\mathbb {A} }_{K}^{2}$) with coordinate functions $x$ and $y$. We consider an inhomogeneous linear equation of type
    $x^{a}t_{1}+y^{b}t_{2}=x^{c}y^{d}\,.$
The fiber of the solution set $T$ over a point $\neq (0,0)$ is one-dimensional, whereas the fiber over $(0,0)$ has dimension two (for $a,b,c,d\geq 1$). Many properties of $T$ depend on these four exponents.
# Forcing algebra/Linear equation/Introduction/Section

We describe now the algebraic setting of systems of linear equations depending on a base space. For a commutative ring $R$, its spectrum $X=\operatorname {Spec} {\left(R\right)}$ is a topological space on which the ring elements can be considered as functions. The value of $f\in R$ at a prime ideal $P\in \operatorname {Spec} {\left(R\right)}$ is just the image of $f$ ander the ring homomorphism $R\rightarrow R/P\rightarrow \kappa (P)=Q(R/P)$. In this interpretation, a ring element is a function with values in different fields. Suppose that $R$ contains a field $K$. Then an element $f\in R$ gives rise to the ring homomorphism
    $K[Y]\longrightarrow R,Y\longmapsto f,$
which gives rise to a scheme morphism
    $\operatorname {Spec} {\left(R\right)}\longrightarrow \operatorname {Spec} {\left(K[Y]\right)}\cong {\mathbb {A} }_{K}^{1}.$
This is another way to consider $f$ as a function on $\operatorname {Spec} {\left(R\right)}$ with values in the affine line.
The following construction appeared first in the work of Hochster in the context of solid closure.

## Definition

Let $R$ be a commutative ring and let $f_{1},\ldots ,f_{n}$ and $f$ be elements in $R$. Then the $R$-algebra
    $R[T_{1},\ldots ,T_{n}]/{\left(f_{1}T_{1}+\cdots +f_{n}T_{n}-f\right)}$
is called the forcing algebra of these elements
The forcing algebra $B$ forces $f$ to lie inside the extended ideal ${\left(f_{1},\ldots ,f_{n}\right)}B$ (hence the name). For every $R$-algebra $S$ such that $f\in {\left(f_{1},\ldots ,f_{n}\right)}S$ there exists a (non unique) ring homomorphism $B\rightarrow S$ by sending $T_{i}$ to the coefficient $s_{i}\in S$ in an expression $f=s_{1}f_{1}+\cdots +s_{n}f_{n}$.
The forcing algebra induces the spectrum morphism
    $\operatorname {Spec} {\left(B\right)}\longrightarrow \operatorname {Spec} {\left(R\right)}.$
Over a point $P\in X=\operatorname {Spec} {\left(R\right)}$, the fiber of this morphism is given by
    $\operatorname {Spec} {\left(B\otimes _{R}\kappa (P)\right)},$
and we can write
    $B\otimes _{R}\kappa (P)=\kappa (P)[T_{1},\ldots ,T_{n}]/{\left(f_{1}(P)T_{1}+\cdots +f_{n}(P)T_{n}-f(P)\right)}\,,$
where $f_{i}(P)$ means the evaluation of the $f_{i}$ in the residue class field. Hence the $\kappa (P)$-points in the fiber are exactly the solutions to the inhomogeneous linear equation $f_{1}(P)T_{1}+\cdots +f_{n}(P)T_{n}=f(P)$. In particular, all the fibers are (empty or) affine spaces.
# Forcing algebra/Regular ring/Roberts/Example

Let $K$ be a field of characteristic $0$ and let
    $B=K[X,Y,Z][U,V,W]/{\left(X^{3}U+Y^{3}V+Z^{3}W-X^{2}Y^{2}Z^{2}\right)}\,.$
Then the ideal ${\mathfrak {a}}=(X,Y,Z)B$ has the property that $H_{\mathfrak {a}}^{3}(B)\neq 0$. This means that in $R=K[X,Y,Z]$, the element $X^{2}Y^{2}Z^{2}$ belongs to the solid closure of the ideal ${\left(X^{3},Y^{3},Z^{3}\right)}$, and hence the three-dimensional polynomial ring is not solidly closed.
# Forcing equation/Line/Example

We consider the line $X={\mathbb {A} }_{K}^{1}$ (or $X=K,\mathbb {R} ,\mathbb {C}$ etc.) with the (identical) function $x$. For $f_{1}=x$ and $f=0$, i.e. for the homogeneous equation $xt=0$, the geometric object $V$ consists of a horizontal line (corresponding to the zero-solution) and a vertical line over $x=0$. So all fibers except one are zero-dimensional vector spaces. For the inhomogeneous equation $xt=1$, $T$ is a hyperbola, and all fibers are zero-dimensional with the exception that the fiber over $x=0$ is empty.
For the homogeneous equation $0t=0$, $V$ is just the affine cylinder over the base line. For the inhomogeneous equation $0t=x$, $T$ consists of one vertical line, almost all fibers are empty.
# Forcing algebra/Relation to tight closure/Local cohomology/Characterization/Fact

