Recent content by V9999

What are the remaining open problems and challenges of nonlinear dynamics and chaos?

Hi, andrewkirk. Thanks for commenting. I see your point. However, I did not understand your last statement. Correct me, if I am not mistaken, but by substituting ##y=-1/2## into ##P(x,y)## we will have ##P(x,-1/2) \equiv \tilde{P}(x)=50x^2+100x+50##, or, simply,##\tilde{P}(x)= 50(x+1)^2##. Based...

Let ##P(x,y)## be a multivariable polynomial equation given by $$P(x,y)=52+50x^{2}-20x(1+12y)+8y(31+61y)+(1+2y)(-120+124+488y)=0,$$ which is zero at ##q=\left(-1, -\frac{1}{2}\right)##. That is to say, $$ P(q)=P\left(-1, -\frac{1}{2}\right)=0.$$ My doubts relie on the multiplicity of this point...

Many, many thanks for the suggestions!

I'm not quite sure if this is an appropriate question in this forum, but here is the situation. I have just finished my graduate studies. Now, I want to explore algebraic geometry. Precisely, I am interested in the following topics: Singular points of algebraic curves; General methods employed...

Hi, Drakkith. I hope you are doing well. This is precisely what I was searching. Thank you very much.

Hello, Mark44. I hope you are doing well! Thanks a lot for your insightful comment. That is exactly what I was thinking. However, how may I mathematically define the "reciprocal" of ##Q_n(x)##? That is to say, is there a specific notation to define the reciprocal of ##Q_n(x)##? Thanks in...

Hi, martinbn, I hope you are doing well. Thanks for commenting. It could be ##n##. However, I would prefer ##J_{n}## rather than simply ##n##.

Hi, WWGD. I hope you are doing well. Thanks for commenting. In my definition stated above, I am interested in the singular points of ##Q_{n}(x)##, which are obtained by the zeros or solutions of ##P_{n}=0##. In as much as ##(Q_{n}(x))^{-1}=P_{n}##, then I have considered...

Hi, Office_Shredder. I hope you are doing well. First, thanks for commenting. Second, I could be P since ##(Q_{n}(x))^{-1}## is ##P_{n}##. In light of the foregoing, the definition would be ##Sup\{\pi(P_{n}(x)=0):\partial P \leq n\}##. Based on the above, is there anything else that I should...

Let ##Q_{n}(x)## be the inverse of an nth-degree polynomial. Precisely, $$Q_{n}(x)=\displaystyle\frac{1}{P_{n}(x)}$$, It is of my interest to use the set notation to formally define a number, ##J_{n}## that provides the maximum number of solutions of ##Q_{n}(x)^{-1}=0##. Despite not knowing...

martinbn, Thanks for commeting! However, my question is exactly about this. Suppose that someone had undoubtedly solved an open problem in the field of algebraic geometry and mathematics. Based on your broad experience, what are the top mathematical journals to be considered first? Take, for...

Hi! Suppose that someone had solved an old but open problem in the great area of mathematics and physics, for instance, dynamical systtems, algebraic geometry and differential equations. Based on your broad experience, what are the best scientific journals to submit such a discovery? In...

Hi, Office_Shredder. I hope you are doing well. Thanks for the great insight and I will take it under consideration.

Hi, FactChecker. I hope you are doing well. Thanks for the great insight and I will take it under consideration.