A UNIFORM GROWTH ESTIMATES OF SOLUTIONS OF ASYMPTOTICALLY ELLIPTIC OPERATORS

51.IntroductionLetusconsideranellipticoperatorLdefinedonRebywithla'jlLco(Rrt)SCandAlS(a'j(x))5AlforsomepositiveconstantsA,A.ThesolutionuofLa=0iscalledtheL-harmonicfunction.Inarecedework[61,LinstudiedtheL-harmonicfunctionsandgaveaLiouvilletypetheorem,providedtheoperatorisasymptoticallyconic.Weareconcernedherewiththe'polynomialgrowthL-harmolilcfunctions,thatis,theL-harmonicfunctionsatisfyinglulSC(1 Ixl)'.Thisproblem,ingeneral,hasnotbeenwellunderstood,exceptthecasesthatforn=2,ListheLapl…     

关于L2空间中的Bernstein-MarkoV不等式

纠正了闵国华（１９９２年）关于Ｌ＾２空间中的Ｂｅｒｎｓｔｅｉｎ－Ｍａｒｋｏｖ不等式的几个错误结果。     

Séparations et transferts dans la hiérarchie polynomiale des groupes abéliens infinis

We prove some results on the polynomial hierarchies of infinite abelian groups. In particular, we show the polynomial hierarchy over an infinite group of exponent a prime number p collapse if and only if it is the case in the classical theory.     

Inhomogeneity of the p‐s‐Degrees of Recursive Functions

The structure of the p‐s‐degrees of recursive functions is shown to be inhomogeneous. There are two p‐s‐degrees a and b above 0 such that [ 0 , a ] is distributive and [ 0 , b ] is nondistributive. Moreover, we will investigate how the number of values of each function reflects on its degree.     

Very degenerate polynomial submersions and counterexamples to the real Jacobian conjecture

Until recently, the only known examples of non-injective polynomial local diffeomorphisms of the plane were the Pinchuk maps discovered in 1994. These maps have the form $(p,q)$, where p is a fixed polynomial of degree 10, and q satisfies certain relation. The lowest possible degree of q in a Pinchuk map is 25. In 2021, with the same p of a Pinchuk map, another example was given with q of degree 15. Aiming to find different examples, with the first components having lower degrees, we look for polynomials of degree less than or equal to 9 sharing some properties with the polynomial p of a Pinchuk map. We find precisely one polynomial of degree 7 and some ones of degree 9. By using one of the polynomials of degree 9 in the first component we construct a non-injective polynomial local diffeomorphism of the plane, with degree 15.