Let $R$ be a normal excellent local domain with maximal ideal ${\mathfrak {m}}$ over a field of positive characteristic. Let $f_{1},\ldots ,f_{n}$ generate an ${\mathfrak {m}}$-primary ideal $I$ and let $f$ be another element in $R$.
$f\in I^{*}$ if and only if $H_{\mathfrak {m}}^{\dim(R)}(A)\neq 0$, where $A=R[T_{1},\ldots ,T_{n}]/{\left(f_{1}T_{1}+\cdots +f_{n}T_{n}+f\right)}$
# Motivation and emotion/Book/2018/Voluntary missing person motivation/Read more
## Incidence of voluntary missing persons
### Incidence:

* United States of America:
National Crime Information Center (NCIC) (2017) received 1,907,657 reports of missing persons in 2017, with 47% of these reports defined as juveniles under the age of 21.
* United Kingdom and Wales:
National Crime Agency (NCA) (2017) recorded 242,317 incidents on a police missing persons system in England and Wales in 2016/2017.
Children account for 60% of missing persons in the UK (122,321), as compared to 80,281 missing adults
* Europe:
In 2016, AMBER Alert Europe reported that 3,536 children were missing across 23 different countries in Europe (AMBER Alert Europe, 2017).
* Australia:
Over 305,000 people were reported missing in Australia from 2008-2015 (Bricknell, 2017), which is estimated to be one person reported missing every 18 minutes (Henderson, Henderson & Kiernan, 2000). Around 38,159 reports are made on average every year (Bricknell, 2017).
* New Zealand:
There are around 8,000 reports of missing persons each year to police in New Zealand (Missing Persons: Myths and facts, 2017)

## Impacts of voluntary missing persons

When someone goes missing, it not only impacts the close family and friends of the missing individual, but the community as a whole. Research has shown that with every one missing person, at least 12 other people were affected. This can be in the form of emotional, psychological, physical or financial concerns. The use of professional health services, taking days off work, and the subsequent effect this has on the workplace has implications for the whole community (AFP, 2017).

## References:

Australian Federal Police (AFP). (2017). Myths and facts: A quick guide to the facts on missing persons in Australia. Retrieved from the Missing Persons website: < https://missingpersons.gov.au/about/myths-and-facts>.
Bricknell, S. (2017). Missing persons: Who's at risk? (Research Report No. 08). Canberra: Australian Institute of Criminology.
Henderson, M., Henderson, P., & Kiernan, C. (2000). Missing persons: Incidence, issues and impacts (Trends & issues in crime and criminal justice No.144). Canberra: Australian Institute of Criminology.
National Crime Agency (NCA). (2017). Missing persons data report 2015/2016 [Version 3.3]. Retreived from: <http://nationalcrimeagency.gov.uk/publications/876-missing-persons-data-report-2015-2016-1/file>.
National Crime Information Centre (NCIC). (2018). 2017 NCIC missing person and unidentified person statistics. Retrieved from: <https://www.fbi.gov/file-repository/2017-ncic-missing-person-and-unidentified-person-statistics.pdf/view>.
# Hyperbolic function/R/Hyperbolic sine/Definition

The function defined for $x\in \mathbb {R}$ by
    $\sinh x:={\frac {1}{2}}{\left(e^{x}-e^{-x}\right)}\,,$
is called hyperbolic sine.
# Hyperbolic functions/R/Derivatives/Exercise

Determine the derivatives of hyperbolic sine and hyperbolic cosine.
# Hyperbolic function/R/Monotonicity properties/Fact

hyperbolic sine is strictly increasing, and the function hyperbolic cosine
$\mathbb {R} _{\leq 0}$
$\mathbb {R} _{\geq 0}$
# Hyperbolic function/R/Monotonicity properties/Fact/Proof

See exercise and exercise.
# Hyperbolic functions/R/Elementary properties/Fact

The functions hyperbolic sine and hyperbolic cosine have the following properties.
    $\cosh x+\sinh x=e^{x}\,.$
    $\cosh x-\sinh x=e^{-x}\,.$
    $(\cosh x)^{2}-(\sinh x)^{2}=1\,.$
# Hyperbolic function/R/Hyperbolic tangent/Definition

