Science topics: MathematicsAlgebra
Science topic
Algebra - Science topic
For discussion on linear algebra, vector spaces, groups, rings and other algebraic structures.
Questions related to Algebra
Is it at all possible to study the class of generalized Kerr-Schild (GKS) spacetimes in dimensions n≥3 and analyze their geometric and algebraic properties in a completely theory-independent setting.??
We assume that the overly complex Einstein tensor algebra of general relativity theory can be successfully replaced by the statistical chains of the transition matrix B.
# 175
Dear He Huang, Shary Heuninckx, Cathy Macharis
I read your paper:
20 years review of the multi actor multi criteria analysis (MAMCA) framework: a proposition of a systematic guideline
My comments:
1- In the abstract you say “emergence of stakeholder-based multi-criteria group decision making (MCGDM) frameworks. However, traditional MCGDM frequently overlooks the interactions and trade-offs among different actors and criteria”
I completely agree with this possibly most important feature in MCDM, as is interaction, that 99% of methods ignore. They prefer to work as if criteria were independent entities and then, adding up results. MCDM does not work with the concept that the result is A U B or sum, when it should be A ∩ B or intersection.
I have been claiming this for years in RG, and yours is the first paper I read that addresses it
Your paper also addresses the very important issue that the stakeholder who decide the alternatives, projects or options as well as the criteria they are subject to.
2- Page 2 “it is necessary to involve more than one decision maker (DM) to appraise the possible alternatives in the interest of, for example, diverse perspectives, increased acceptance of decision, and reduced bias”
In my opinion, the DM, in the first stage of the process, is only an instrument that receives information and demands form the stakeholders, translates them to the decision matrix, and selects the MCDM method.
His most Important function is to analyze the result, make corrections as per his/her know-how and expertise., and recommend the solution to the stakeholders. They are the decision-makers.
3- Page 2 “. The stakeholders can be defined as individuals or interest groups that have vested interests in the outcome of a particular issue or the decision being considered (Freeman et al. 2010).”
Absolutely correct, because each one is responsible for an area of the project. This is the people that know what is needed or wished, and you also emphasise it.
4- Page 3 “The original objective of MAMCA is to help actors understand the preferences and priorities of all relevant stakeholders, and to identify and evaluate different alternative solutions for which a consensus can be reached (Macharis & Bernardini, 2015). It is a decision-support framework with ’stakeholder involvement’ as a keyword”.
5- In my opinion, the word ‘preferences’ should be banned in MCDM. Normally, a stakeholder does not have preferences. A production manager does not have preference to fabricate a product A or product B, or on the importance of each product; he follows instructions on a plan that has been decided at the highest levels. It is absurd to think for instance that rejects are 3 times more important than quality, when this comes from a person that possibly does not have the faintest idea on production. The stakeholder has a production plan and has to comply with it.
In my opinion, and after reading hundreds of papers I realized that many authors have only a theoretical vision of the problem and ignore the reality, and try to solve a problem that is only in papers.
Another for me inappropriate word is “consensus”. IN MCDM consensus is a weird word, because most of the time there is a fight among the different stakeholders and components, where some must give and others receive.
In 1974 Zeleny defined the MCDM problem as a ‘compromise’, a balance between all parts, and that is only possible using a MCDM method, that is, it is the method which for example, must decrease a production goal to satisfy another goal as is the financial objective of a return of say 6 %. It is impossible for a human being to consider all the hundreds of interactions necessary to reach a balanced solution.
The MCDM knows nothing about consensus, but knows how to find an equilibrium or balance for the whole system
6- Page 4 “The most relevant criteria are selected for every stakeholder and weights are elicited that reflect their importance”
I am afraid I don’t concur on weights. Weights are useful to quantify the relative importance of criteria, using either subjective or objective procedures.
In the first kind, they are useless in MCDM, while in the second kind they are very useful. In countless publications as in yours, it is said that there is fundamental in MCDM. This is an intuitive concept without any mathematical support.
I however agree that in general, in most projects, criteria have different importance, no doubt about it, and that the experience of the DM is valuable, and it must be incorporated in the MCDM process, but at the right time and in the proper mode.
Just think that criteria are linear equations and as that, subject to the laws of lineal algebra.
Linear equations can be graphically represented as straight lines in a x-y graphic, and have different slopes that depend on their two values.
When you apply a weight to a criterion it multiplies each value within it. This provokes that a criterion line displaces parallel to itself, but the distances between values are preserved. When this is done for other criteria, that are multiplied by different weight values, the respective lines displace parallel to themselves, because in each one the distance between values is the same.
