Mumtaz Hussain

Mathematician

Papers

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  <h1>Publications/Talks/Reviews of Mumtaz Hussain</h1>

  

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Most of my publications are available on <a href= “http://arxiv.org/find/all/1/all:+AND+Mumtaz+HUssain/0/1/0/all/0/1”> arXiv </a> and

can also be accessed from <a href=”http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=858704 “>Mathscinet</a>. However, if for any reason, you can’t download them,

send me an email and I will be happy to send you a copy. </br></br>

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<h2> Pre-prints </h2>

<li> The Hausdorff measure version of Gallagher’s theorem–closing the gap and beyond Pre-Print: <a href=”https://arxiv.org/abs/1612.00139″> arXiv:1612.00139. </a>

  or it can be downloaded from <a href=”1612.00139v1.pdf”>here.</a> (with David Simmons). </li> </br>

<li> A problem in non-linear Diophantine approximation. Pre-Print: <a href=”http://arxiv.org/abs/1505.06057″> arXiv:1505.06057. </a>

  or it can be downloaded from <a href=”1505.06057v1.pdf”>here.</a> (with Stephen Harrap and Simon Kristensen). </li> </br>

  

<li> Layered Interference Alignment: Achieving the Total DoF of MIMO X Channels. Pre-Print:

<a href= “http://arxiv.org/abs/1412.7188″>arXiv:1412.7188. </a> or it can be downloaded from <a href=”1412.7188.pdf”>here. </a> (with S. H. Mahboubi, A. S. Motahari, A. K. Khandani). </li></br>

<li> Metrical theorems on systems of small inhomogeneous linear forms. Pre-Print: <a href= “http://arxiv.org/abs/1406.3930”>arXiv:1406.3930. </a> (with S. Kristensen) We have rewritten this paper to include results on winning properties of badly approximable points. The preprint will be uploaded soon</li></br>

<h2> Published</h2>

<li> An Inhomogeneous Jarnik type theorem for planar curves. Pre-Print:<a href= “http://arxiv.org/abs/1503.04981”>arXiv:1503.04981.</a> To appear in

<a href =”https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/an-inhomogeneous-jarnik-type-theorem-for-planar-curves/77E560EFDDBD02891EBE3A13A7EFEEA5″>Mathematical Proceedings of

the Cambridge Philosophical Society</a>. It can be downloaded from <a href=”1503.04981v2.pdf”>here.</a> (with Dzmitry Badziahin, Stephen Harrap). </li></br>

<li> A note on badly approximable sets in projective space. <a href=”http://link.springer.com/journal/209″> Mathematische Zeitschrift. </a> DOI: 10.1007/s00209-016-1705-y. </a> (with S. Harrap). <a href=”Projective_MZ.pdf”>Preprint. </a></li></br>

<li> Incidence, Time of Occurrence and Response to Heart Failure Therapy in Patients with Anthracycline Cardiotoxicity.

<a href=”http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1445-5994″>Internal Medicine Journal. </a>  (with

A. Khan, A. Ashraf, R. Singh, A. Rahim, W.  Rostom, N. Collins and I. Renner) </li></br>

<li>Echocardiographic assessment of pulmonaryartery systolic pressure following treadmillstress testing.<a href=”http://ehjcimaging.oxfordjournals.org/”> European Heart Journal – Cardiovascular Imaging </a>(2016) 0, 1-5.

  (with A. Khan,  A. Ekmejian, Q. Laurent, I. Renner, A. Boyle, S. Turner). </li></br>

<li> A dichotomy law for the Diophantine properties in $\beta$–dynamical systems.

<a href=”http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10324585&fulltextType=RA&fileId=S0025579316000085″>Mathematika 62 (2016) 884–897.</a> (with M. Coons and Bao-Wei Wang). </a>  <a href=”CHW_Mathematika.pdf”>Preprint. </a></li></br>

   <li> A Jarnik type theorem for planar curves: everything about the parabola.

