Number Theory with an Emphasis on the Markoff Spectrum


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Volume s , Issue 2. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. If the address matches an existing account you will receive an email with instructions to retrieve your username. LMS Membership lms. Joan S. Search for more papers by this author. Tools Request permission Export citation Add to favorites Track citation.

Share Give access Share full text access. Share full text access. In mathematics, the Markov spectrum devised by Andrey Markov is a complicated set of real numbers arising in Markov Diophantine equation and also in the theory of Diophantine approximation. The formulation with the reciprocal is awkward, but the traditional definition invites it; looking at the set of c instead allows a definition instead by means of an inferior limit.

For that, consider. Freiman's constant is the name given to the end of the last gap in the Lagrange spectrum, namely:. Real numbers greater than F are also members of the Markov spectrum. On the other hand, the final part of these sets lying after Freiman's constant are also equal, but a continuous set.

Boundaries are so important as our relationships with our children progress and we will talk about a few ways to set them with babies, toddlers and into childhood. Within 5 minutes, we can go from feeling like we are going to pull our hair out, to feeling like our hearts are going to burst with joy and love for our kids.

How can we balance the ideas of living in the present moment and cherishing our children with just surviving the difficult, patience testing storms? Today we will give you concrete tips on how to both reframe your perspective and also increase your parenting tools which will make finding moments to enjoy a bit easier. There is a way to maintain balance and contentment while experiencing the entire messy spectrum that is parenting, and we hope to help you discover it. Finding Light Through Hard Times.

If we can find peace within our own hearts we will be able to make it through hard things and come out better for them. If we can teach this to our kids imagine the endless life they will have! None of us get through this life without dealing with loss of some kind or another. We lose loved ones, experience the grief associated with loss of expectations, and many experience betrayal and our own regret.

In a family, we not only have our own grief to process, but we also watch our partners and children grieve. Today we are going to delve into our own personal experiences with grief and some things we have found helpful while processing our own as well as guiding our families through the waters of loss. Comparison vs. We see all the achievement of others and none of the downfall. When in reality we only have this exact moment we are in, so how can we remember that? By interviewing many people on this concept, we have found some great tips that will hopefully help you with that.

In this episode, we cover what it means to be content with your current stage and not torture yourself with all the other infinite options available to you , while still making sure you are fulfilled on the inside by still growing on the inside and connecting with yourself and your purpose. Parenting with Unconditional Love. This episode is close to our hearts.

When we react to our children with anger, it makes them focus their attention on OUR reaction, not their own action. Of course we love our children unconditionally, and expressing anything other than that is inauthentic. Are our actions showing that? Are we accepting all their big, scary or sad emotions as well as their big positive emotions?

On this episode we will walk you through specific examples of different common parenting scenarios and ways to reframe them without anger, threats, or bribes. What is Love? Cultivating Unconditional Love. Do you feel like your love for yourself or your spouse is conditional? There are so many misconceptions about connection and love. This episode we are sharing some of the concepts that have really shifted our whole perception of what love is.

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Here are the links to books we mentioned this episode! How To: Create Pockets of Peace. The daily grind of life has a tendency to make some of us feel squeezed, so today we are going to talk about preserving or creating pockets of daily decompression time. Emotions Pt. Next to our processing our own emotions, we usually deal with a lot of negative emotions from others.

This technique is powerful because you will learn to respond to others with so much more kindness and awareness when you realize you can keep the power for your own emotions, while allowing others the space to feel and process their own negative feelings. We hope you find the freedom in it as well!

In this episode, we mention one of our favorite childcare experts, Janet Lansbury. Here is a link to one of her books that we absolutely love, called Elevating Childcare. We explore the word magic and talk about what we do to bring more of it in our life. The key is being in the present moment, but how do we actually do that?

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We talk about that. We have you covered. At the end of most days, do you feel like you are failing or succeeding? We will help you discover for yourself what is essential for YOU to become your best self and to feel like you are succeeding.

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Most of us spend most of our day doing important things, but miss doing the essential things that are truly aligned with our core values, and over time, will help us create our best life. Here are the steps to discover and implement YOUR essentials: 1. Make 3 lists of the important things you do or would like to do in your day, separating them into 3 lists: Essentials, Super Important, and Good to Do.

Then look at your lists again and move things around until the items left in your essentials are truly a SHORT list of things that help you become who you want to become. Our lists are below as examples of possibilities. Both of us have our Miracle Morning Routine on it, which centers on us taking time to connect with ourselves, with our goals, and with God.

Our miracle morning routines includes Meditation Silence , affirmations, visualization, exercise, reading, writing scribing. We have one for us and for our kids. Make it non-negotiable. Think of something already non-negotiable in your life, and figuratively put into that same space.

Roy : Markoff–Lagrange spectrum and extremal numbers

Eliminate decision making fatigue. Make a quick list of how doing these essentials over your time in your life will make you feel. Keep asking the question until you get to a feeling: happy? Take a minute to tap into that feeling NOW so you can come from a place of abundance. Mark off each day you do your essentials list.

We do one slash of an X for personal, and one for kids or career. The idea is to fill up as much of the year as possible, and not to worry when you miss a day. Over a year, a decade, or a life, all the days add up, and there is no such thing as all or nothing with this.


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Morning Routines for a 30 day transformation. Meet Taralyn! My cohost for Find the Magic! She is sharing her morning routines in this insightful episode. Hone your perfect morning routine! We are breaking down our morning routines and tools to make them happen. My meditation I invite you to try for 30 days: 1. Gratitude Breaths: 3 super deep breaths, thinking of one thing you are grateful for per breath, 2. Loving kindness meditation: Picture someone you love in front of you, and take a deep breath, and imagine all of the cells in your body lighting up with love and awesome energy.

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Then, take a super deep breath in and exhale that love out to your whole home or building. Do that same thing with your city, state, country, earth, and universe imagining the love coming back to you on each inhale and sending it out on the exhale. Mantra Meditation: take deep breaths, repeating the word ONE in your mind.

Just come back to the word ONE and take a few more breaths. Sit down with a journal, book, and timer. Document your state! Write down your current ratings on a scale of of Balance 1 being totally unbalanced and 10 being perfectly balanced and Contentment: 1 being not content with yourself or any aspect of life and 10 being perfectly content with yourself and your life.

Number Theory with an Emphasis on the Markoff Spectrum Number Theory with an Emphasis on the Markoff Spectrum
Number Theory with an Emphasis on the Markoff Spectrum Number Theory with an Emphasis on the Markoff Spectrum
Number Theory with an Emphasis on the Markoff Spectrum Number Theory with an Emphasis on the Markoff Spectrum
Number Theory with an Emphasis on the Markoff Spectrum Number Theory with an Emphasis on the Markoff Spectrum
Number Theory with an Emphasis on the Markoff Spectrum Number Theory with an Emphasis on the Markoff Spectrum

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