What is not the same is the existing distance between two criteria, because they depend on the different weight values. As can be seen, there is nothing in these weights that are used to evaluate alternatives.
It is different with entropy, where each criterion obtains an entropic value that quantitatively informs the degree of dispersion between the values. It is precisely this property what makes them useful, because a criterion with high entropy denote a closeness of the criterion distances between values.
The complement to 1 indicates the amount of information each criterion has to evaluate alternatives, that is, the Shannon Theorem.
Therefore, weights only show the geometrical displacement of a whole criterion, while entropy shows the discrimination of values withing each criterion.
7- Page 4 “Different MCDM methods can be used, like for example analytic hierarchy process (AHP)”
You are contradicting yourself when at the beginning you talk about interaction and now, you mention using AHP where interaction is not allowed (Saaty dixit, not me)
8- “A primary difference lies in MAMCA’s high regard for stakeholder autonomy; stakeholders are empowered to introduce criteria that reflect their interests and to evaluate alternatives based on personal preferences”
9- I agree excerpt in the word ‘preferences’
I do not know you, but I have worked in project management and in several countries, in large hydro, mining, oil, paper, and metallurgical projects, assisting at many meetings and I do not remember that somebody was asking or expressing preferences.
We were the stakeholdersand as other fellows, I was just following the direction from the highest levels. Of course, they were open discussions and everybody was free to express his opinions. Nobody was saying that “my preferences are…..”
Where the scholars in MCDM got that preference word? We expressed the needs in our own departments, and our opinions, discusssd with other colleagues, usually the financial guy, about what we need and explain why, and usually it was the project manager who closed the discussion trlough his own opinion
This is how the real world works, not with classroom examples. From there the DM must consider without discussion what each manager said, and put it in a matrix format. Normally the DM has no authority to decide if criterion environment is less or more important than criterion transportation. A DM is a specialist in decision making, involving, mathematics, knowledge, and experience on other projects, similar or not,something than in general is unknown to stakeholders. Thus, each one must operate in his own field: the stakeholders provide information and needs, and the DM process that, analyzes the result, modify it if necessary, and submit it to stakeholders.
Imagine that if in his/her presentation, the DM is interrupted by a stakeholder, asking for the origin of data in the matrix, and the DM responds that come from pair-wise comparison and thus, involving intuition. What do you think would be the reaction of the stakeholder other than incredulity on what he is hearing? I certainly know what would be mine
These are some of my comments. Hope they can be of service
Nolberto Munier
Hello everyone, I am a grad student currently taking a course on research and evaluation in education. I would like to know your thoughts on research vs evaluation. Do you feel there is distinguishing characteristics between or do you feel the overlap? Is there one that your prefer? As a high school algebra teacher, I do believe evaluation has the biggest influence in education especially when I do formal and summative assessments with my students. Thank you so much for taking time out of your day to answer my question and I look forward to hearing back from you.
A number of Python modules exisit for modelling the quantum outputs of quantum optical systems. With only one or two optical components and simple quantum states, system outputs can be calculated by hand. However, when the complexity increases, the benefits of having a Python module to check results or just save time is obvious. With quantum comms, computers and sensors being investigated seriously, the complexity is already high.
The availability of symbolic algebra programs in Python and Octave certainly are valuable for checking algebra, so you could start from scratch yourself to build somethings. However, in the case of quantum optics there are more rules for how things like creation operators and annihilation operators, hamiltonians etc act on states, so building from scratch is far from trivial.
Given a number of Python modules exist for performing this symbolic algebra, would there be any kind of consensus as to which one might be the best and most versatile to use, with the greatest number of users?
many thanks,
Neil
Is there a supervisor or assistant with whom I can continue learning algebraic number theory from scratch? Is algebraic number theory related to other branches of mathematics?
As we know irrational numbers are of two type-Transcendental & Algebraic. Here we want to find transcendental numbers between any two algebraic numbers & vice versa?
A very interesting find related to my journey if He-4 over 10 years and still going on in a sense since 2017 off and on.
Think that so many constraints, 7 known and 3 more discovered, have series of magics going on.
When you project a higher dimension to lower dimension there is a loss of factor of 2.
Like Hemisphere becomes a circle and the area is 2 times circle’s area. For sphere there is a double cover projection. 2 Hemispheres become 1 circle.
When you project a cube it looks like Hexagon in 2D.
In over simplified view of SU(3) I took 3 sides of a corner of 3D cube cut at mid points.
