Let F be a cellular automaton on the space of all sequences from a finite alphabet. From the local description of F a finite labeled digraph is constructed with a distinguished subdi graph. The surjectivity and openness of F are proved to correspond to properties of these digraphs. Similarly, another finite labeled digraph is constructed with a distin guished subset of its vert ex set . Th e in...

Here we prove the necessary analytic results to construct a Morse theory for the YangMills-Higgs functional on the space of Higgs bundles over a compact Riemann surface. The main result is that the gradient flow with initial conditions (A, φ) converges to a critical point of this functional, the isomorphism class of which is given by the graded object associated to the HarderNarasimhan-Seshadri...

Let X be a smooth quasi-projective variety over the algebraic closure of the rational number field. We show that the cycle map of the higher Chow group to Deligne cohomology is injective and the higher Hodge cycles are generated by the image of the cycle map as conjectured by Beilinson and Jannsen, if the cycle map to Deligne cohomology is injective and the Hodge conjecture is true for certain ...

A mapping f : Z → Z is called residue-class-wise affine if there is a positive integer m such that f is affine on residue classes (mod m). The smallest such m is called the modulus of f . In this article it is shown that if the mapping f is surjective but not injective, then the set of moduli of its powers is not bounded. Further it is shown by giving examples that the three other combinations ...

We propose an inexact version of the proximal point method and study its properties in nonreflexive Banach spaces which are duals of separable Banach spaces, both for the problem of minimizing convex functions and of finding zeroes of maximal monotone operators. By using surjectivity results for enlargements of maximal monotone operators, we prove existence of the iterates in both cases. Then w...

We consider a new fractional impulsive differential hemivariational inequality, which captures the required characteristics of both inequality and equation within same framework. By utilizing surjectivity theorem fixed point we establish an existence uniqueness for such problem. Moreover, investigate perturbation problem to prove convergence result, describes stability solution in relation data...

In the theory of inverse systems, in order to study the properties of a space X or a map f : X → Y between spaces, one expands X to an inverse system X or expands f to a map f : X → Y between the inverse systems, and then work on X or f . In this paper, we define approximate injectivity (resp., surjectivity) for approximate maps, and show that a map f : X → Y between compact metric spaces is in...

Let Σ̄ be a Noetherian subalgebra equipped with a p-adic, one-to-one, completely parabolic equation. A central problem in potential theory is the computation of functions. We show that every measurable, analytically closed path is Minkowski. A central problem in arithmetic is the derivation of almost everywhere abelian paths. Therefore in future work, we plan to address questions of injectivity ...