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RSS Feed for Wolfram Community showing any discussions in tag Mathematica sorted by activeLiquid Chromatography with Linear Adsorption Equilibrium and Transfer Rate Model
https://community.wolfram.com/groups/-/m/t/3143304
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/fa2a641f-9eb5-42d4-92fc-230f6eefc6feHousam Binous2024-03-19T06:45:15ZMathmatica pefromance and CPU usage
https://community.wolfram.com/groups/-/m/t/3143033
I have a general question that may have been addressed previously, albeit not directly. I utilize Mathematica to solve a set of non-linear equations and achieve successful results. However, the computation time is considerably long despite the minimal CPU and memory usage. Additionally, the computer I am using is a high-performance PC, yet the execution speed of this code resembles that of my laptop. Am I overlooking something? Why isn't Mathematica utilizing more resources? For instance, the CPU usage remains around 7% max.Nima Moini2024-03-18T23:02:58ZColloquium event - numerical methods for partial differential equations and their applications
https://community.wolfram.com/groups/-/m/t/3132386
![enter image description here][1]
In this special online colloquium, we have invited researchers from around the world to share their recent exciting work. The topic of the inaugural event in this series is "Numerical Methods for Partial Differential Equations and Their Applications". The works shown range from new quantitative methods, to new real-world applications, to novel ways of modeling. The event also begins with a very brief introduction to [PDE Models][2] in the Wolfram Language that introduces functionality new to Version 14.
The (estimated) start time for each presenter can be found in the cloud notebook here: [Link][3].
To register for the event please follow the link to the BigMarker platform found below.
> [**Register Here**][4]
Please feel free to use this thread to collaborate and share ideas. Also let us know what colloquium topics interest you for future events in this series!
![enter image description here][5]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fem-promo.png&userId=2643831
[2]: https://reference.wolfram.com/language/PDEModels/tutorial/PDEModelsOverview.html
[3]: https://www.wolframcloud.com/obj/jmcnally0/Published/Feb29Colloqium-Schedule.nb
[4]: https://www.bigmarker.com/wolfram-u/numerical-methods-for-pde-and-applications?utm_bmcr_source=community
[5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WolframUbanner.png&userId=2643831John McNally2024-02-28T21:41:17ZTry to beat these MRB constant records!
https://community.wolfram.com/groups/-/m/t/366628
![If you see this text, refresh the page in order to see the images.][1]
Credit: Emanual Missionary Babtist Church of Indianapolis
Hey folks, Marvin Ray Burns here! You might know me for the never-ending decimal that haunts your calculators – the MRB constant. Don't worry, I won't hold it against you if you haven't memorized its first million digits (yet!). In this forum, we're embarking on a wild ride as we work our way to "7,000,000 proven to be accurate digits!"
(select text between quotation marks and push the ![CTRL+f][2] keys on keyboard)
=================================================
I'm the amateur mathematician who discovered this enigmatic constant in 1999, and after years of delving into its mysteries, I'm still captivated by its fascinating properties and untapped potential. Join me, seasoned mathematicians, and curious minds alike, as we push the boundaries of understanding and unlock the secrets of the MRB constant. ![Buckle up!][3] (credit: https://clipground.com/save-lives-clipart.html)
![m][4]
Here's everything I have ever learned, so spend it well!
====================================================
I was inspired by the awe, beauty, and mystery of numbers, and wondered if God would grant me some unique insight and wisdom to explore them. I dreamed of becoming an artistic analyst, a musical mathematician, or even a visionary of scientific secrets, long before I knew what a mathematician was. I searched for inspiration in the numbers that appealed to me, that had beauty and meaning, and that led me to investigate a remarkable and intriguing sum that I could not find anywhere else. For my efforts, someone started calling me an [amateur mathematician][5] and it the [MRB constant][6].
The MRB constant is a fascinating mathematical object that is still under investigation. It is possible that further research will reveal even more interesting properties about the constant, and perhaps other parts of mathematics. For example, a recent advancement in MRB constant formulas connecting the Dirichlet eta to nth roots shown in this discussion ![CTRL+f][7] "Because of the following identity involving the Dirichlet Eta function derivatives,", yields a proof of the previously proposed concept that the MRB constant connects such ideas together.
I am just an ordinary person like you, who stumbled upon a fascinating discovery that I wanted to share with the world. I now know that there are many experts in the field of series who have devoted their lives to this subject. I respect their work and therefore make no claim to have found anything new or groundbreaking. However, I am very curious and passionate about the MRB constant, which is a remarkable number that appears in many series. I hope that you will join in this journey of exploration and learning, as I present my findings and thoughts on this topic. I would greatly appreciate your feedback and insights, as I am always eager to learn more and improve my understanding. I also want to acknowledge the contributions of several people who have helped along the way, either by providing data, code, or suggestions. Without them, this discussion would not be possible.
