General Mathematics

1208 Submissions

[3] viXra:1208.0244 [pdf] submitted on 2012-08-31 13:12:22

A New Conjecture Towards the Proof of the Hodge Conjecture

Authors: Jaivir S. Baweja
Comments: 3 Pages.

In this paper, we review important facts related to the Hodge conjecture. Also, we review Chow classes and their importance to the problem. At the end of this survey, we pose a new conjecture that would advance work on it if proven true, to further the development of the important Millennium prize problem
Category: General Mathematics

[2] viXra:1208.0222 [pdf] submitted on 2012-08-27 08:11:04

Proof of the SYZ Conjecture

Authors: Jaivir S.Baweja
Comments: 5 Pages.

In this short paper, we prove that the Strominger-Yau-Zaslow (SYZ) conjecture holds by showing that mirror symmetry is equivalent to T- duality under fibrations from Lagrangian tori. In order to do this, we use some recent developments on Ooguri- Vafa spaces to construct such fibers. Moreover, we show that this is only possible under the trivial vector bundle {0}, thus giving an equivalence between the triangulated categories D^b Fuk_0 (Y,ω) and D_0^b (Y ̌).
Category: General Mathematics

[1] viXra:1208.0019 [pdf] submitted on 2012-08-06 05:59:47

On the Affine Nonlinearity in Circuit Theory

Authors: Emanuel Gluskin
Comments: 34 Pages. This is the set of the slides for my first NDES 2012 lecture, which significantly extends the content of the associated proceedings article.

According to the definition of the linear operator, as accepted in system theory, an affine dependence is a nonlinear one. This implies the nonlinearity of Thevenin's 1-port, while the battery itself is a strongly nonlinear element that in the 1-port's "passive mode" (when the 1-port is fed by a "stronger" circuit) can be replaced by a hardlimiter. For the theory, not the actual creation of the equivalent 1-port, but the selection of one of the ports of a (linear) many-port for interpreting the circuit as a 1-port, is important. A practical example of the affine nonlinearity is given also in terms of waveforms of time functions. Emphasizing the importance of the affine nonlinearity, it is argued that even when straightening the curved characteristic of the solar cell, we retain the main part of the nonlinearity. Finally, the "fractal-potential" and "f-connection-analysis" of 1- ports, which are missed in classical theory, are mentioned.
Category: General Mathematics