   <a href=”http://journals.cambridge.org/abstract_S0305004115000195″ >

   Math. Proc. Camb. Phil. Soc. (2015), 159, 47–60 </a>or download a preprint  <a href= “1309.7112.pdf”>pdf. </a></li></br>

<li> A converse to linear independence criteria, valid almost everywhere. <a href=”http://link.springer.com/journal/11139″> Ramanujan J (2015) 38:513–528.</a>  (with S. Fischler,  S. Kristensen and J. Levesley). </li></br>

<li>A note on the weighted Khintchine–Groshev theorem, <a href= “http://jtnb.cedram.org/jtnb-bin/browse”>

Journal de Theorie des Nombres de Bordeaux, 26(2014), 385-397. </a>  (with T. Yusupova).</li></br>

<li>  The metrical theory of simultaneously small linear forms, <a href= “http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.facm/1371586154&page=record”>Funct. Approx. Comment. Math.

48(2013), No. 2, 167-181. </a> (with J. Levesley).</li></br>

<li> Metrical results on systems of small linear forms, <a href= ” http://www.worldscinet.com/ijnt/”>

Int. J. of Number Theory 09(2013), No. 03, 769-782.</a> (with S. Kristensen). </li></br>

<li> On weighted inhomogeneous Diophantine approximation on planar curves, <a href= “http://journals.cambridge.org/action/displayJournal?jid=PSP”>Math. Proc. Camb. Phil. Soc. (2013), 154, 225-241. </a>(with T. Yusupova). </li></br>

<li> Badly approximable systems of linear forms in absolute value, <a href= “http://www.boku.ac.at/math/udt/”>Uniform Distribution Theory 8 (2013), no.1, 7-15.  </a>(with S. Kristensen).</li></br>

<li> The metric theory of mixed type linear forms, <a href= “http://www.worldscinet.com/ijnt/”> Int. J. of Number Theory,9 (2013), 77-90. </a> (with D. Dickinson).</li></br>

<li>  A note on badly approximable linear forms, <a href= “http://www.austms.org.au/Bulletin”> Bull. Aust. Math. Soc. 83 (2011), 262-266.</a></li></br>

<li> On fully fuzzy idempotent near-rings, <a href=”http://www.seams-bull-math.ynu.edu.cn/archive.jsp”> Southeast Asian Bull. of Math. 34(2010), no. 5, 959-970. </a>   (with M. Shabir).</li></br>

<li> Fully fuzzy idempotent gamma near-rings, Int. J. Math. Anal.3 (2006), no. 1, 19-37. (with M. Shabir and R.S. Tariq). </a></li></br>

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  <h2>Theses and other writings</h2>

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   <li> M. Hussain. Appendix for the book Neverending fractions by Jonathan Borwein, Alf van der Poorten, Jefrey Shallit, and Wadim Zudilin..</li></br>

<li> M. Hussain. Metric Diophantine approximation: the absolute value theory. D. Phil. thesis. University of York, 2011..</li></br>

<li> M. Hussain. Near-rings characterized by the properties of their fuzzy ideals. M.Phil. dissertation. Quaid-i-Azam University, Islamabad, Pakistan.</li></br>

  </ul>

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  <h2>Reviews for Mathscinet and Zentralblatt MATH</h2>

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  <li> <a href=”https://zbmath.org/?q=an:06460522″>Zbl 1325.11064</a>Multiplicatively badly approximable matrices in fields of power series. Proc. Am. Math. Soc. 143, No. 9, 3791-3800 (2015).</li></br>

  

   <li> <a href=”https://zbmath.org/?q=an:06420782″>Zbl 1325.11073 </a>On metric Diophantine approximation in matrices and Lie groups. (Approximation diophantienne métrique dans les matrices et les groupes de Lie.) C. R., Math., Acad. Sci. Paris 353, No. 3, 185-189 (2015).