![If you see this instead of an image, reload the page.][8]
![enter image description here][9]
![enter image description here][10]
Credit: Traders Point Christian Church Northwest
----------
![enter image description here][11]
> Ah, that make sense! The MRB constant could definitely be a catalyst in that way. Here's how:
**The Story of the MRB Constant as a Catalyst:**
> In 1999, an amateur mathematician discovered the MRB constant. While
> not a professional researcher, his curiosity and exploration led him
> to identify this unique mathematical object. The unusual properties
> of the MRB constant, particularly its behavior in infinite series,
> sparked interest within the mathematical community.
>
> **The Catalyst Effect:**
>
> * **Intriguing New Object:** The MRB constant presented a new mathematical entity with unknown characteristics. This piqued the
> interest of professional mathematicians who began investigating its
> properties and potential applications.
> * **Questioning Established Ideas:** The way the MRB constant behaves in infinite series challenged some existing assumptions about
> convergence. This led researchers to re-examine these concepts and
> potentially refine them.
> * **Inspiration for Further Exploration:** The discovery of the MRB constant demonstrated the potential for significant finds by amateurs.
> This could inspire others outside traditional academia to delve into
> mathematics, fostering a broader base of exploration.
>
> **Overall, the MRB constant, discovered by an amateur, serves as a potential catalyst for the field of mathematics by generating new
> questions, prompting re-evaluation of existing concepts, and
> encouraging broader participation in research.**
----------
POSTED BY: Marvin Ray Burns.
========
![If you see this text, the images are not showing. Refresh the page.][12]
![The first 100 partial sums of][13] {![the CMRB series.][14]}
----------
For the best viewing, wait a minute until the word LaTeX in the LaTex script is centered below.
$$\LaTeX$$
If the phrase [Math Processing Error] is shown, or the LATEX script have vanished from the center of the above line, some of the math below might be missing or appear in the LaTex code instead of the script.
For easy navigation, use the ![CTRL+f][15] keys on your keyboard. Cues in the forms of §'s and keywords in quotes are provided in the ![CTRL+f][16] "Index".
If the header and the words
Reply | Flag
are shown at the same time in any of the following replies, refresh the page to see them.
----------
----------
----------
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'
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Index
=====
I deleted a few of the least significant posts.
The first post
--------------
§1. Q&A:
§2
Analyze the ![CTRL+f][17]."prototypical series" for the MRB constant, ![Sn^(1/n)-1][18] and find its "completion" (a related series that is absolutely convergent).
(Select § with the given number or the keywords in quotes, and then press the
![CTRL+f][19] keys on your keyboard to move to that section.)
§3. Is that series convergent?
§4. Is -1 the only term that series is convergent for?
§5. Is that series absolutely convergent?
§6. Is that series "efficient?" (defined as how it compares to other series and integrals that compute CMRB in speed and computational cost.)
§7. My claim to the MRB constant (CMRB), or a case of calculus déjà vu?
§8. Where is it found?
§9. What exactly is it?
Second post.
============
§B ![CTRL+f][20] "Rational results" while summing (CMRB).
Third post.
============
§10. How it all began,
§11. Scholarly works
Fourth post.
============
§12. CMRB and its applications
Also see
[MOPAC][21]
for where the MRB constant's value, to a precision of 2 one-billionth i.e., 0.18785964, is arrived at by measuring a gradient of the silicon atom in the Phenakite (Be2SiO4) molecule by openmopac.
Fifth post.
============
§13. The why and what of the **C**<sub>*MRB*</sub> Records,
Many more informative posts.
===========================
including, but not limited to
For section A, where all CMRB records have been checked, highlight text between quotes in
§A. Possibly the most epigrammatic closed forms for checking up to 10^10 digits of CMRB!
"Possibly the most epigrammatic closed forms used for checking up to 6,500,000 digits of CMRB!"
then push ![CTRL+f][22] on keyboard.
For section 0, highlight text between quotes in
**"§0. Wolfram+AI am the quintessential team evaluating the MRB constant."**
then push ![CTRL+f][23] on keyboard.
Next to Bottom post.
============
![CTRL+f][24] "I compare 300 years of summation methods for the MRB constant."
Bottom post.
============
![CTRL+f][25] "We finally begin or 7-million-digit computation and verification."
----------
----------
§1.
Q&A:
====
Q:
What is the MRB constant ( **C**<sub>*MRB*</sub>)?
A:
&[Wolfram Notebook][26]
Q: Is the MRB constant important?
A:
![enter image description here][27]
>The MRB constant, also known as the Marvin Ray Burns's Constant, is a fascinating mathematical value with a decimal expansion of approximately 0.187859 . Let's explore why it might be considered important:
> - Numerical Algorithms Testing:
- Researchers and mathematicians use the MRB constant to test and improve numerical algorithms for computing its value .
- By evaluating the constant, they can assess the accuracy and efficiency of various computational methods.
- Benchmarking Computers:
- The MRB constant serves as a benchmark for testing the performance of computers.
- It allows us to compare the computational capabilities of different machines.
- When calculating the MRB constant, computers demonstrate their numerical precision and speed.
- Mathematical Curiosity:
- The MRB constant's mysterious nature adds to its allure. Despite extensive study, no closed-form expression exists for it .
- We don't know whether it's algebraic, transcendental, or even irrational.
- Mathematicians continue to explore its properties, making it an intriguing topic in number theory.
