  # drufae

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• Birthday November 11

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all areas fascinate me
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1. To ajb: My apologies for not making myself clear. I meant under our current understanding of physics is it possible (not necessarily practical) to create a fields that do not naturally exist. To bob: I am not familiar with quasi-particles or microelectronics yet, so I do not know if you are accurately describing what I had in mind.I would appreciate it if you elaborated your post. Thanks a lot , both of you, for your prompt replies.
2. Just a passing thought: We know of several types of fields electromagnetic/gravitational,etc.Each one of these fields has some fundamental property which is required to create it (there are exceptions e.g. light is a combination of fields independent of a producing particle) .For example charge is required for an electric field,mass for a gravitational field,other types of fields also exit for other attributes. But is it possible to synthesize a brand new field (even theoretically) not simply make a composition of existing attributes. please note : I understand that fields are representations of interactions, and under this perspective my question still stands as , can we design our own type of interaction completely independent of other existing interactions.
3. While using several operators(e.g.grad,div,curl) we often separate them and treat them as vectors in their own right,performing most algebraic and vector operation on them.How is this possible? are not operators and their operands inexorably linked together.In order to separate them we would need to define a whole set of specialized rules just to use them. This is not an isolated example several times while solving differential equations we replace the differential operator with a variable ,say 's'(and hence this technique in some areas gets its name as the s-operator method) (ref:http://en.wikibooks.org/wiki/Circuit_Theory/Second-Order_Solution)and proceed to manipulate it as a variable. If there is indeed a technique or theory which allows us to dichotomize operands and operators then it is that which i hope to discuss in this post.If not then how do these techniques hold up? p.s.I'm sorry if I have posted this in the wrong place but the topic seems to belong to general mathematics rather than a specialized field.
4. The Uniqueness theorem states that if a solution of the Poisson's eq. is found to satisfy the boundary conditions then it will be the only solution.However in order to apply the theorem the scenario must have no varying magnetic fields thereby making $\nabla \times E$ zero.This allows us to describe E in terms of a scalar field and thus allows us to use an eq expressible as the Poisson's eq(Helmholtz decomposition). In the case of light (and perhaps other solutions) there clearly exist a varying magnetic field ($\nabla \times E = - \frac{\partial B}{\partial t} \neq 0$)hence Poisson's eq cannot be used to describe it.
5. Light exist without any matter, charge or anything else for that matter.It consists of 2 fields ( a magnetic and an electric) which oscillate.Both of them sustain each other. The thing which amazes me is that the the existence of the fields is independent of any causing 'thing' along with it.The wave representation of light can clearly be explained as a solution of maxwell's equations in a vacuum .I was wondering are e.m. waves the only solution to these equations.If not what are the others and how would one go about creating other such stable configurations of fields. (please note I intended for this thread to be a general discussion and do not mind even if it drifts slightly away from the topic .. thought not too much )
6. When does the generic equation of the 2nd degree not represent a conic section or does it always represent a conic section (unless it has no possible solutions in real numbers)? The other topic I would like like to devote this thread to is families (or sometime called pencils) of conics. $C_1 + \lambda C_2 = 0$ represents the zero sets of the family of conics passing through the intersection points of conics $c_1 and c_2$ please note that $\lambda$ is a parameter and assumes all possible real values. $C_1 + C_2 = 0$ is the same as the logical operation of this must satisfy both $C_1 AND C_2 = 0$.however there is an incongruity: suppose $C_1|_{(x_1,y_1)} = -1$ and $C_2|_{(x_1,y_1)} = 1$. this still satisfies the original equation of the 2 conics.But ${(x_1,y_1)}$ does not belong to the zero set of either original conic .i.e. it does not satisfy either of the original conic equations. Furthermore the generated shape will have all the points of both conics plus some extra.thus while the resulting equation is a general equation of the second degree it forms no recognizable conic. Is my reasoning correct or have have really missed out a lot of logic?
7. how many whole integral solutions does the equation $x_1 +x_2 + ...... x_n = c$ have if $0 < x_1 < k_1 , 0 < x_2 < k_2 .......0 < x_n < k_n$ and c and k are constants. This problem is analogous to the to this if a number of people have each some amount of money(may or may not be the same amount) , in how many ways can they pay a bill. I cannot understand how to do this question please help.
8. Hi, does anyone know a good book or site I could refer to for conic section related formula,properties(the whole lot).I will be requiring very detailed covering almost everything esp. focusing on the tangents , normal and other associated figures and their various forms(i.e parametric ,slope,point, etc..). Thanks
9. I've tried to find the answer but can't seem to get it yet. Here is the question: For what values of 'a' will the tangents to the parabola $y^2 = 4ax$from a point not on the y axis will be normal to the parabola $x^2 = 4y$? in case this help the answer is $a < -2 \sqrt{2} or a > -2 \sqrt{2}$. sorry for this repost. Does anyone know if I could delete it. thanks for deleting the other one
10. http://en.wikipedia.org/wiki/Geographic_information_system GIS stands for global informatics system this is a link to the wikipedia article on it. It is basically a system which stores data about the ground, water bodies ,etc.I am not adverse to using any other form of information for ndvi but I need highly detailed info.(i.e. each sq k.m (you get the idea)).
11. Hi, Computers have been used to analyse several geographical factors(in my case I need to measure ndvi index to measure plant growth.) Can anybody help me out .how is GIS used .Are there any alternatives to using GIS .And does anyone know any GIS information repositories. (I program in java,so would appreciate it if the replies would use this language) I know this is a more ecology topic but I anyone could offer a better( yet simple) way of estimating plant growth in a region, I would would be thankfull.
12. I think this question uses the same thechniques as the one I posted (see combinatorics problem in homework help) if you come up with anything please tell me.
13. q1) you can draw them the same way you draw normal systems just show the single pair. q2)sorry don't know q3)there are 2 ways .1 by assuming each atom in the molecule will have the same oxidation staet creating an equation and solving for your element(this only works in simple situations). the 2nd ways is by looking at the structure of the molecule.if the bond is ionic the more electronegetive gets a full -1 charge added to its oxidation state,if between the 2 atoms participating in the bond one is more electropositive it gets +1 added.in case of co-valent bonds the same concept applies eevn though the electrotrons are not completely transferred.(you can think of it as heterolytic fission of all covalent bond before calculating the O.N.).As for co ordinate bonds There is absolutely no differnece in co valent and coordinate bonds after their formation.therefore if the bond is natural i.e. form an general electron donor to an general electron acceptor it is counted and a chage of 2( sign depends on atom) is added.if the opposite happens the bond is completely disregarded while calculating the O.N.
14. you could make the problem simpler by shifting your axes.i.e. take the components of all the forces along either the slope or perpendicular to it. At the end you should get an f.b.d of the block some what like this: giving the equations $f_k = \mu mgcos \theta; F + mgsin\theta - f_k = ma$ shifting axes usually works really well in most kinematics problems.
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