OTO STRAUCH

(doc. RNDr. Oto Strauch, DrSc.)

 

Curriculum Vitae | List of PublicationsArticles | Books | Others

 

Curriculum vitae

Name and surname: Oto Strauch

Date and place of birth: May 15, 1943, Pezinok (Slovak Republic).

Education: In 1971 I graduated at the Faculty of Natural Sciences,

Comenius University, Bratislava (I absolved mathematical analysis),

where I spent the next fifteen years as graduate student and assistant

professor. In 1980 I defended on Comenius University thesis Metric

Theory of Diophantine Approximations under the guidance of Prof.

T. Šalát, obtaining CSc.-degree (Candidatus scientiarum). In 1997

I defended habilitation thesis and in 2002 doctor thesis (DrSc.-degree)

entitled Distribution of sequences. Since 1986 at present I work at the

Mathematical Institute SAV, where I am engaged in the study of

diophantine approximations and uniform distribution theory.

Address: Mathematical Institute of the Slovak Academy of Sciences,

Štefánikova 49, SK-814 73 BRATISLAVA, Slovakia.

E-mail:  oto.strauch@mat.savba.sk

List of publications:

Articles:

[1] STRAUCH, O.: Minimal covering of a closed interval (in Slovak),

      Acta Fac. Rerum Nat. Univ. Comenian. 28 (1972), 1—15 (MR 47 \#3603).

[2] STRAUCH, O.: Injective choice functions (in Slovak),  Acta Fac. Rerum

      Nat. Univ. Comenian. 33 (1977), 87—95 (MR 81f:04005).

[3] STRAUCH, O.: A theorem equivalent to the axiom of choice, Acta Fac. Rerum

      Nat. Univ. Comenian. 34 (1980), 121—123 (MR 84b:04003).

[4] STRAUCH, O.: The decomposition of uncountable closed sets of real numbers,

      Acta Fac. Rerum Nat. Univ. Comenian. 34 (1980), 41—45 (MR 82e:26001).

[5] STRAUCH, O.: Duffin--Schaeffer conjecture and some new types of real sequences

      Acta Math. Univ. Comenian. 40-41 (1982), 233—265 (MR 84f:10065).

[6] STRAUCH, O.: A coherence between the diophantine approximations and the Dini

     derivates of some real functions,  Acta Math. Univ. Comenian. 42—43 (1983),

     97—109 (MR 86c:11021).

[7] STRAUCH, O.: Some new criterions for sequences which satisfy Duffin--Schaeffer

      conjecture, I,  Acta Math. Univ. Comenian. 42-43 (1983), 87—95 (MR 86a:11031).

[8] STRAUCH, O.: Some new criterions for sequences which satisfy Duffin--Schaeffer

conjecture, II, Acta Math. Univ. Comenian. 44-45 (1984), 55—65 (MR 86d:11059).

[9] STRAUCH, O.: Two properties of the sequence mod1, Acta Math.

      Univ. Comenian. 44-45 (1984), 67—73 (MR 86d:11057).

[10] STRAUCH, O.:  Some new criterions for sequences which satisfy Duffin--Schaeff

        conjecture, III,  Acta Math. Univ. Comenian. 48-49 (1986), 37—50 (MR 88h:11053).

[11] STRAUCH, O.:  Some application of FraneŚs integral, I, Acta Math. Univ. Comenian.

       50-51 (1987/1988), 237—245 ( MR 90d:11028; Zbl 667.10023; RŽ 1989, 10A136).

[12] PORUBSKÝ, Š.- ŠALÁT, T.-STRAUCH, O.: Transformations that preserve uniform

        distribution,  Acta Arith.  49 (1988), 459—479 (MR 89m:11072).

[13] STRAUCH, O.:  Some applications of Franel--Kluyver's integral, II, Math. Slovaca

        39 (1989), 127—140 (MR 90j:11079; Zbl 671.10002; RŽ 1989, 9A103).