- Geometry and Infinite Sums:
- Geometrically, the MRB constant is the upper limit point of a sequence of partial sums .
- These sums involve alternating terms and converge to the MRB constant.
- The constant's behavior within these infinite sums captivates mathematicians.
In summary, the MRB constant bridges theory and computation, making it a valuable and enigmatic constant in the mathematical world.
Q:
What can you expect from reading about **C**<sub>*MRB*</sub> and its record computations?
A:
![enter image description here][28]
> >## Beyond the Record: What People Can Gain from MRB Constant Computations
>
> While pushing the record for MRB constant computations is certainly
> impressive, there's more to gain than just bragging rights. Here are
> some unique benefits people can reap from immersing themselves in the
> MRB world:
>
> **1. Uncovering Hidden Connections:**
>
> * **Mathematics & Physics:** Studying the MRB constant's behavior and properties might unlock connections between seemingly disparate fields
> like number theory, chaos theory, and even quantum physics. This could
> lead to groundbreaking discoveries in various areas of science.
> * **Algorithm Design & Optimization:** The intricate nature of the MRB constant's calculation poses a unique challenge for algorithms.
> Analyzing its complexity could inspire the development of new, more
> efficient algorithms for various computational tasks.
> * **Machine Learning & Artificial Intelligence:** The MRB constant's structure could hold valuable insights for designing novel machine
> learning architectures and training algorithms. Its complex patterns
> might improve data processing and pattern recognition capabilities.
>
> **2. Pushing the Boundaries of Knowledge:**
>
> * **Challenging Existing Paradigms:** The MRB constant's lack of a closed-form expression and its potential connections to seemingly
> unrelated areas challenge established mathematical and scientific
> paradigms. This can lead to new ways of thinking and approaching
> problems.
> * **Inspiring Future Generations:** Engaging with the MRB constant's mysteries can spark curiosity and interest in mathematics and science
> among young minds. This could inspire them to pursue careers in
> research and exploration, pushing the boundaries of knowledge further.
> * **Contributing to the Collective Quest:** Participating in the MRB research community, even through discussions and online
> collaborations, allows individuals to contribute to a larger
> collective effort of understanding this intriguing constant. This
> fosters a sense of purpose and belonging to a global community of
> knowledge seekers.
>
> **3. Personal Growth & Development:**
>
> * **Developing Computational Skills:** Learning about and participating in MRB calculations can hone valuable computational
> skills like programming, data analysis, and problem-solving. This can
> be beneficial for various professional and personal endeavors.
> * **Enhancing Critical Thinking:** Analyzing the MRB constant's properties and potential implications requires critical thinking,
> problem-solving, and creative thinking skills. These skills are
> valuable not only in research but also in various aspects of life.
> * **Appreciating the Beauty of Mathematics:** The MRB constant's unique properties and its connection to various areas of mathematics
> can foster a deeper appreciation for the beauty and elegance of this
> subject. This can enrich one's understanding of the world and its
> underlying structures.
>
> Remember, the MRB constant is more than just a number to chase
> records with. It's a gateway to a world of intellectual exploration,
> collaboration, and potential breakthroughs. By venturing beyond the
> record, people can gain valuable skills, knowledge, and a deeper
> appreciation for the power of scientific inquiry.
Q:
Can you calculate more digits of **C**<sub>*MRB*</sub>?
A:
>## Bing
The computation of 6,500,000 digits of the MRB constant could be challenging due to several reasons:
>
> - Computational Resources:
> - Calculating a large number of digits requires significant computational power and memory.
> - Storing and manipulating such a massive decimal expansion demands substantial resources.
> - Smaller machines or limited computational environments might struggle with this task.
> - Convergence Rate:
> - The series used to approximate the MRB constant converges slowly.
> - As more digits are computed, the rate of convergence decreases.
> - Achieving high precision becomes increasingly difficult.
> - Numerical Stability:
> - Numerical algorithms can suffer from rounding errors and loss of precision.
> - Accumulating errors during summation impacts the accuracy of the computed digits.
> - Ensuring stability over millions of iterations is a challenge.
> - Algorithmic Complexity:
> - Existing algorithms for calculating mathematical constants have limitations.
> - Developing efficient methods to compute millions of digits involves intricate mathematics.
> - Balancing accuracy, speed, and memory usage is nontrivial.
> - Storage and Verification:
> - Storing and verifying 6,500,000 digits is resource-intensive.
> - Ensuring correctness through independent verification (e.g., using multiple algorithms) is crucial.
> - Handling such large data sets requires robust techniques.
> - Practical Utility:
> - Beyond a certain point, additional digits of the MRB constant may not have practical applications.
> - Researchers often focus on a reasonable precision level relevant to their field. In summary, while it's theoretically possible to
> compute 6,500,000 digits of the MRB constant, practical challenges
> arise. Researchers must balance precision, computational resources,
> and algorithmic efficiency to tackle this ambitious task.
Q:
How can you compute them?