You have in projection an Equilateral Triangle in 2D with 3 diagonals meeting at center.
And the cube becomes Cuboctahedron and that projected has a bigger hexagon over laid with one small one in 2D. Total 12 points. The CCP packing with highest density covers that.
3D Cube 8 points become 6 points in Hexagon in 2D and 2 in center.
3D Cuboctahedron has 12 points and they become 2 Hexagons with 2 points in center in 2D Projection. Small Hexagon is made of N pointing Equilateral T above big Hexagonal and S pointing E T. This is CCP Packing of 12 plus 1 sphere.
Diving deep into Cartan Alegbra, after Lie Algebra, and Roots, in last 6 months, I found to my amazement that all that over simplified intuition was correct! The Cartan A is a semester course needing many revisions. This is more abstract than Tensor Calculus.
There are two kinds of learning - one is taught and another one is like what Rishis did and reflected in Einstein and Bruce Lee. Yes both were Yogis. I do both.
But now I find that the solution to (x^3-2) = 0. It has 3 roots which are part of SU(3) and Hexagon. The first 3 roots are (1,0), (1/2, “3^1/2”/ 2 and (1/2, -“3^1/2”/ 2). Rest of 3 are with negative signs and reflections of 3 positive Root vectors.
The Cube of volume Size 2 becomes Hexagon with diagonal size of 1!
Galileo tried to unify the Group Theory of Symmetries, which whole Physics is about, with Polynomial Theory.
Think of Polynomial as products of a series of “vector operator minus eigen values” as part of diagonal matrices which form many kinds of algebra such as Lie snd Cartan A and Lie, Weyl, Coxeter, etc. group theory. Coxeter I communicated in 90s and known as the Last Geometrician and his one puzzle I could solve, mentioned in my blog, but forgot. Need to revisit. But I think it is connected here. 🙏
#physics
#quantummechanics
#qcd
#strongforce
#nucleus
#qcd
#atomicphysics
#gravity
#generalrelativity
#mathematics
#liealgebra
#su(3)
#cartanalgebra
#roots
#packing
#molecules
#chemistry
Dear Research Community
I would like to invite Elctrical Engineering specialists to solve problems related to Ternary Algebra or tripple sets
I have an algorithm that places in relation three component vector and decimal number (pls see the attachment) Can anyone connect that to the components of a sine such as amplitude period frequency etc.?
Pls see the two attached files that follow
Thank you
Updated information of my thoughts and activities.
This is meant to be a one-way blog, albeit you can contribute with your recommendations and comments.
There has been recent interest in expanding the introduction of data science ideas in K-12 education. How often are these ideas connected to the linear/matrix algebra foundations of the subject?
Hi,
I am interested in joining algebra research group for collaboration. I bring a strong background in algebra and a passion for research.
Open to ongoing projects and eager to contribute, I'd appreciate the opportunity to connect and discuss potential collaborations.
I have a question about integer partitions. I am familiar with 2 algebraic notations (example: (5, 5, 5, 4, 3, 3, 3, 3, 3, 1, 1, 1, 1) as (5^3, 4^1, 3^5, 1^4). I would like to know if there are other notations and if you have any good references to recommend on this topic?
Is there a connection between fixed point theory and algebric topology
The strings in matrix B predict this statement.
As a numerical example, the sum of the entire series 0.99 + 0.99^2 + 0.99^3 + . . . . +0.99^N increases to 190 as N goes to infinity.
Additionally, B-matrix chains provide rigorous physical proof.
The question arises whether a pure mathematical proof can also be found?
Since the generally accepted theory of gravity is GRT, one could try to derive it from some algebraic theory. The basic thing in this theory should be the Dirac algebra, in which the Minkowski space is naturally embedded. Thus, we need to find some dynamical algebra that would be locally equivalent to the Dirac algebra. Where does such a Miracle live?
Giuseppe Piano was the first to establish the axioms of vector space, where the group axioms were linked to the axioms proposed regarding the second law, “number multiplication,” with a basic concept of compatibility.
From your cognitive and scientific point of view, can you give an explanation of this compatibility , which is the secret of the composition of this structure ''vector space'', in a way different from the usual explanation ?
Thanks in advance.
Article Topic: Some Algebraic Inequalitties
I have been collecting some algebraic inequalities, soonly it has been completed and published on Romanian Mathematical Magazine.
In the study of quantum deformations of Witt and Virasoro algebras, the notion of a Hom-Lie algebra first appeared, so is deformation theory insufficient to justify how algebraic structures such as Lie-algebras, ... are deformed, which requires the intervention of the concept of ''Hom'' to define the concepts that have recently appeared, such as Hom-groups...with reasoning ?
