Related papers: The Dimension Conjecture Implies The Jacobi Bound …

In this paper, we proved a special case of the DDVV Conjecture.

A proof of Sendov's conjecture is given.

Several results about the union-closed sets conjecture are presented.

The Jacobian algebras are introduced and their various properties are studied.

In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.

The Jacobian Conjecture has been reduced to the symmetric homogeneous case. In this paper we give an inversion formula for the symmetric case and relate it to a combinatoric structure called the Grossman-Larson Algebra. We use these tools…

Jacobi's triple product identity is proved from one of Euler's $q$-exponential functions in an elementary way.

Recent developments of affine algebraic geometry, especially the theory of open algebraic surfaces, provide means to systematically explore geometric and topological properties of polynomials in two variables. Nevertheless, there is one…

Any counterexample to the two-dimensional Jacobian Conjecture gives a rational map from one projective plane to another. We use some ideas of the Minimal Model Program to study the combinatorial structure of a rational surface, that is…

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

In this paper, using some arithmetic properties of Jacobi sums, we investigate some products involving Jacobi sums and reveal the connections between these products and certain cyclotomic matrices. In particular, as an application of our…

We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.

Assuming a lower bound on the dimension, we prove a long standing conjecture concerning the classification of global solutions of the obstacle problem with unbounded coincidence sets.

We study finite-dimensional commutative algebras, which satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a classification in dimensions $n<7$ over algebraically closed fields of…

We construct a non-proper set of two variables polynomial maps and study the nowhere vanishing Jacobian condition of the Jacobian conjecture for this set. We obtain some classes of polynomial maps satisfying the 2-dimensional Jacobian…

In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the…

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

We obtain new partial results supporting the spectral set conjecture in dimension 1.

A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse…

We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.