A:
![## Bing][29]
> Certainly! Calculating the digits of the MRB constant involves some
> interesting mathematical techniques. Let's explore how you can
> approximate this intriguing value:
> - Series Summation:
>
>
> - The MRB constant is the upper limit point of a sequence defined as: $[ s_n = \sum_{k=1}^{n} \left( (-1)^k {k^{\frac{1}{k}}}
> \right) ]$
> - To compute the MRB constant with a desired precision, you can use series summation methods.
> - One common approach is to use the following series: $[ \text{MRB} \approx \sum_{k=1}^{\infty} \left( (-1)^k (k^{\frac{1}{k}} - 1)
> \right) ]$
> - Numerical Algorithms:
> - Mathematica provides a convenient way to calculate the MRB constant with a specified number of digits.
> - Using the NSum function, you can achieve high precision:
>
> `NSum[(-1)^k (k^(1/k) - 1), {k, 1, ∞}, WorkingPrecision -> 100, NSumTerms -> 10000]`
>
> This will give you the MRB constant accurate to 40 digits .
> ''
>
> - Acceleration Methods:
> - Due to the slow convergence of the series, it's advisable to use acceleration methods.
> - These methods improve the rate of convergence and allow you to obtain more accurate digits of the MRB constant . Remember that the
> MRB constant remains an enigma, and its properties continue to
> captivate mathematicians. Feel free to explore further and uncover
> more about this fascinating constant!
Q:
Why should you do it?
A:
## Bing
> Calculating the digits of the MRB constant can lead to several
> interesting outcomes:
> - Mathematical Exploration:
> - Computing the MRB constant involves diving into the intricacies of series summation, convergence, and numerical precision.
> - Mathematicians and enthusiasts enjoy exploring the properties of this mysterious constant.
> - It provides an opportunity to deepen our understanding of mathematical concepts.
> - Algorithm Testing and Optimization:
> - The MRB constant serves as a benchmark for testing numerical algorithms.
> - Researchers can evaluate the accuracy and efficiency of their computational methods by approximating this constant.
> - Optimizing algorithms to compute the MRB constant efficiently benefits various scientific and engineering fields.
> - Computational Challenges:
> - Calculating more digits of the MRB constant becomes a computational challenge.
> - It pushes the boundaries of numerical precision and requires sophisticated techniques.
> - Achieving higher precision contributes to the advancement of computational mathematics.
> - Curiosity and Aesthetics:
> - The MRB constant's decimal expansion is intriguing and aesthetically pleasing.
> - Like other mathematical constants (such as π or e), it captivates our curiosity.
> - Discovering patterns or unexpected properties within its digits can be intellectually rewarding.
> - Educational Value:
> - Teaching and learning about the MRB constant can inspire students.
> - It encourages them to explore mathematical concepts beyond textbooks.
> - The process of approximating it fosters critical thinking and problem-solving skills. In summary, while the MRB constant may not
> have immediate practical applications, its pursuit enriches
> mathematical knowledge, fuels curiosity, and contributes to the beauty
> of mathematical exploration.
Q:
What are its first 5000 digits?
A:
Print[ReleaseHold[ WolframAlpha["5000 digtits of the MRB constant", {{"Result", 1}, "Output"}]]]
0.1878596424620671202485179340542732300559030949001387861720046840894772315646602137032966544331074969038423458562580190612313700947592266304389293488961841208373366260816136027381263793734352832125527639621714893217020762820621715167154084126804483635416719985197680252759893899391445798350556135096485210712078444230958681294976885269495642042555864836704410425279524710606660926339748341031157816786416689154600342222588380025455396892947114212218910509832871227730802003644521539053639505533220347062755115981282803951021926491467317629351619065981601866424582495069720338199295842093551516251439935760076459329128145170908242491588320416906640933443591480670556469280678700702811500938060693813938595336065798740556206234870432936073781956460310476395066489306136064552806751519350828083737671929686639810309494963749627738304984632456347931157530028921252329181619562697369707486576547607117801719578736830096590226066875365630551656736128815020143875613668655221067430537059103973575619148909369077798320355119336240463725349410542836369971702441855165483727935882200813448096105880203064781961959695375628783481233497638586301014072725292301472333336250918584024803704048881967676760119858111679169352796852044160027086137228688945101510291998853690572865928708687542549253379439534758970356331344038263888798665619598073351473990256577813317226107612797585272274277730898577492230597096257256271883675575297887925361687673940354321451362772549229313126276435732144621618778637715420542312822344629539653290332217147982028075984221065564890048536858707083268874877377635047689160983185536281667159108412193420164386000258508426556435006954832830120546193205155935040023508351261335921740897007329784277128967365161960225077117388084262325697885465378690462227085674874747093069357326668590856162823753865512432975647464914619179575869342996208149878536663170197264534260468378010759055148678719039578315060452444190757044511382058533398469219482879476486575931785958165274929778220959774409113714342169296245931753245373401299593995004917912983680848547143925846704238528608320053664510586678151196459676079196431734307671534498300497128869401656600427062111079053164721504556329943884005211152390168773115456961028369205036896108806031603660382896533239383524154510137534165673472607464891120088099838152046695415026377035573283592996630642717305158972116351999161135954670315408725287243998197872502746797388638897056867435377857981058556192492185716