</li></br>

   

    <li> <a href=”https://zbmath.org/?q=an:06431297″>Zbl 06431297 </a>Rational approximation and arithmetic progressions. Int. J. Number Theory 11, No. 2, 451-486 (2015).</li></br>

    

    

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<li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=MR&pg5=TI&pg6=PC&pg7=JOUR&pg8=ET&r=1&review_format=html&s4=MR3319052&s5=&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq”>MR3319052:</a> Generalized Markoff equations and Chebyshev polynomials, J. Number Theory 152 (2015), 1–20.</li></br>

  <li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=MR&pg5=TI&pg6=PC&pg7=JOUR&pg8=ET&r=1&review_format=html&s4=MR3393163&s5=&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq”>MR3393163:</a> Quadratic approximation to automatic continued fractions, J. Th\’eor. Nombres Bordeaux 27 (2015), no. 2, 463–482.</li></br>

  

   <li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=MR&pg5=TI&pg6=PC&pg7=JOUR&pg8=ET&r=1&review_format=html&s4=MR3361821%20&s5=&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq”> MR3361821 :</a>A quantitative result on Diophantine approximation for intersective polynomials, Integers 15A (2015), Paper No. A12, 8~pp. .</li></br>

   

    <li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=MR&pg5=TI&pg6=PC&pg7=JOUR&pg8=ET&r=1&review_format=html&s4=MR3348767&s5=&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq”>MR3348767:</a> A purely combinatorial approach to simultaneous polynomial recurrence modulo 1.  Proc. Amer. Math. Soc. 143 (2015), no. 8, 3231–3238.</li></br>

<li> <a href=”http://www.ams.org/mathscinet-getitem?mr=3319058″>MR3319058:</a> Transcendence and CM on Borcea-Voisin towers of Calabi-Yau manifolds.

J. Number Theory 152 (2015), 118–155.</li></br>

<li> <a href=”http://www.ams.org/mathscinet-getitem?mr=3310967″>MR3310967:</a>On transcendental analytic functions mapping an uncountable class of $U$-numbers into Liouville numbers.

  Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 2, 25–28.    </li></br>

  

  <li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?pg1=RVRI&pg3=authreviews&s1=858704&vfpref=html&r=1&mx-pid=3310934″> MR3310934:</a>

A useful application of Brun’s irrationality criterion. Expo. Math. 33 (2015), no. 1, 121–134. </li></br>

<li> <a href=”http://www.ams.org/mathscinet-getitem?mr=3284126″>MR3284126:</a> On simultaneous approximations to zeta-values.

Mosc. J. Comb. Number Theory 3 (2013), no. 3-4, 240–251.

   </li></br>

   

  <li> <a href=”http://www.ams.org/mathscinet-getitem?mr=3280947″> MR3280947:</a> Schmidt’s subspace theorem for moving hypersurface targets.

   Int. J. Number Theory 11 (2015), no. 1, 139–158.  </li></br>

<li> <a href=”http://www.ams.org/mathscinet-getitem?mr=3265301″>MR3265301:</a>

  Uniform distribution of prime powers and sets of recurrence and van der Corput sets in $\mathbbZ^k$. Israel J. Math. 201 (2014), no. 2, 729–760. </li></br>

<li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?pg1=INDI&s1=878101&vfpref=html&r=1&mx-pid=3198754.”>MR3198754:</a>

  Multiplicity estimates for algebraically dependent analytic functions.  Proc. Lond. Math. Soc. (3) 108 (2014), no. 4, 989–1029.</li></br>

<li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?pg1=INDI&s1=140915&vfpref=html&r=2&mx-pid=3194134″>MR3194134:</a>

  Variant of a theorem of Erdos on the sum-of-proper-divisors function. Math. Comp. 83 (2014), no. 288, 1903–1913. </li></br>

<li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?pg1=INDI&s1=710209&vfpref=html&r=2&mx-pid=3155464″>MR3155464:</a>

A note on the Duffin-Schaeffer conjecture. Unif. Distrib. Theory 8 (2013), no. 2, 151–156</li></br>

<li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?pg1=RVRI&pg3=authreviews&s1=858704&vfpref=html&r=1&mx-pid=3084308″>MR3084308:</a> A two-dimensional singular function via Sturmian words in base $\beta$.