Following the findings in the field of deformable algebra, can deformation of an n-dimensional vector space contribute to changing its initial dimension?
How will this contribute to finding the appropriate deformations for infinite-dimensional algebra on the basis that algebra is a vector space with an additional structure, with the hope that this will lead to new physical systems with an infinite number of symmetries, and thus complementarity in the hope of enhancing one of what the theory of strings aspires to ?
Unbelievable is make believable in the world we connected prime number in matrix algebra form and I change history of math
Please see it
The leibniz rule reads
D(xy)=xdy +dx y
But a subtraction of two slightly
Different rectangles gives an extra term dx dy.
People have ddbated ever since
Tje smallest positive number doed not exist.
We will fix this with an ideal in algebra
he, with e a nilpotent element ee=0?
Methods: interviews w teachers, focus groups, observation) Leaning towards social constructivist, but was told I should probably broaden my search. Help!
I am starting a new area of research that is Algebraic topology. Kindly suggest some latest problems and related publications
Dear All,
I am a MSc in Theoretical Physics and I am finishing my master thesis on Algebraic geometry over Lie algebras in Tabriz University . I am searching a PhD position.
If anyone is interested in a PhD student, please feel free to contact me.
Thanks in advance,
Sona Samaei
My name is Sona and I have received my master degree in Lie Algebra from Public University of Tabriz (PUT).
In my master thesis, we have studied the algebraic geometry over Lie algebras. Also, I have passed Advanced algebra , finite group, manifold geometry and Real analysis and received IELTS certificate.
If there is an open position and I will be ready for an in-person interview if it is needed.
Best Regards,
Sona Samaei
Dear ResearchGate Community,
I am currently conducting research in the field of algebraic geometry, and I am in need of the Magma (computer algebra system) for my analysis. Unfortunately, my university does not have access to this software, and it seems unlikely that it will be made available in the near future.
I would be incredibly grateful if anyone could provide me with a student version of Magma, as it would be crucial for my research progress. If anyone has a copy, I would be very appreciative of your assistance.
Thank you in advance for your help and support in advancing the field of algebraic geometry.
It would be very interesting to obtain a database of responses on this question :
What are the links between Algebra & Number Theory and Physics ?
Therefore, I hope to get your answers and points of view. You can also share documents and titles related to the topic of this question.
I recently read a very interesting preprint by the mathematician and physician Matilde Marcolli : Number Theory in Physics. In this very interesting preprint, she gave several interesting relations between Number Theory and Theoretical physics. You can find this preprint on her profile.
We know that ideals of a lattice are dual of its filters. Moreover, Heyting Algebra is a special class of lattice. Can we define an ideal of a Heyting Algebra dually to its filter?
Some physicists say”everything is quantum”? Why would they say so? And what is the meaning of this sentence? No one doubts that quantum theory is successful. But from this statement it does not follow that everything is quantum! Therefore these physicists are making logically unjustified conclusions. Do they use quantum logic to ascertain conclusions that are only probable?
The essence of the quantum formalism is algebra. A generic algebra, for instance a von Neumann algebra, has a nontrivial center – consisting of those elements that commute with other elements. The elements of this center correspond to what we may call „classical observables”. Algebras with trivial center are special; they are called „factors”. Why should we assume that algebra is governing our world, if there is such has a nontrivial center? What is the basis of such a bold assumption?
It is true that every algebra can be decomposed into factors. It is true that every algebra can be factored by its center. But it is not true that such a quotient contains all the information contained in the original algebra. Some information is lost. Why should we lose information?
Or, in easier terms: wave functions in quantum theory depend on parameters: space, time, and other numbers. These parameters are classical, not quantum. Of course operators of multiplication by functions depending on these parameters belong to the quantum formalism, but not the parameters themselves. Can a theory be constructed that has no classical parameters at all? No space, no time, no structure, no „nothing?” In such a theory nothing would ever be deduced.
If so, why not accept that once the dream of „everything is quantum” is contradictory and self-destructive, why not to start with a more reasonable assumption that not everything is quantum and draw the consequences of such an assumption? If not everything is quantum, the what exactly is it that is not quantum? Space? Time? Group? Homogeneous space? Some geometry that organizes the algebra structure?
I noticed that there is a structural similarity between the syntactic operations of Bealer's logic (see my paper "Bealer's Intensional Logic" that I uploaded to Researchgate for my interpretation of these operations) and the notion of non-symmetric operad. However for the correspondence to be complete I need a diagonalisation operation.
