相关论文: On the algebraic non-integrability of the Halphen …
We prove that there is no consistent polynomial quantization of the coordinate ring of a basic non-nilpotent coadjoint orbit of a semisimple Lie group.
The theory of integrals is used to analyse the structure of Hopf algebroids, introduced in math.QA/0302325. We prove that the total algebra of the Hopf algebroid is a separable extension of the base algebra if and only if it is a…
In this paper we prove non-existence of nontrivial partial difference sets in Abelian groups of order 8p^3, where p \geq 3 is a prime number.
We determine a considerable class of nonlinear partial differential equation systems which have global regular solutions. Uniqueness is not a direct general consequence of this method. The scheme can be applied to the incompressible Navier…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
We show an example of a non-symmetric integro-differential equation of order $\alpha$, for $\alpha \in (0,1)$, for which H\"older estimates do not hold even though the kernels are comparable to the fractional Laplacian.
The Sasano sytem of type $A^{(2)}_5$ is a four-dimensional non-linear system of ordinary differential equations, which has an affine Weyl group of symmetries of type $A^{(2)}_5$. It is also a tipe dependent Hamiltonian system, which can be…
The bases of the theory of integrals for multidimensional differential systems are stated. The integral equivalence of total differential systems, linear homogeneous systems of partial differential equations, and Pfaff systems of equations…
In the theory of complex valued functions of a complex variable arguably the first striking theorem is that pointwise differentiability implies $C^{\infty}$ regularity. As mentioned in Ahlfors's standard textbook there have been a number of…
We establish that the sequences formed by logarithms and by "fractional" powers of integers, as well as the sequence of prime numbers, are non-holonomic, thereby answering three open problems of Gerhold [Electronic Journal of Combinatorics…
In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily…
It is shown that the pillars of transfinite set theory, namely the uncountability proofs, do not hold. (1) Cantor's first proof of the uncountability of the set of all real numbers does not apply to the set of irrational numbers alone, and,…
In this short note, the simplicity of the first eigenvalue of a nonlinear system is shown by an alternative proof; thereby, it states that the first eigenfunctions are unique up to modulo scaling.
Pick a formal system. Any formal system. Whatever your favourite formal system is, as long as it's capable of reasoning about elementary arithmetic. The First Spectral Gap Incompleteness Theorem of [CPGW15] proved that there exist…
Generalized Halphen systems are solved in terms of functions that uniformize genus zero Riemann surfaces, with automorphism groups that are commensurable with the modular group. Rational maps relating these functions imply subgroup…
We give different proofs and prove new results on the non complete solvability of some systems of complex first order p.d.e.'s, especially related to the analysis on CR manifolds.
The systems of complex analytic second order ordinary differential equations whose solutions close up to become rational curves (after analytic continuation) are characterized by the vanishing of an explicit differential invariant, and turn…
In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances. The main results extend some of the previous…
In this paper we obtain three undecidable results for exponential diophantine equations over the field $\mathbb Q$ of rational numbers. For example, we prove that there is no algorithm to decide the solvability of a general exponential…
We show that there is no theory that is minimal with respect to interpretability among recursively enumerable essentially undecidable theories.