The function
    $\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto \tanh x={\frac {\sinh x}{\cosh x}}={\frac {e^{x}-e^{-x}}{e^{x}+e^{-x}}},$
is called hyperbolic tangent.
# Hyperbolic functions/Addition theorems/Exercise

Prove the addition theorems for the hyperbolic functions, that is,
a)
    $\sinh(x+y)=\sinh x\cosh y+\cosh x\sinh y\,.$
b)
    $\cosh(x+y)=\cosh x\cosh y+\sinh x\sinh y\,.$
# Hyperbolic functions/R/Elementary properties/Fact/Proof/Exercise

Prove the following properties of the hyperbolic sine and the hyperbolic cosine
    $\cosh x+\sinh x=e^{x}\,.$
    $\cosh x-\sinh x=e^{-x}\,.$
    $(\cosh x)^{2}-(\sinh x)^{2}=1\,.$
# Hyperbolic function/R/Hyperbolic cosine/Definition

The function defined for $x\in \mathbb {R}$ by
    $\cosh x:={\frac {1}{2}}{\left(e^{x}+e^{-x}\right)}\,,$
is called hyperbolic cosine.
# Linear system/Inhomogeneous/3014/2201/4601/1350/Is 4023/Exercise

Solve the following system of inhomogeneous linear equations.
    ${\begin{matrix}3x&\,\,\,\,\,\,\,\,&+z&+4w&=&4\\2x&+2y&\,\,\,\,\,\,\,\,&+w&=&0\\4x&+6y&\,\,\,\,\,\,\,\,&+w&=&2\\x&+3y&+5z&\,\,\,\,\,\,\,\,&=&3\,.\end{matrix}}$
# Linear system/Equating method/Remark

Another method to solve a linear system is the equating method. Here, the variables are also successively eliminated, but in another way. In this method, in every equation $G_{i}$, $i=1,\ldots ,m$, we isolate one fixed variable, say $x_{1}$. Suppose that (after reordering) $G_{1},\ldots ,G_{k}$ are the equations where the variable $x_{1}$ occurs with a coefficient different from $0$. These equations are brought into the form
    $G_{i}':\,\,\,x_{1}=F_{i},$
where in $F_{i}$, the variable $x_{1}$ does not occur. The linear system consisting in
    $G_{1}',F_{1}=F_{2},F_{1}=F_{3},\ldots ,F_{1}=F_{k},G_{k+1},\ldots ,G_{m}$
is equivalent to the original system. We continue with this system without $G_{1}'$.
# Linear system/Not in standard form/Remark

It might happen that a system of linear equations is given in such a way that there are variables on both sides of the equations, like in
    $3x-4+5y=8z+7x\,,$
    $2-4x+z=2y+3x+6\,,$
    $4z-3x+2x+3=5x-11y+2z-8\,.$
In this case, one first transforms this system to the standard form by simple additions and processing the coefficients in each equation.
# Linear system/Inhomogeneous/1234/2345/1010/1551/Is 1790/Exercise

Solve the following system of inhomogeneous linear equations.
    ${\begin{matrix}x&+2y&+3z&+4w&=&1\\2x&+3y&+4z&+5w&=&7\\x&\,\,\,\,\,\,\,\,&+z&\,\,\,\,\,\,\,\,&=&9\\x&+5y&+5z&+w&=&0\,.\end{matrix}}$
# Nonlinear finite elements/Model problems
## Model problems

Let us look at a couple of model problems.

### Problem 1: First-order homogeneous ODE

The first problem involves a homogeneous first order differential equation and is stated as:
    ${\text{(1)}}\qquad {\begin{aligned}{\text{Find}}~u(t)&~{\text{such that it satisfies}}\\&{\frac {du}{dt}}+u=0,\qquad t>0\\&u(0)=1\end{aligned}}$
The exact solution is
    ${\text{(2)}}\qquad {u(t)=e^{-t}~.}$

### Problem 2: Second-order inhomogeneous ODE

The second problem involves an inhomogeneous second order differential equation and is stated as:
    ${\text{(3)}}\qquad {\begin{aligned}{\text{Find}}~u(x)&~{\text{such that it satisfies}}\\&-{\frac {d^{2}u}{dx^{2}}}+u=x,\qquad x\in (0,1)\\&u(0)=0,\qquad u(1)=0\end{aligned}}$
The exact solution is
    ${\text{(4)}}\qquad {u(x)=x-{\frac {\sinh(x)}{\sinh(1)}}~.}$