J. Number Theory 133 (2013), no. 11, 3982–3994.</li></br>

<li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?pg1=RVRI&pg3=authreviews&s1=858704&vfpref=html&r=2&mx-pid=3028171″>MR3028171:</a>A note on the Hausdorff dimension of some liminf sets appearing in simultaneous Diophantine approximation.

Mathematika 59 (2013), no. 1, 56–64.</li></br>

<li> <a href=”http://www.ams.org/mathscinet/search/publdoc.html?pg1=RVRI&pg3=authreviews&s1=858704&vfpref=html&r=3&mx-pid=3028170″>MR3028170:</a> On multiplicatively badly approximable numbers. Mathematika 59 (2013), no. 1, 31–55.</li>

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<h2> Selected Talks</h2>

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  <li> 10 Dec 2015: An inhomogeneous wave equation, exceptional sets and Diophantine approximation, Annual ANZAMP meeting, Newcastle, NSW, Australia. </li>

<li>18 Nov 2015:  Absolute value theory and applications in MIMO, the University of York, UK. </li>

  

  <li> 28 Sep 2015: Non-linear metric Diophantine approximation, 59th AustMS meeting, Flinders University, Adelaide, Australia.</li><br>

  <li> 23 Aug 2015: Solubility of inhomogeneous wave equation and metric Diophantine approximation, Workshop on

Analysis and its Applications in Honour of “Brailey Sims”, the University of Newcastle, Australia.</li><br>

<li> 19 May 2015: Metric Diophantine approximation: the dependent theory, The University of Melbourne, Australia.</li></br>

<li> 18 May 2015: Metrical theory on manifolds, La Trobe University, Australia.</li></br>

<li> 29 Apr 2015: Metric Diophantine approximation: well approximable theory on manifolds, University of New South Wales (UNSW), Australia.</li></br>

<li> 7 Apr 2015: Measure theoretic results on manifolds, Australian National University, Australia.</li></br>

<li>  6 Feb 2015: Metric Diophantine approximation: an introduction, Lahore University of Management Sciences (LUMS), Pakistan.</li></br>

<li> 21 Jan 2015: Studying in Australia, the University of Punjab and at Government College of Science Wahdat Road Lahore, Pakistan.</li></br>

<li> 3-Oct 2013: Metric Diophantine approximation: the projective space, 57th Australian Mathematical Society conference, Sydney, Australia.</li></br>

<li> 10-Sep 2013: Measure theoretic results for small linear forms, CARMA, Newcastle, Australia.</li></br>

<li> 17-Aug 2013: Metric Diophantine approximation: an introduction, CARMA retreat, Newcastle, Australia.</li></br>

<li> 18-Jun 2013: The badly approximable sets in projective space, Arctic number theory workshop, Saariselk\”{a} Lapland, Finland.</li></br>

<li> 27-Sep 2012: Metrical results in absolute value theory, 56th Australian Mathematical Society conference, Ballarat, Australia.</li></br>

<li> 7-July 2011: Metric Diophantine approximation: the absolute value

theory. Department of Mathematics, Aarhus University, Denmark.</li></br>

<li>  Nov 2008: On the metric theory associated with the

    small linear forms. Graduate seminar series, department of

    mathematics, University of York, UK.</li></br>

<li> Feb 2008: Digit frequency and the Diophantine

    approximation. Number theory study group, University of York, UK.</li></br>

<li> May-Jun 2007: Series of talks (4) on “Heterogeneous

    ubiquitous systems in d-dimensional Eucledian space and the

    Hausdorff dimension” at the department of mathematics, University

    of York, UK. </li></br>

<li> Mar 2007: Lacunary sequences and Khintchines

    theorem. Number theory study group, University of York, UK. </li></br>

  

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