Consider an operad P with P(n) the set of functions from the cartesian product X^n to X.
Then I need operations Dij : P(n) -> P(n-1) which identify variables xi and xj.
Has this been considered in the literature ?
I see the study of Drapeau et al. (2016), The algebra of conditional sets and the concepts of conditional topology and compacness, Journal of Mathematical Analysis and Applications. They bring the new concept of 'conditional set' (Definition 2.1):
A conditional set X of a non-empty set X and a complete Boolean algebra A is a collection of objects x|a for x in X and a in A such that
- if x|a = y|b, then a = b;
- if x,y in X and a,b in A with a <= b, then x|b = y|b implies x|a = y|a;
- if (ai) in p(1) and (xi) is a family of elements in X, then there exists exactly one element x in X such that x|ai = xi|ai for all i.
In my naive reading, it seems that the traditional axioms of ZFC set theory fit just fine this definition, e.g. axiom schema of separation is defined on the common properties of set elements, for these 'properties' refer (to me) as the 'conditions' in the Drapeau et al. (2016) study.
The thing is that I could combine a set of 'properties/conditions' and the basic set operations (union, inclusion,...), so to create an algebra of conditions satisfying the usual properties.
Is there something I do not see in the Drapeau et al. (2016) study?
Why do algebraic multiplicity of eigenvalues of skew-symmetric matrix pencils are even?
That an n degree polynomial CAN always be factored up into n factors containing Complex roots has been shown true, but there are things not explained in the phrase.
Teachers will not usualy explain alternatives.
Say (Z-x)(Z-x) =0 CAN have the solution Z=x, but can also have Z=x+ey where ee=0 is an
nilpotent element.
Just as i can be made real in 2 by 2 matrices, so can e. Just as we use i or -i dupliciously,
without knowing which, we can use e or e(T) , the transpose of e. One can define i=e-e(T)
using ee=0 , e(T) e(T) =0 and e e(T)+e(T)e =I to show ii=-1. Now substitute this everywhere you see i, and the factorization carries out the same.
Defining ww=1, one can also claim w=e +e(T).
Reading attentively the fundamental theorem of algebra, we find the funny phrase that it is not derivable from algebra...well no wonder.
Dont really have a good name for these elements, i plus whatever else there is. The supra real? Hyper real is already occupied by non standard elements. Neither have they seemingly been well studied well beyond quadratic, though they do exist...
This means a gap in knowledge? Or stuborn historical usage?
I did not understand from the author how he arrived at these specific equations ?
what is phi^1 ,phi^2 ,...
Let $A=(a_{ij})\in M_{m \times n}(\mathbb{R_{+}})$ and $B=(b_{ij}) \in M_{n \times l}(\mathbb{R}_{+}).$ The product of $A$ and $B$ in max algebra is denoted by $A\otimes B,$ where $(A\otimes B)_{ij}=\displaystyle\max_{k=1,\ldots,n} a_{ik}b_{kj}.$
A set $\mathcal{X}_{n \times k} \subset M_{n \times k}(\mathbb{R}_{+})$ is defined by
$$\mathcal{X}_{n \times k}= \{X \in M_{n \times k}(\mathbb{R}_{+}): X^{t}\otimes X = I_{k}\}.$$
It is known that for the case $k = n,$ $\mathcal{X}_{n \times n}$ is equal to $\mathcal{U}_{n},$ where $\mathcal{U}_{n}$ is a unitary matrix in max algebra.
Irrational numbers are uncomputable with probability one. In that sense, numerical, they do not belong to nature. Animals cannot calculate it, nor humans, nor machines.
But algebra can deal with irrational numbers. Algebra deals with unknowns and indeterminates, exactly.
This would mean that a simple bee or fish can do algebra? No, this means, given the simple expression of their brains, that a higher entity is able to command them to do algebra. The same for humans and machines. We must be able also to do quantum computing, and beyond, also that way.
Thus, no one (animals, humans, extraterrestrials in the NASA search, and machines) is limited by their expressions, and all obey a higher entity, commanding through a network from the top down -- which entity we call God, and Jesus called Father.
This means that God holds all the dice. That also means that we can learn by mimicking nature. Even a wasp can teach us the medicinal properties of a passion fruit flower to lower aggression. Animals, no surprise, can self-medicate, knowing no biology or chemistry.
There is, then, no “personal” sense of algebra. It just is a combination of arithmetic operations.There is no “algebra in my sense” -- there is only one sense, the one mathematical sense that has made sense physically, for ages. I do not feel free to change it, and did not.
