Mumtaz Hussain RSS Feed
https://opal.latrobe.edu.au/authors/Mumtaz_Hussain/9484700
RSS feed for Figshare Profile Mumtaz Hussain<![CDATA[Metrical Properties for the Weighted Products of Multiple Partial Quotients in Continued Fractions]]>https://opal.latrobe.edu.au/articles/journal_contribution/Metrical_Properties_for_the_Weighted_Products_of_Multiple_Partial_Quotients_in_Continued_Fractions/25211570
https://opal.latrobe.edu.au/articles/journal_contribution/Metrical_Properties_for_the_Weighted_Products_of_Multiple_Partial_Quotients_in_Continued_Fractions/25211570
Fri, 16 Feb 2024 05:15:17 GMT<![CDATA[Hausdorff dimension for sets of continued fractions of formal Laurent series]]>https://opal.latrobe.edu.au/articles/journal_contribution/Hausdorff_dimension_for_sets_of_continued_fractions_of_formal_Laurent_series/25130984
https://opal.latrobe.edu.au/articles/journal_contribution/Hausdorff_dimension_for_sets_of_continued_fractions_of_formal_Laurent_series/25130984
Mon, 12 Feb 2024 05:46:59 GMT<![CDATA[JARNÍK TYPE THEOREMS ON MANIFOLDS]]>https://opal.latrobe.edu.au/articles/journal_contribution/JARN_K_TYPE_THEOREMS_ON_MANIFOLDS/22705582
https://opal.latrobe.edu.au/articles/journal_contribution/JARN_K_TYPE_THEOREMS_ON_MANIFOLDS/22705582
Tue, 21 Nov 2023 23:45:16 GMT<![CDATA[An exponentially shrinking problem]]>https://opal.latrobe.edu.au/articles/journal_contribution/An_exponentially_shrinking_problem/24589545
https://opal.latrobe.edu.au/articles/journal_contribution/An_exponentially_shrinking_problem/24589545
0 and {qj}j≥1 be a sequence of integers. We calculate the Hausdorff dimension of the set Λdθ(τ)={x∈[0,1)d:‖qjxi−θi‖]]>Mon, 20 Nov 2023 03:24:01 GMT<![CDATA[Higher-Dimensional Shrinking Target Problem for Beta Dynamical Systems]]>https://opal.latrobe.edu.au/articles/journal_contribution/Higher-Dimensional_Shrinking_Target_Problem_for_Beta_Dynamical_Systems/19407059
https://opal.latrobe.edu.au/articles/journal_contribution/Higher-Dimensional_Shrinking_Target_Problem_for_Beta_Dynamical_Systems/19407059
1$ ) with general errors of approximation. Let $f, g$ be two positive continuous functions. For any $x_0,y_0\in [0,1]$ , define the shrinking target set $$ \begin{align*}E(T_\beta, f,g):=\left\{(x,y)\in [0,1]^2: \begin{array}{@{}ll@{}} \lvert T_{\beta}^{n}x-x_{0}\rvert where $S_nf(x)=\sum _{j=0}^{n-1}f(T_\beta ^jx)$ is the Birkhoff sum. We calculate the Hausdorff dimension of this set and prove that it is the solution to some pressure function. This represents the first result of this kind for the higher-dimensional beta dynamical systems.]]>Fri, 08 Sep 2023 03:53:40 GMT<![CDATA[A note on badly approximable systems of linear forms over a field of formal series]]>https://opal.latrobe.edu.au/articles/journal_contribution/A_note_on_badly_approximable_systems_of_linear_forms_over_a_field_of_formal_series/22639777
https://opal.latrobe.edu.au/articles/journal_contribution/A_note_on_badly_approximable_systems_of_linear_forms_over_a_field_of_formal_series/22639777
Mon, 17 Apr 2023 05:39:25 GMT<![CDATA[Metrical theorems for unconventional height functions]]>https://opal.latrobe.edu.au/articles/journal_contribution/Metrical_theorems_for_unconventional_height_functions/20225160
https://opal.latrobe.edu.au/articles/journal_contribution/Metrical_theorems_for_unconventional_height_functions/20225160
Wed, 13 Jul 2022 00:44:46 GMT<![CDATA[Dynamical Borel–Cantelli lemma for recurrence theory]]>https://opal.latrobe.edu.au/articles/journal_contribution/Dynamical_Borel_Cantelli_lemma_for_recurrence_theory/14403626
https://opal.latrobe.edu.au/articles/journal_contribution/Dynamical_Borel_Cantelli_lemma_for_recurrence_theory/14403626
Wed, 20 Oct 2021 03:42:59 GMT<![CDATA[A generalised multidimensional Jarník-Besicovitch theorem]]>https://opal.latrobe.edu.au/articles/chapter/A_generalised_multidimensional_Jarn_k-Besicovitch_theorem/14406398
https://opal.latrobe.edu.au/articles/chapter/A_generalised_multidimensional_Jarn_k-Besicovitch_theorem/14406398
Tue, 20 Apr 2021 00:56:44 GMT<![CDATA[Metrical properties for continued fractions of formal Laurent series]]>https://opal.latrobe.edu.au/articles/journal_contribution/Metrical_properties_for_continued_fractions_of_formal_Laurent_series/14401691
https://opal.latrobe.edu.au/articles/journal_contribution/Metrical_properties_for_continued_fractions_of_formal_Laurent_series/14401691
Tue, 20 Apr 2021 00:51:56 GMT<![CDATA[The sets of Dirichlet non-improvable numbers versus well-approximable numbers]]>https://opal.latrobe.edu.au/articles/journal_contribution/The_sets_of_Dirichlet_non-improvable_numbers_versus_well-approximable_numbers/13520165
https://opal.latrobe.edu.au/articles/journal_contribution/The_sets_of_Dirichlet_non-improvable_numbers_versus_well-approximable_numbers/13520165
is related with the classical set of -approximable numbers in the sense that. Both of these sets enjoy the same -dimensional Hausdorff measure criterion for. We prove that the set is uncountable by proving that its Hausdorff dimension is the same as that for the sets and. This gives an affirmative answer to a question raised by Hussain etA al [Hausdorff measure of sets of Dirichlet non-improvable numbers. MathematikaA 64(2) (2018), 502-518].]]>Wed, 06 Jan 2021 01:32:30 GMT