Related papers: The Pitchfork Bifurcation

We introduce a linear algebraic object called a bidiagonal triad. A bidiagonal triad is a modification of the previously studied and similarly defined concept of bidiagonal triple. A bidiagonal triad and a bidiagonal triple both consist of…

We propose a conic transformation method to solve the Perspective-Three-Point (P3P) problem. In contrast to the current state-of-the-art solvers, which formulate the P3P problem by intersecting two conics and constructing a degenerate conic…

We introduce new obstructions to rationality for geometrically rational threefolds arising from the geometry of curves and their cycle maps.

An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.

We define the tangential derivative, a notion of directional derivative which is invariant under diffeomorphisms. In particular this derivative is invariant under changes of chart and is thus well-defined for functions defined on a…

We argue that traditional formulations of the reduction thesis that tie it to privileged relational operations do not suffice for Peirce's justification of the categories, and invite the charge of gerrymandering to make it come out as true.…

We suggest a method of solving the problem of existence of a triangle with prescribed two bisectors and one third element which can be taken as one of the angles, the sides, the heights or the medians, or the third bisector.

This is the announcement of an alternative approach to the 3-dimensional Poincar\'e Conjecture, different from Perelman's big and spectacular breakthrough. No claim concerning the other parts of the Thurston Geometrization Conjecture, come…

The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence…

In this paper, we define some new notions of triangular Banach algebras and we investigate the derivations on these algebras.

This paper suggests a new interpretation of the Dempster-Shafer theory in terms of probabilistic interpretation of plausibility. A new rule of combination of independent evidence is shown and its preservation of interpretation is…

The authors modify the Balazard-Saias criterion for the Riemann hypothesis by changing the cutoff of the Dirichlet series. They establish some asymptotic results related to the modified criterion.

This paper has been withdrawn since it contains some discrepancy with othe authers's recent result. We will not post this until this discrepancy is resolved.

Bifurcations of one dimensional dynamical systems are discussed based on some ultradiscrete equations. The ultradiscrete equations are derived from normal forms of one-dimensional nonlinear differential equations, each of which has…

New cases of the multiplicity conjecture are considered.

Bifurcation with symmetry is considered in the case of an isotropy subgroup with a two-dimensional fixed point subspace and non-zero quadratic terms. In general, there are one or three branches of solutions, and five qualitatively different…

The theory of non-symmetric Jack polynomials is developed independently of the theory of symmetric Jack polynomials, and this theory together with the relationship between the non-symmetric, symmetric and anti-symmetric Jack polynomials is…

Static stability problem for axially compressed rotating nano-rod clamped at one and free at the other end is analyzed by the use of bifurcation theory. It is obtained that the pitchfork bifurcation may be either super- or sub-critical.…

This is the second part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using abstract theorems in the first part we obtain many new bifurcation results for quasi-linear…

In this article, the theory of sheaves is studied from a categorical point of view. This perspective vastly generalizes the usual theory of sheaves of sets to a more abstract setting which allows us to investigate the theory of sheaves with…