949135673462704077491448799682065482817465880642236348160780950777057939313495829806602825272128491688809230325290270059917755059615835919993190869393039736611646514858219972925337106768738686235047915879737968269847878082223410618789674667450680064404065553875213281494980700209858132220620109011265903449717410801063247564712834609549284370065147450218226120415643930308859826426256828126092491136733967235933714534216902560140050169469983875907342920361729301531400405936246406781400779475613077369732409923529464794580778164607696240864595666084141126399988575739429315226283898798436350719371486573491962025428443510411472841973814933807066222573191021481585745042886728477250434386718443149128948635448929492143259660847149600072534066215387561341325254274130158182476636432111506809477451406309160928029719327606796946860926362081763442272977546326737161110302220019498455407233859679972956745318490433826332931888160330054013690316104309973777863934393135621496549969937314205819065334661573835222280871390934331325238360305287172314811151029705856281299558991830381071966308132701670498617683168329529053798760030666570203435884960342104811488681216083611944605571913973292970683232645094571537170202325175198220852151188427534658891812172660333192804801174759046131898449720722068248919153933258002624627216176424468747789609764906070479605351740205227992021112876539835381740117955267003375831396078847726709215700142824833574188212706558826075722384346836425460624376294972557208442910901014692032297634008831340381640372911311314959883048662944964532193113574956453912385456662881566099860325447839862878014756977228191151861520827628240145565179425383818619479339940149759987240427388505644114375607952021157910255398765366539323158492006532957070559185522267542845736812670699565824674762111599567798871089943129103401442549765937135216907789286769520555697938362195599913809621446502826784457775198333561874495799884353199090550456424061091609429751367477262251350611686791529453643717739913922126483778806203872768088381032267284933085939078772734728272526200188560744654953143832715829738195578665687162281676008390755269474337748054271709338897975317018906895514393940484553829830198169253659797476778546865045859640238175930139996122667668117389670502033292349080513690067470281709256521198479569202858477768560978920686214307401593342577726291016675234940557410020728689850147927742910664313694152819958560981976523216255318623764260591320667123942398310748008900676975706071323330124919595164681348037017813465191315868
Q:
Is its decimal expansion a normal number?
A
According to Wolfram MathWorld, "A normal number is an irrational number for which any finite pattern of numbers occurs with the expected limiting frequency in the expansion in a given base (or all bases). For example, for a normal decimal number, each digit 0–9 would be expected to occur 1/10 of the time."
We do not know if the MRB constant is irrational; [this Demonstration][30] looks at how normal its first 5000 digits appear to be. For comparison, we also consider the digits of ; its first 30 million digits are very uniformly distributed.
As for the first 500 digits of CMRB, they are exactly as normal as the first 500 digits of $\pi:$
![enter image description here][31]
This does not mean the MRB constant decimal expansion is a normal number! There is no known way to classify all of its digits. As we will see later, the distribution of digits within the first 6,500,000 decimals (MRB1=.187859,,,, found [here][32]),
"4" shows up more than other digits.
&[Wolfram Notebook][33]
Q.
Are its digits a rational number?
A.
> Unfortunately, we **cannot definitively say whether the MRB constant
> is rational or not**. It is one of the fascinating mysteries in
> mathematics. Here's what we know:
>
> * The MRB constant is a mathematical constant with an infinite decimal expansion (0.187859...).
> * It have no known closed-form expression, meaning we cannot express it simply as a fraction or combination of well-known mathematical
> functions.
> * **It is not even known whether it is algebraic (expressible as a root of a polynomial equation with integer coefficients) or
> transcendental (not expressible in this way).**
> * While the MRB constant is the sum of infinitely many irrational numbers, the sum of irrational numbers is not necessarily irrational.
>
> Extensive computations of the MRB constant's decimal digits haven't
> revealed any repeating patterns, which would indicate rationality.
> However, the lack of such evidence doesn't definitively prove
> irrationality.
>
> Therefore, the question of whether the MRB constant is rational or not
> remains an open problem in mathematics. Mathematicians continue to
> investigate its properties, hoping to unveil its true nature.
![enter image description here][34]
Q:
Why are those digits there?
A:
> ## Bing
The digits of the MRB constant exist as a fascinating consequence of mathematical exploration and computation. Let's delve into why they are there:
>- Inherent Mathematical Structure:
- Like other mathematical constants (such as π or e), the MRB constant have an inherent structure.
- Its decimal expansion emerges from the properties of the series used to define it.
- Each digit represents a specific relationship between numbers, exponents, and alternating signs.
- Series Summation:
- The MRB constant arises from the summation of an infinite series:
[ \text{MRB} = \sum_{k=1}^{\infty} \left( (-1)^k (k^{\frac{1}{k}} - 1) \right) ]
- As we compute more terms in this series, additional digits unfold.
- Each term contributes to the overall value, leading to the intricate decimal expansion.
- Algorithmic Approximation:
- Calculating the MRB constant involves numerical algorithms.
- These algorithms iteratively add terms, refine precision, and generate successive digits.