But we can reveal new facets of it. In that, we have already revealed several exact algebraic expressions for irrational numbers. Of course, the task is not even enumerable, but it is worth compiling, for the weary traveler. Any suggestions are welcome.
Our answer is YES. Irrationals, since the ancient Greeks, have had a "murky" reputation. We cannot measure physically any irrational, as one would require infinite precision, and time. One would soon exhaust all the atoms in the universe, and still not be able to count one irrational.
The set of all irrationals does not even have a name, because there seems to be no test that could indicate if a member belongs to the set or not. All we seem to know is it is not a rational number -- but what is it?
The situation is clarified in our book Quickest Calculus, available at lowest price in paper, for class use. See https://www.amazon.com/dp/B0BHMPMMTY/
There, Instead of going into complicated values of elliptic curves, and infinite irrationals, algebra allows us to talk about "x".
No approximating rational numbers need to be used, nor Hurwitz Theorem.
Thus, one can "tame" irrationals by algebra, with 0 (zero) error. For example, we know the value of pi. It is 2×arcsin(1) exactly, and we can calculate it using Hurwitz Theorem, approximately.
GENERALIZATION: Any irrational number is some function f(x), where x belongs to the sets Z, or Q -- well-defined, isolated, and surrounded by a region of "nothingness". The set of all such numbers we call "E", for Exact. It is an infinite set.
What is your qualified opinion?
I define the omega-th Cayley-Dickson Algebra as the union of all the finite-dimensional Cayley-Dickson algebras (over the reals).
Let k be a field of characteristic zero and let E=E(x,y) be an element of k[x,y].
Define t_x(E) to be the maximum among 0 and the x-degree of E(x,0).
Similarly, define t_y(E) to be the maximum among 0 and the y-degree of E(0,y).
The following nice result appears in several places:
Let A,B be two elements of k[x,y] having an invertible Jacobian (= their Jacobian is a non-zero scalar); such A,B is called a Jacobian pair.
Assume that the (1,1)-degree of A is >1 and the (1,1)-degree of B is >1.
Then the numbers t_x(A),t_y(A),t_x(B),t_y(B) are all positive.
Question: Is the same result holds in the first Weyl algebra over k, A_1(k)? where instead of the Jacobian we take the commutator.
Of course, we must first define t_x(A),t_y(A),t_x(B),t_y(B) in A_1(k); it seems to me that the same definition holds for A_1(k), or am I missing something? Perhaps it is not possible to consider E(x,0), where E is an element of A_1(k)?
Thank you very much! Please see https://mathoverflow.net/questions/334897/a-non-commutative-analog-of-a-result-concerning-a-jacobian-pair
As is well known, camera calibration in photogrammetry and with the use of Bundle Adjustment with self-calibration, the coordinates of the principal points cannot be recovered from parallel images. This situation calls for convergent images to recover the coordinates of the principal point. A common explanation is attributed to the algebraic correlation between the exterior orientation parameters and the calibration parameters. Now the question in other words, Is there is any deep explanation about the nature or the type of this algebraic correlation? Is there is any analytical proof for this correlation? or we have to accept this empirical finding (we need convergent images for camera calibration)
I am primarily interested in 2-player combinatorial games with perfect information. Useful wiki links are below.
How to linearize any of these surface functions (separately) near the origin?
I have attached the statement of the question, both as a screenshot, and as well as a PDF, for your perusal. Thank you.
This paper is a project to build a new function. I will propose a form of this function and I let people help me to develop the idea of this project, and in the same time we will try to applied this function in other sciences as quantum mechanics, probability, electronics …
I don't need this anymore
Here the text:
Do these two algebraic modeling languages for optimization totally similar? Or they have some differences? Any comparison of similarities and differences would be highly appreciated.
Thanks!
If I wanted to link algebra and topology in order to specialize in algebraic topology (mathematics), what researches would you recommend me to start reading with?
Here we discuss about one of the famous unsolved problems in mathematics, the Riemann hypothesis. We construct a vision from a student about this hypothesis, we ask a questions maybe it will give a help for researchers and scientist.
Most current methods of NP vs P solution are solved by reduction of one problem to another problem. Is it possible to proof NP vs P using only algebra transformation, e.g. in how we solve quadratic equation using completing the square and prove of Trigonometric Identities?