[14] PORUBSKÝ, Š.- ŠALÁT, T.-STRAUCH, O.: On a class of uniform distributed sequences,

        Math. Slovaca 40 (1990), 143—170 (MR 92d:11076).

[15] STRAUCH, O.:  On the L2 discrepancy of distances of points from a finite sequence,

        Math. Slovaca 40 (1990), 245—259 (MR 92c:11078).

[16] STRAUCH, O.: An improvement of an inequality of Koksma,  Indag. Mathem., N.S.

        3 (1992), 113—118 (MR 93b:11098).

[17] STRAUCH, O.- PORUBSKÝ, Š.: Transformations that preserve uniform distribution, II,

        Grazer Math. Ber. 318 (1993), 173—182 (MR 94e:11083).

[18] STRAUCH, O.: A new moment problem of distribution functions in the unit interval,  Math.

        Slovaca 44 (1994), 171—211 (MR 95i:11082).

[19] STRAUCH, O.: L2 discrepancy, Math. Slovaca 44 (1994), 601—632 (MR 96c:11085).

[20] STRAUCH, O.: Uniformly maldistributed sequences in a strict sense,  Monatsh. Math. 120

        (1995), 153—164 (MR 96g:11095).

[21] STRAUCH, O.: On set of distribution functions of a sequence, in: Proc. Conf. Analytic and

        Elementary Number Theory, In Honor of E. Hlawka's 80th Birthday, Vienna, July 18-20, 1996,

        Universität Vien and Universität für Bodenkultur, Vienn, eds: W. G. Nowak and J. Schoissengeier,

        1997,  214—229.

[22] STRAUCH, O.:  On distribution functions of ξ(3/2)n mod1, Acta Arith. LXXXI (1997), no. 1,

        25—35 (MR 98c:11075).

[23] GRABNER, P. J. - STRAUCH, O. - TICHY, R. F.: Maldistribution in higher dimensions,

        Math. Panonica 8 (1997), no. 2, 215—223 (MR 99a:11094).

[24] STRAUCH, O.: A numerical integration method using the Fibonacci numbers, Grazer Math. Ber.

        333 (1997), 19—33 (MR 99h:65038).

[25] STRAUCH, O.- TÓTH, J. T.: Asymptotic density of AN and density of the ratio set R(A),

        Acta Arith.  LXXXVII (1998), no.1, 67—78 (MR 99k:11020).

[26] GRABNER, P. J. - STRAUCH, O. - TICHY, R. F.: Lp-discrepancy and statistical independence

        of sequences, Czechosl. Math. J. 49 (124) (1999), 97—110 (MR 2000a:11108).

[27] STRAUCH, O.: Moment problem of the type \int_0^1\int_0^1F(x,y)d g(x)d g(y)=0, in: Algebraic

        Number Theory and Diophantine Analysis, Proceedings of the International Conference held in Graz,

       Austria, August 30 to September 5, Graz, 1998, eds: F. Halter-Koch and R. F. Tichy, Walter de Gruyter,

       Berlin, New York, 2000,  423—443 (MR 2001d:11079).

[28] KOSTYRKO, P.- MAČAJ, M.- ŠALÁT, T.-STRAUCH, O.: On statistical limit points,Proc. Amer.

        Math. Soc. 129 (2001), 2647—2654 (MR 2002b:40003).

[29] STRAUCH, O.- TÓTH, J. T.: Distribution functions of ratio sequences,  Publ. Math. (Debrecen)

        58/4 (2001), 751—778 (MR 2002h:11068).

[30] STRAUCH, O.- TÓTH, J. T.: Corrigendum to Theorem 5 of the paper "Asymptotic density of AN, 

        and density of ratio set R(A), (Acta Arith. 87 (1998), 67--78) Acta Arith. 103.2 (2002), 191—200.

[31] STRAUCH, O.- PAŠTÉKA, M.- GREKOS, G.: Kloosterman's uniformly distributed sequence,

        J. Number Theory 103 (2003), no. 1, 1—15.

[32] STRAUCH, O.: On distribution functions of sequences generated by scalar and mixed product,

        Math. Slovaca 53 (2003) no. 5, 467—478.