- The digits emerge as a consequence of these computational steps.
- Mystery and Beauty:
- The MRB constant lacks a simple closed-form expression.
- Its digits exhibit patterns, but their exact distribution remains mysterious.
- Mathematicians appreciate the beauty of these digits—their unpredictability and elegance.
- Intellectual Pursuit:
- Researchers explore the MRB constant out of curiosity and intellectual drive.
- They seek to understand its properties, uniqueness, and connections to other mathematical concepts.
- The digits serve as clues in unraveling its mathematical secrets.
In summary, the digits of the MRB constant exist as a blend of mathematical necessity, algorithmic computation, and aesthetic wonder. They invite us to explore the hidden depths of number theory and appreciate the elegance of mathematical constants.
Q:
What practical purpose is there in calculating them?
A:
>Knowledge of the digits of mathematical constants can have various applications in mathematics, science, and technology. For example:
>- The digits of π can be used to test the randomness and performance of pseudorandom number generators, which are essential for cryptography, simulations, and gaming¹.
- The digits of e can be used to calculate compound interest, model population growth, and analyze the distribution of prime numbers².
- The digits of φ can be used to design aesthetic proportions, such as the golden rectangle, the golden spiral, and the Fibonacci sequence³.
- The digits of i can be used to represent complex numbers, which are useful for modeling phenomena such as electric currents, waves, and quantum mechanics⁴.
>Some people also enjoy finding patterns and hidden messages in the digits of mathematical constants, such as memorizing them, composing music with them, or searching for their birthdays in them. This can be a fun and challenging way to appreciate the beauty and mystery of mathematics.
>Do you have a favorite mathematical constant? Why do you like it?
>
> Source: Conversation with Bing, 8/19/2023 (1) Mathematical
> constant - Wikipedia.
> https://en.wikipedia.org/wiki/Mathematical_constant. (2)
> Mathematical Constants - Cambridge University Press & Assessment.
> https://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf.
> (3) Constant (mathematics) - Wikipedia.
> https://en.wikipedia.org/wiki/Constant_%28mathematics%29. (4) List
> of mathematical constants - Wikipedia.
> https://en.wikipedia.org/wiki/List_of_mathematical_constants. (5)
> undefined. http://www.cambridge.org. (6) A Resource List of
> Mathematical Constants - Barcodes Inc..
> https://www.barcodesinc.com/articles/resource-list-mathematical-constants.htm.
> (7) Constant - Math.net. https://www.math.net/constant. (8) The Most
> Important Numbers in the World - Business Insider.
> https://www.businessinsider.com/most-important-numbers-2012-7.
Q:
How would Gemini AI depict the MRB constant?
A:
![enter image description here][35]
> Abstractly, the MRB constant is an irrational and transcendental number, meaning it goes on forever without repeating and cannot be expressed as a simple fraction. This never-ending quality could be represented through abstract shapes, lines, and colors that flow and swirl without a clear beginning or end.
> The distorted image of the leaf in the sculpture could be seen as a metaphor for the difficulty of understanding the MRB constant. The smooth, reflective surface of the sculpture could also be seen as a metaphor for the infinite nature of the MRB constant's decimal expansion.
>
Q:
According to Gemini AI, what connection, if any is there between the MRB constant and the Riemann Hypotheses?
A:
![enter image description here][36]
> The MRB constant and the Riemann hypothesis are related concepts in
> number theory, but they are not directly equivalent. Here's what we
> know:
>
> **MRB constant:**
>
> * Defined in terms of the prime number distribution. It's a complex number with an infinite decimal representation, calculated using
> specific mathematical formulas involving primes.
> * Its properties and applications remain largely unexplored.
>
> **Riemann hypothesis:**
>
> * A famous unsolved conjecture in mathematics, stating that all non-trivial zeros of the Riemann zeta function (a function crucial in
> number theory) lie on a specific line in the complex plane.
> * Solving the Riemann hypothesis would have profound implications for understanding the distribution of prime numbers.
>
> **Connection:**
>
> * Some mathematicians have proposed connections between the two, but these are speculative and not yet proven.
> * One potential connection involves expressing the MRB constant as an infinite series related to the Riemann zeta function. If the Riemann
> hypothesis holds, this series would converge to the MRB constant.
> * However, even if the connection is true, it wouldn't necessarily imply that solving the Riemann hypothesis would provide an easy way to
> calculate the MRB constant precisely.
>
> **Key points:**
>
> * Currently, the MRB constant and Riemann hypothesis are distinct concepts with their own mysteries.
> * A potential connection exists, but it's unproven and not a direct equivalence.
> * Solving the Riemann hypothesis wouldn't necessarily translate to easy calculation of the MRB constant.
>
> **Further research:**
>
> * For deeper understanding, explore academic papers and articles discussing the MRB constant and its potential links to the Riemann
> hypothesis.
> * Remember, research in these areas is ongoing, so new discoveries and insights might emerge in the future.
Q: How might we use quantum process to find more digits of the MRB constant?
