OTO STRAUCH

(doc. RNDr. Oto Strauch, DrSc.)

Curriculum Vitae | List of Publications – Articles | 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 nα 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.: L^p-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 p_n/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.