### Remarks

Both model problems have exact solutions. However, in most situations, such solutions may be impossible to get because:
* No solution exists since the data are not smooth enough.
* Even if a solution exists, it cannot be found in closed form because of the complexity of the problem.
To overcome these problems, we can do the following :
* Reformulate the problem so that it admits weaker conditions on the solution and its derivatives. Thus the equation no longer needs to be satisfied at all points in the domain. These are called weak or variational formulations.
* Break the domain up into smaller pieces and require the equation to be satisfied at only a few points within each piece.
* Assume that the approximate solution has a known form.
Finite element methods use a weak (or variational) formulation of the original strong problem.
# Nonlinear finite elements/Motion in Lagrangian form
## Motion in Lagrangian form

The motion is given by
    ${x=\varphi (X,t)=x(X,t)~,~~\qquad X\in [0,L_{0}]~.}$
For the reference configuration,
    $X=\varphi (X,0)=x(X,0)~.$
The displacement is
    ${u(X,t)=\varphi (X,t)-X=x-X~.}$
For the reference configuration,
    $u_{0}=u(X,0)=\varphi (X,0)-X=X-X=0~.$
The deformation gradient is
    ${F(X,t)={\frac {\partial }{\partial X}}[\varphi (X,t)]={\frac {\partial x}{\partial X}}~.}$
For the reference configuration,
    $F_{0}=F(X,0)={\frac {\partial }{\partial X}}[\varphi (X,0)]={\frac {\partial X}{\partial X}}=1~.$
The Jacobian determinant of the motion is
    ${J={\cfrac {A}{A_{0}}}F~.}$
For the reference configuration,
    $J_{0}={\cfrac {A_{0}}{A_{0}}}F_{0}=1~.$
# Nonlinear finite elements/Natural vibration
## Special case : natural vibrations

Recall that the finite element system of equations has the form
    $\mathbf {M} ~{\ddot {\mathbf {u} }}=\mathbf {f} _{\text{ext}}-\mathbf {f} _{\text{int}}~.$
We could also have written this equation as
    $\mathbf {M} ~{\ddot {\mathbf {u} }}+\mathbf {K} ~\mathbf {u} =\mathbf {f} ~.$
For natural vibrations, the forces and the displacements are assumed to be periodic in time, i.e.,
    $\mathbf {u} =\mathbf {u} ^{0}~\exp(i\omega t)~.$
and
    $\mathbf {f} =\mathbf {f} ^{0}~\exp(i\omega t)~.$
Then, the accelerations take the form
    ${\ddot {\mathbf {u} }}=(i\omega )^{2}~\mathbf {u} ^{0}~\exp(i\omega t)=-\omega ^{2}~\mathbf {u} ^{0}~\exp(i\omega t)~.$
Plugging these into the FE system of equations, we get
    $[-\omega ^{2}~\exp(i\omega t)]\mathbf {M} ~\mathbf {u} ^{0}+\exp(i\omega t)~\mathbf {K} ~\mathbf {u} ^{0}=\exp(i\omega t)~\mathbf {f} ^{0}~.$
After simplification, we get
    ${\left(-\omega ^{2}\mathbf {M} +\mathbf {K} \right)~\mathbf {u} ^{0}=\mathbf {f} ^{0}~.}$
If there is no forcing, the right hand side is zero, and we get the finite element system of equations for free vibrations
    ${\left(-\omega ^{2}\mathbf {M} +\mathbf {K} \right)~\mathbf {u} ^{0}=0~.}$
The above equation is similar to the eigenvalue problem of the form
    $\mathbf {A} ~\mathbf {x} =\lambda ~\mathbf {x} \qquad \equiv \qquad \left(\mathbf {A} -\lambda \mathbf {I} \right)\mathbf {x} =0~.$
Since the right hand side is zero, the finite element system of equations has a solution only if
    ${\det(\mathbf {K} -\omega ^{2}\mathbf {M} )=0~.}$
For a two noded element,
    $\mathbf {K} ={\begin{bmatrix}K_{11}&K_{12}\\K_{21}&K_{22}\end{bmatrix}}~{\text{and}}~\mathbf {M} ={\begin{bmatrix}M_{11}&M_{12}\\M_{21}&M_{22}\end{bmatrix}}~.$
Therefore,
    $\mathbf {K} -\omega ^{2}~\mathbf {M} ={\begin{bmatrix}K_{11}-\omega ^{2}~M_{11}&K_{12}-\omega ^{2}~M_{12}\\K_{21}-\omega ^{2}~M_{21}&K_{22}-\omega ^{2}~M_{22}\end{bmatrix}}~.$
The determinant is
    $\det(\mathbf {K} -\omega ^{2}~\mathbf {M} )=(K_{11}-\omega ^{2}~M_{11})(K_{22}-\omega ^{2}~M_{22})-(K_{12}-\omega ^{2}~M_{12})(K_{21}-\omega ^{2}~M_{21})~.$
This gives us a quadratic equation in $\omega ^{2}$ which can be solved to find the natural frequencies of the element.