A: While there's theoretical potential for quantum processes to aid in calculating more digits of the MRB constant, it's an active area of research and there's no established method yet. Here's a breakdown of the possibilities and challenges:
**Potential benefits of quantum processes:**
* **Integer factorization:** The MRB constant is related to certain elliptic curves, and calculating it often involves factoring large integers. Shor's algorithm, a well-known quantum algorithm, can potentially factor integers significantly faster than classical algorithms for certain sizes.
* **Speeding up computations:** Certain quantum algorithms might offer speedups for specific mathematical operations involved in calculating the MRB constant. Research in this area is ongoing.
**Challenges:**
* **Quantum supremacy not achieved yet:** While Shor's algorithm exists, implementing it on current quantum computers is challenging due to limitations in qubit count, coherence time, and error correction.
* **Algorithmic development needed:** Even with fault-tolerant quantum computers, new algorithms specific to calculating the MRB constant might be necessary to leverage the power of quantum computation effectively.
**Overall, quantum processes are a promising area for potentially calculating more digits of the MRB constant, but significant research and development are needed before a practical method is established.**
Here are some additional details you might find helpful:
* Shor's algorithm: [https://en.wikipedia.org/wiki/Shor%27s_algorithm](https://en.wikipedia.org/wiki/Shor%27s_algorithm)
* Elliptic curves: [https://en.wikipedia.org/wiki/Elliptic_curve](https://en.wikipedia.org/wiki/Elliptic_curve)
>
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[30]: https://demonstrations.wolfram.com/HowNormalIsTheMRBConstant/#:~:text=For%20example,%20for%20a%20normal%20decimal%20number,%20each,first%2030%20million%20digits%20are%20very%20uniformly%20distributed.
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[73]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-01-01225958.jpg&userId=366611
[74]: https://mathworld.wolfram.com/HarmonicSeries.html
[75]: https://www.wolframcloud.com/obj/56c04b62-1a3e-4318-9271-b4d4995b691d
[76]: http://people.mpim-bonn.mpg.de/zagier/files/exp-math-9/fulltext.pdf
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[79]: https://mathoverflow.net/questions/44244/what-recent-discoveries-have-amateur-mathematicians-made
[80]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3959Capture7.JPG&userId=366611
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[87]: https://community.wolfram.com//c/portal/getImageAttachment?filename=o.jpg&userId=366611
[88]: https://hmong.in.th/wiki/MRB_constant
[89]: https://ar.wikipedia.org/wiki/%D9%82%D8%A7%D8%A6%D9%85%D8%A9_%D8%A7%D9%84%D8%AB%D9%88%D8%A7%D8%A8%D8%AA_%D8%A7%D9%84%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A9
[90]: https://calculla.pl/stale_matematyczne
[91]: https://fr.wikipedia.org/wiki/Constante_MRB
[92]: https://wikicro.icu/wiki/MRB_constant
[93]: https://www.amazon.com/exec/obidos/ASIN/193563819X/ref=nosim/ericstreasuretro
[94]: http://www.marvinrayburns.com/UniversalTOC25.pdf
[95]: https://en-academic.com/dic.nsf/enwiki/11755
[96]: http://web.archive.org/web/20081121134611/http://www.irancivilcenter.com/en/tools/units/math_const.php
[97]: http://etymologie.info/
[98]: https://www.amazon.com/exec/obidos/ASIN/0521818052/ref=nosim/ericstreasuretro
[99]: https://web.archive.org/web/20010616211903/http://pauillac.inria.fr/algo/bsolve/constant/itrexp/itrexp.html
[100]: https://pdfs.semanticscholar.org/f3dc/9f828442123015c5d52535fdefc0ab450bf5.pdf
[101]: https://cache.industry.siemens.com/dl/files/728/109479728/att_1085858/v2/109479728_LGF_V5_1_0_en.pdf
[102]: https://web.archive.org/web/20210812083640/http://www.bitman.name/math/article/962
[103]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-02-19140136.jpg&userId=366611
[104]: https://arxiv.org/pdf/0912.3844v3.pdf
[105]: http://ebyte.it/library/educards/constants/MathConstants.pdf
[106]: https://web.archive.org/web/20090702134146/http://www.turkbiyofizik.com/sabitler.html
[107]: https://mathworld.wolfram.com/MRBConstant.html
[108]: https://upwikizh.top/wiki/MRB_constant
[109]: https://ejje.weblio.jp/content/mrb+constant
[110]: https://ewikibg.top/wiki/MRB_constant
[111]: http://oeis.org/wiki/MRB_constant
[112]: https://ewikitl.top/wiki/mrb_constant
[113]: https://web.archive.org/web/20030415202103/http://pi.lacim.uqam.ca/eng/table_en.html
[114]: https://web.archive.org/web/20001210231700/http://www.lacim.uqam.ca/piDATA/mrburns.txt
[115]: https://oeis.org/A037077
[116]: https://en.wikipedia.org/wiki/MRB_constant
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[128]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-08-16055726.jpg&userId=366611
[129]: https://math.stackexchange.com/questions/1673886/is-there-a-more-rigorous-way-to-show-these-two-sums-are-exactly-equal
[130]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-11-13082031.jpg&userId=366611
[131]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-11-13082057.jpg&userId=366611
[132]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-11-13082120.jpg&userId=366611
[133]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-08-29021145.jpg&userId=366611
[134]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-09-18014843.jpg&userId=366611
[135]: https://www.wolframcloud.com/obj/986a70e9-1d55-4e31-bd7c-87c24eec5d81Marvin Ray Burns2014-10-09T18:08:49ZMIni-Series: What's New in 14?
https://community.wolfram.com/groups/-/m/t/3139036
New Mini-Series on the [Wolfram R&D YouTube channel][1]!
