<p>We investigate some properties of locally scaling transformations on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {Z}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> having bijective restrictions <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(f_{N}:\{0, \ldots , 2^{N}-1\}\rightarrow \{0, \ldots , 2^{N}-1\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>f</mi> <mi>N</mi> </msub> <mo>:</mo> <mrow> <mo stretchy="false">{</mo> <mn>0</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msup> <mn>2</mn> <mi>N</mi> </msup> <mo>-</mo> <mn>1</mn> <mo stretchy="false">}</mo> </mrow> <mo stretchy="false">→</mo> <mrow> <mo stretchy="false">{</mo> <mn>0</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msup> <mn>2</mn> <mi>N</mi> </msup> <mo>-</mo> <mn>1</mn> <mo stretchy="false">}</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We study various transitivity conditions of these restrictions.</p>

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NOTES ON SOME CLASSES OF LOCALLY SCALING FUNCTIONS ON \(\mathbb {Z}_{2}\)

  • Nacima Memić,
  • Demir Papić

摘要

We investigate some properties of locally scaling transformations on \(\mathbb {Z}_{2}\) Z 2 having bijective restrictions \(f_{N}:\{0, \ldots , 2^{N}-1\}\rightarrow \{0, \ldots , 2^{N}-1\}\) f N : { 0 , , 2 N - 1 } { 0 , , 2 N - 1 } . We study various transitivity conditions of these restrictions.