[33] STRAUCH, O.: Some modifications of one-time pad cipher, Tatra Mt. Math. Publ. 29 (2004), 157—171.

[34] BALÁŽ, V. - STRAUCH, O. – ŠALÁT, T.: Remarks on several types of convergence of bounded

        sequences, Acta Mathematica Universitatis Ostraviensis 14 (2006), 3—12.

[35] STRAUCH, O. - BLAŽEKOVÁ, O.: Distribution of the sequence pn/n mod1, Uniform Distribution Theory

        1 (2006) no. 1, 45—63.

[36] GREKOS, G. - STRAUCH, O.: Distribution functions of ratio sequences, II, Uniform Distribution Theory

         2 (2007), no. 1, 53—77.

[37]  BLAŽEKOVÁ, O. - STRAUCH, O.:  Pseudo-randomnes of quadratic generators,  Uniform Distribution Theory

        2 (2007), no. 2,  105—120.

[38]  GIULIANO ANTONINI, R. - STRAUCH, O.:  On weighted distribution functions of sequences, Uniform Distribution

        Theory  3 (2008), no. 1,  1—18.

[39]  STRAUCH, O.:  Appendix , in: M. Weber, On localization in Kronecker's diophantine theorem, Uniform Distribution

        Theory 4 (2009), no. 1, 97—116,  113—115.

[40]  PORUBSKÝ, Š. - STRAUCH, O.:  Binary sequences generated by $\{n\alpha\}$, $n=1,2,\dots$,  Publ. Math. Debrecen

        77 (2010), no. 1—2, 139—170.

[41]  BALÁŽ, V. - NAGASAKA, K. - STRAUCH, O.:  Benford's law and distribution functions of sequences in $(0,1)$,

        (Russian)  Matematiceskie zametki 88 (2010), no.  4, 485—501,  English translation: Mathematical Notes

        88 (2010), no. 4, 449—463.

[42]  BALÁŽ, V. - LIARDET, P. - STRAUCH, O.:  Distribution functions of the sequence $\phi(M)/M$, $M\in(K,K+N)$

        as K,N, go to infinity,  INTEGERS 10 (2010), no. 4,  705—732.

[43]  FIALOVÁ, J. - STRAUCH, O.: On two-dimensional sequences composed by one-dimensional uniformly distributed

        sequences,  Uniform Distribution Theory  6 (2011), no. 2, 101—125.

[44]  MIŠÍK, L. - STRAUCH, O.:  Diophantine approximation generalized,  Proceedings of the Steklov Institute of Mathematics

        276 (2012), no. 1, 193—207.

[45]  BALÁŽ, V. - MIŠÍK, L. - STRAUCH, O. - TÓTH, J.T.:  Distribution functions of ratio sequences, III,  Publ. Math.

        Debrecen (2012), in print.

[46]  BALÁŽ, V. - MIŠÍK, L. - STRAUCH, O. - TÓTH, J.T.:  Distribution functions of ratio sequences, IV,  Periodica

        Math. Hungarica (2012), in print.

 

 

Books:

 [1] STRAUCH, O. - PORUBSKÝ, Š.: Distribution of Sequences: A Sampler,  Schriftenreihe der Slowakischen

      Akademie der Wissenschaften, Band 1, Peter Lang, Frankfurt am Main, 2005, pp. 569.

 [2] STRAUCH, O. : Unsolved Problems,  Unsolved Problems Section on the home-page of Uniform Distribution Theory,

       http://www.boku.ac.at/MATH/udt/unsolvedproblems.pdf, 2012, pp. 85.

 [3] STRAUCH, O.: Duffin-Schaeffer conjecture; Gallagher ergodic theorem,  in: Encyclopaedia of Mathematics,

      Supplement II, ed. M. Hazewinkel, Kluwer Academic Publishers, Dordrecht, 2000, pp. 172—174, 242—243.