- One may define the scalar product in a vector space in terms of vectors. Alternatively, one may first define the space of co-vectors and then define the scalar product in terms of vectors and co-vectors. The first mentioned way is simpler. Then for what reasons do some prominent authors, e.g., Van der Waerden in his "Algebra", choose the second mentioned way?
In fact I want to express expm(D * M) as a product exponential matrix.
Thanks for your tips
I need some suggestions what are the growing topics in algebraic combinatorics and graph theory for research? Thank you in advance to everyone who will answer.
Hello all researcher,
i have an idea to learn about fuzzy and algebra, how can we deal with algebras in any fuzzy theorem?
In general in mathematics we work with groups that includ numbers, generally we work with constants.
So for exempel: For any x from R we can choose any element from R we will find it a constant, the same thing for any complex number, for any z from C we will find it a constant.
My question say: Can we find a group or groups that includ variabels not constants for exemple, we named G a group for any x from G we will find an x' it's not a constant it's another variabel ?
and if it exisit can you give me exempels ?
Thank you !
In 2010, Dr. Khmelnik has found the suitable method of resolving of the Navier-Stokes equations and published his results in a book. In 2021, already the sixth edition of his book was released that is attached to this question for downloading. Here it is worce to mention that the Clay Mathematics Institute has included this problem of resolving of the Navier-Stokes equations in the list of seven important millennium problems. Why the Navier-Stokes equations are very important?
I have confirmed that the Hessenberg determinant whose elements are the Bernoulli numbers $B_{2r}$ is negative. See the picture uploaded here. My question is: What is the accurate value of the Hessenberg determinant in the equation (10) in the picture? Can one find a simple formula for the Hessenberg determinant in the equation (10) in the picture? Perhaps it is easy for you, but right now it is difficult for me.
I have drived a formula of computing a special Hessenberg determinant. See the picture uploaded here. My question is: Can this formula be simplified more concisely, more meaningfully, and more significantly?
What lessons and topics are prerequisites for algebraic number theory and analytic number theory?
Please tell me the exact topic of each lesson.
More precisely, if the Orlik-Solomon algebras A(A_1) and A(A_2) are isomorphic in such a way that the standard generators in degree 1, associated to the hyperplanes, correspond to each other, does this imply that the corresponding Milnor fibers $F(A_1)$ and $F(A_2)$ have the same Betti numbers ?
When A_1 and A_2 are in C^3 and the corresponding line arrangements in P^2 have only double and triple points, the answer seems to be positive by the results of Papadima and Suciu.
See also Example 6.3 in A. Suciu's survey in Rev. Roumaine Math. Pures Appl. 62 (2017), 191-215.
I got to know about Mliclos schweitzer Competition(named after the brilliant Hungarian mind who unfortunately left us in World War-II) .These problems are so lively and motivating,and AOPS contains problems upto its 2020 edition,which means it is still going on.
I wanted to know any website for Mliclos schweitzer competition,2021 or its past editions;and how to enroll to sit for this,And who all are eligible. Kindly respond if you have any information.
Thanks in advance!
P.S. Feel free to have discussion over the commen section regarding this,but I hereby declare this to be closed(notifications) as of now.The suggested book in the comment section is really interesting,and highly reccomended.
The aim of this Conference was more far-reaching than the presentation of the latest scientific results. It consisted of finding connections between this fundamental theoretical branch of mathematics and other fields of mathematics, applied mathematics, and science in general, as well as the introduction of top scientists with paragraded structures, which would lead to the connection and cooperation of scientists working in various fields of abstract algebra and algebraic theory of numbers, ultrametric and p-adic analysis, as well as in graph theory and mathematical logic.
SARAJEVO JOURNAL OF MATHEMATICS, Vol. 12 (25), No.2-Suppl.
This issue is dedicated to the memory of Professor Marc Krasner, Officier des Palmes de l'Academie des Sciences de Paris on the occasion of the 30th anniversary of his death.