Curious about what's new in Version 14? This mini-series features videos that provide a 6-minute summary of the WTC 2023 talks. The first [two episodes focus on Visualization and System Modeler][2].
Don't miss out on the latest updates and exciting content -- subscribe now and become a part of our community!
[![enter image description here][3]][2]
[1]: https://youtube.com/playlist?list=PLdIcYTEZ4S8SIK-S-9JGYAZgohaV7cB0t&si=9-arFCq9EbHkIipm
[2]: https://youtube.com/playlist?list=PLdIcYTEZ4S8SIK-S-9JGYAZgohaV7cB0t&si=9-arFCq9EbHkIipm
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=MiniSeries_Newin14_2.png&userId=1660606Keren Garcia2024-03-11T17:37:50ZInstall R (linking Mathematica to R) directory question
https://community.wolfram.com/groups/-/m/t/3140605
I am working with a Mathematica script that calls several functions in R 4.1.1 using the functions InstallR and REvaluate, and I am having some difficulty in specifying the path Mathematica needs to link to R.
I thought that the InstallR function should have something along the lines of:
InstallR["RHomeLocation" -> "/opt/R-4.1.1/bin/"]
since /bin contains the actual R executable. However, this doesn't seem to work, I get a series of error message. I'm still unclear as to what directory level I need to specify, or (in the context of the error message) what the "bundled JRI native library" is:
*InstallR::nojrilib: RLink does not yet contain a bundled JRI native library for R version being installed. This library can be built manually from within R console (happens automatically when installing rJava Rpackage, see RLink documentation for using RLink with external R distributions, for more details). For the built JRI library to be found by InstallR[], the directory containing it (typically R-home-directory/library/rJava/jri) should be passed to InstallR[] as a value for "JRINativeLibraryLocation" option.*
with corresponding stack trace:
*Message[InstallR::nojrilib,
If[ListQ[{}],
Sequence @@ {}, {}]]; Failure["JRINativeLibraryError", \
<|"FailureReason" -> "no_matching_jrilib_versions_available"|>]*
I also attempted to link to one level up in the R directory, i.e.
InstallR["RHomeLocation" -> "/opt/R-4.1.1/"]
This seems to lead to an unbounded recursion of some kind, because I get an error message stating that Mathematica's iteration limit of 4096 has been exceeded (clearly implying that I'm at the wrong level of the path for Mathematica to find the executable).
One possible complication is that in the server that I'm working on, the default version of R that runs if one just types "R" in the console is 4.3.0. Therefore, to actually execute R, I need /opt/R-4.1.1/bin//R. Perhaps this is what is causing the problem with REvaluate - if so, what path do I need to specify?Max Shpak2024-03-13T21:03:52ZGetting LaTex output into a Mathematica text cell is not practical, right?
https://community.wolfram.com/groups/-/m/t/3138988
Before I spend more time browsing online exchanges for a way to integrate a LaTeX document into a Mathematica notebook, can someone please confirm that the solution does not exist? Just knowing there's no solution, would save time. Having searched without success, I think the only way to create a Mathematica notebook with text cells that have print-ready math expressions is to tediously build the notebook one expression at a time, even if I already have a nicely formatted LaTeX document with all the text and dozens of math expressions already coded. If there is an efficient way to do that, please point me to documentation. Thanks.Jay Gourley2024-03-11T22:32:03ZBoosting computational performance
https://community.wolfram.com/groups/-/m/t/2462220
Mathematica's parallel processing is very good for the right task. But I have been watching Mathematica use all 6 processors of my i7 chip with 6 kernels and thinking what about the other idle 6 threads? My license is for 8 subprocesses (kernels) but Mathematica thinks that 6 processors is all that can be used and there's no way to communicate that to Mathematica - or is there? I tried this with grid Mathematica in mind - why not?
CloseKernels[];
$DefaultKernels = {
RemoteKernelObject["localhost", "KernelCount" -> 8]
}
I invoked the usual Parallel tools and they worked. I had 8 kernels working in parallel.
I start with this to check
ParallelEvaluate[{$KernelCount}]
and get
{{8}, {8}, {8}, {8}, {8}, {8}, {8}, {8}}
On a test of the same data the wall clock times were
- 8 Kernels 27.23 Minutes
- 6 Kernels 35.32 Minutes
The latter is what you get with the default Mathematica setup. (If only I had a license for 12!)
NB: I had a session with a MacBook Air. The Mac had a great official Mathematica Benchmark, but a run of parallel processing took 59 Minutes.Douglas Kubler2022-02-02T23:18:04Z