We live in a 3-dimensional world. We know 2-dimensional objects as those we can see on paper. But what would an object with a nonnatural number (a number that isn\u27t a whole positive number) dimension look like? These dimensions exist and some unique mathematical sets have such dimensions, like log2/log3 . We call such dimensions and its tool Hausdorff dimension. In my talk, I examine Hausdorff dimension and its famous examples including the Cantor Set and multiple manipulations of it
AbstractWe investigate a class of Cantor sets, which has the striking property such that their Hausd...
AbstractWe give a new method for finding the Hausdorff dimension of the sets En consisting of the re...
The Hausdorff dimension of a product $X\times Y$ can be strictly greater than that of $Y$, even when...
We live in a 3-dimensional world. We know 2-dimensional objects as those we can see on paper. But wh...
In the thesis we pursue the term Hausdorff measure and dimension. Hausdorff measure is a non-negativ...
In our everyday experiences, we have developed a concept of dimension, neatly expressed as integers,...
This paper is a summary of some interesting properties of the Cantor ternary set and a few investig...
In this paper, we prove the identity Hausdorff dimension, FRdand :[0,1][0,1]din a more general setti...
Funding: The work was supported in part by an EPSRC Standard Grant EP/R015104/1.This article surveys...
openIn this thesis we introduce the concepts of Hausdorff dimensions and box-counting (or Minkowski-...
Master of ScienceDepartment of MathematicsHrant HakobyanWhen studying geometrical objects less regul...
Master of ScienceDepartment of MathematicsHrant HakobyanWhen studying geometrical objects less regul...
In this paper, we prove the identity dimH(F)=d⋅dimH(α−1(F)) , where dimH denotes Hausdorff dimension...
Abstract. The theory of Hausdorff dimension provides a general notion of the size of a set in a metr...
How many fractals exist in nature or the virtual world In this work, we partially answer the second ...
AbstractWe investigate a class of Cantor sets, which has the striking property such that their Hausd...
AbstractWe give a new method for finding the Hausdorff dimension of the sets En consisting of the re...
The Hausdorff dimension of a product $X\times Y$ can be strictly greater than that of $Y$, even when...
We live in a 3-dimensional world. We know 2-dimensional objects as those we can see on paper. But wh...
In the thesis we pursue the term Hausdorff measure and dimension. Hausdorff measure is a non-negativ...
In our everyday experiences, we have developed a concept of dimension, neatly expressed as integers,...
This paper is a summary of some interesting properties of the Cantor ternary set and a few investig...
In this paper, we prove the identity Hausdorff dimension, FRdand :[0,1][0,1]din a more general setti...
Funding: The work was supported in part by an EPSRC Standard Grant EP/R015104/1.This article surveys...
openIn this thesis we introduce the concepts of Hausdorff dimensions and box-counting (or Minkowski-...
Master of ScienceDepartment of MathematicsHrant HakobyanWhen studying geometrical objects less regul...
Master of ScienceDepartment of MathematicsHrant HakobyanWhen studying geometrical objects less regul...
In this paper, we prove the identity dimH(F)=d⋅dimH(α−1(F)) , where dimH denotes Hausdorff dimension...
Abstract. The theory of Hausdorff dimension provides a general notion of the size of a set in a metr...
How many fractals exist in nature or the virtual world In this work, we partially answer the second ...
AbstractWe investigate a class of Cantor sets, which has the striking property such that their Hausd...
AbstractWe give a new method for finding the Hausdorff dimension of the sets En consisting of the re...
The Hausdorff dimension of a product $X\times Y$ can be strictly greater than that of $Y$, even when...