All manuscripts of this issue were presented at International Scientific Conference "Graded Structures in Algebra and their Applications" held in Inter University Center, Dubrovnik Croatia, September 22-24, 2016
Contents of Vol. 12, No. 2-Suppl. DOI: 10.5644/SJM.12.2.00
Professor Marc Krasner - photos DOI: 10.5644/SJM.12.3.01
Mirjana Vuković, Remembering Professor Marc Krasner DOI: 10.5644/SJM.12.3.02
Alain Escassut, Works involving Marc Karsner and French mathematicians DOI: 10.5644/SJM.12.3.03
Emil Ilić-Georgijević, Mirjana Vuković, A note on radicals of paragraded rings DOI: 10.5644/SJM.12.3.04 Emil Ilić-Georgijević, Mirjana Vuković, A note on general radicals of paragraded rings
DOI: 10.5644/SJM.12.3.05
Mirna Džamonja, Paragraded structures inspired by mathematical logic DOI: 10.5644/SJM.12.3.06
Vlastimil Dlab, Towers of semisimple algebras, their graphs and Jones index DOI: 10.5644/SJM.12.3.07
Elena Igorevna Bunina, Aleksander Vasilevich Mikhalev, Elementary equivalence of linear groups over graded rings with finite number of central idempotents DOI: 10.5644/SJM.12.3.08
Nadiya Gubareni, Tensor algebras of bimodules and their representations DOI: 10.5644/SJM.12.3.09 Dušan Pagon, On codimension growth of graded PI-algebras DOI: 10.5644/SJM.12.3.10
Smiljana Jakšić, Stevan Pilipović, Bojan Prangoski, Spaces of ultradistributions of Beurling type over ℝd+ through Laguerre expansions DOI: 10.5644/SJM.12.3.11
Alexei Panchishkin, Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups DOI: 10.5644/SJM.12.3.12
Siegfried Böcherer, Quasimodular Siegel modular forms as p-adic modular forms DOI: 10.5644/SJM.12.3.13
Alain Escassut, Kamal Boussaf, Abdelbaki Boutabaa, Order, type and cotype of growth for p-adic entire functions DOI: 10.5644/SJM.12.3.14
1. Functions
2. Matrix algebra & eigenvectors
3. Vector algebra
4. Complex numbers
I was wondering is there any
- model theory of number theory ,hence are there model theorists working in number theory
- the development of arithmatic geometry ,does it have anything to do with questions in logic;and is there any group studying this interaction.
- Anyone is welcome and up for collaboration
- I am interested in finding interaction between algerraic and arithmatic number theory with logic,and to study it to answer logical questions about Arithmatic
Last year (August 2020) I uploaded the algebraic approach to the construction of a regular nonagon DOI 10.13140/RG.2.2.26286.95044/1 which in fact was the trisection of an angle of 60 degrees and so the tangent of the angle of 20 degrees was found to be 0.36387622008. Some years ago (2014) I published with IOSR Journal of Mathematics a paper for the trisection of every angle equal or less than 180 degrees the "Angle Trisection by Straighedge and Compass Only". A trisection, done by the intersection of two circumferences. Now, taking for trisection an angle of 60 degrees, for the intersection of the two circumferences we get the system of equations:
x^2 + (y + sqrt27)^2 = 36
(8 - x)^2 + y^2 =49
and the tangent of the angle of 20 degrees to be: y/(3-x) = 0.36345134567644, differing from the one calculated last year with the algebraic approach to the construction of the regular nonagon.
Where do you think that the difference of the two calculations of the same tangent is due?
We have seen a stability in the supply chains of goods, food in particular, during the current pandemic of Covid19 continue, mostly undisturbed.
It is very reassuring at a time of uncertainty and macro-risks falling onto societies.
How much do we owe to the optimised management and supervision of Container transport, and multimodal support to it with deep sea vessels, harbour feeder vessels, trains and trucks/lorries?
What is the granularity involved? Hub to hub, regional distribution, local delivery?
Do we think that the connectivity models with matrices, modelling the transport connections, the flows per category (passengers, freight, within freight: categories of goods), could benefit from a synthetic model agreggation of a single matrix of set federating what has been so far spread over several separate matrices of numbers?
What do you think?
Below references on container transport, and on matrices of sets
REF
A) Matrices of set
[i] a simple rationale
[ii] use for containers
[iii] tutorial
B) Containers
[1] Generating scenarios for simulation and optimization of container terminal logistics by Sönke Hartmann, 2002
[2] Optimising Container Placement in a Sea Harbour, PhD thesis by by Yachba Khedidja
[3] Impact of integrating the intelligent product concept into the container supply chain platform, PhD thesis by Mohamed Yassine Samiri
- The Chu-Construction allows to obtain a *-autonomous category from the data of a closed symmetric monoidal category and a dualizing element.
- The Cayley-Dickson-construction builds an algebra B = A + A with involution from the data of an algebra A with involution *. Applied to the field of real numbers it gives successively the field of complex numbers, then the skew-field of quaternions, then the non-associative algebra of octonions, etc.
Due to closeness of the expressions of multiplication m: B \otimes B -> B for the multiplicative unit B we believe that there is an intimate link between both notions.
Has such a link been described in a reference text ?
Bibliography:
