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

05 June 2015 8,415 0 View

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

09 October 2014 6,025 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...

31 December 2013 1,229 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?

11 December 2013 3,637 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.

10 November 2013 2,425 8 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...

04 May 2013 2,279 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 4,132 3 View

Any specific pipeline or parameter to analyse total transcriptomics study of brain tissue samples?

I have two groups of brain samples, control and treated for example. It was total RNA nova seq sequencing. I tried all the available pipeline like: star+rsem+deseq2, Hista+stringtie+cuffdiff,...

27 February 2021 356 6 View

How to find the right number of integration points in second order 3d finite elements?

I am familiar with finite element simulations and numerical schemes like the Gauss Legendre quadrature. I also know that the Gauss integration yields exact values for polynomials up to degree 2n-1...

27 February 2021 6,818 3 View

How can we determine the positive definiteness of multivariable polyomial? Is there any MATLAB function available for that?

Can we check the positive definiteness of a multivariable polynomial using MATLAB functions? Of course in literature, there are few complex methods that use tensor algebra. However, before going...

16 February 2021 1,218 3 View

How do you interpret theoretical vs. experimental reaction orders with respect to a reactant?

I recently came across a paper focusing on the hydrodeoxygenation of oxygen-containing compounds. The paper linearized the rate equation in order to determine the experimental reaction order with...

14 February 2021 8,254 2 View

Can I get the design of circular cylinder to fix thermocouple on the surface and cartridge heater in core ?

Respected Scientific Community. I'm interested to carry out experimental studies on a circular cylinder. But even after doing literature review I unable to get the exact design of the cylinder...

10 February 2021 6,221 1 View

Infinite order of Laguerre?

If Lmn(x) is the Laguerre polynomial of order m and degree n Is there a means of computing Lmn(x) for 1) m goes to infinity 2) n goes to infinity

08 February 2021 6,320 4 View

Any recommendations for open-source survey form builder, which has option for semantic differential scale questions apart from Likert scale?

Asking this as Google forms doesn't allow multiple items in a semantic differential format.

04 February 2021 5,869 4 View

How can I implement a Generalized Estimating Equation method on spatially autocorrelated time-series data?

I used Generalized Estimating Equations (geepack in R) on my regularly monitored (twice a year) plant abundance data in grid cells to evaluate their trends of density. Since these are time-series...

26 January 2021 3,833 1 View

How to prove possibility/impossibility to analytically solve the functional equation f(a ln x^2)/f(x)=x/2a; and how to find out the solution?

This is my very first encounter with functional equation of this kind, and methods of series solution and differential equations are of not much help. The solution to this problem, or at least the...

25 January 2021 6,053 5 View

How to find nature of extremum of a functional? what are the mathematical prerequisites to understand it?

For a function, usually sign of second derivative (and if it is zero, even/odd index of higher order derivative whose numerical value is zero) is enough to detect whether the extreme point is...

25 January 2021 7,703 3 View