Gro Hovhannisyan

8 Questions 84 Answers 0 Followers

Questions related from Gro Hovhannisyan

For which complex numbers bj , we have b0= \sum_{j=1}^3 bj exp(i vj) for some real vj?

Obvious necessary conditions are |b0|≤ |b1|+ |b2|+ |b3|, |b0|≥|b1|- |b2|- |b3| .

06 June 2015 8,498 0 View

What is a time-space scale version of KdV equation?

Time-space scale versions of integrable nonlinear Schrodinger equation and some other equations are deduced in my recent publication: Ablowitz-Ladik hierarchy of integrable equations on a...

10 October 2014 6,115 0 View

If sin(a sk)/a= sin(b sk)/b for the sequence sk\to infty as k \to infty for some a not equal to b, then a/b is rational and sk=2k pi/b? Is it true?

For particular case b=2a we have sin(2b sk)/(2b)= sin(b sk)/b which yields cos(b sk)=1 or sk=2k pi/b. It is true also if the sequence sk that approaches infinity as k approaches infinity is...

01 January 2014 1,291 4 View

Are there unbounded solutions of (1-cos(x pi))/x-(1-cos(y pi))/y+(1-cos((x-y)pi))/(x-y)=0 but with even integers?

The sequence x=2k y=2n where k and n are natural numbers solves this equation. Is there any other unbounded sequence of solutions?

12 December 2013 3,713 7 View

Quadratic equation (complex coefficients) have roots with equal real parts if and only if discriminant is real, non-positive. What about quartic?

z^2-(2+3i)z+3i-1=0 has discriminant=-1, roots (1+i) and (1+2i) have equal real parts. Find a similar statement for the quartic equation: z^4+az^2+bz+c=0.

11 November 2013 2,502 8 View

2 roots of x^3+6a x+2b=0 where a, b are complex have the equal real parts if a, b are real and discriminant is non-positive. Is it true?

For the quadratic equations with complex coefficients 2 roots have the equal real parts if and only if the discriminant is nonpositive.

08 August 2013 3,039 4 View

e^(z_1)+e^(z_2)=0 if and only if Re(z_1)=Re(z_2) and Im(z_2-z_1)=pi(2n+1), where z_1, z_2 are complex numbers. Is there a similar statement for the sum of 4 exponents e^(z_1)+e^(z_2)+e^(z_3)+e^(z_4)=0 ?

This question is connected with the oscillations of differential equations. Since every solution of the linear equation with constant coefficients is the linear combination of exponents this...

05 May 2013 2,356 51 View

Mobius transformation maps arcs of circles to arcs of circles. Is there similar geometric property for the quotient of quadratic functions?

The quotient of linear functions with complex variable z (Mobius transformation) maps arcs of circles to arcs of circles. Is there similar geometric meaning for the quotient of quadratic functions...

01 January 1970 4,213 3 View