Emil Daniel Schwab Professor of Mathematics University of Texas at El Paso
Department of Mathematical Sciences University of Texas at El Paso 500 W. University Ave. El Paso, Texas 79968-0514	Office: Bell Hall 201 Phone: 915-747-6758 Fax: 915-747-6502 email: eschwab@utep.edu

EDUCATION:

• Ph.D. in Mathematics, "Babes-Bolyai" University of Cluj-Napoca, Romania.
  Thesis Title: ”Contribution to the Study of Multiplicativity and Additivity in Incidence Algebras” (communicated on Sept. 13^th, 1995).
• Licentiate in Mathematics, West University of Timisoara, Romania. Thesis Title: ”Inverses in Special Categories” (June 1987).

ADMINISTRATIVE:

• Associate Dean for Research, College of Science, UTEP (10/2014 – 08/2015)
• Assistant Dean - Scientific Coordinator, College of Sciences, Univ. of Oradea, Romania (09/1996 – 08/1998)

TEACHING:

• undergraduate courses: Abstract Algebra, Linear Algebra, Elementary Number Theory, Geometry, Discrete Mathematics.
• graduate courses: Special Topics in Abstract Algebra, Combinatorics, Number Theory

GRANTS:

RESEARCH:

• Number Theory – Arithmetical Functions
• Algebraic Structures – Inverse Semigroups and Division Categories
• Algebraic Combinatorics –Möbius Function and Möbius Categories
• Mathematics Education – Problems Solving and Heuristic Strategies

PUBLICATIONS:

• BOOKS
  • Silberberg, G., Schwab, E. D., (2003). Problems in Finite Group Theory. (pp. 90 pgs). Tempe, Arizona
  • Schwab, E. D., Schwab, E. H., (1997). Algebraic Structures. Modules. Homological Methods. (pp. 201 pgs.). Crican, Romania
  • Schwab, E. D., (1994). Algebraic Structures. Rings. (pp. 103 pgs). Multiprint, Romania
• JOURNAL ARTICLES
  • Schwab, E. D., (2016). A Half-Factorial Locally Right Garsaide Monoid and the Inverse Monoid of Cofinite Monotone Partial Bijections on N*. Semigroup Forum, Springer, 92(2), 393-413.
  • Bede, B., Rudas, I. J., Schwab, E. D., Schwab, G., (2015). Approximation Properties of Lukasiewicz Fuzzy Systems. IEEE (DOI: 10.1109/NAFIPS-WConSC.2015.7284 188).
  • Schwab, E. D., Schwab, G., (2015). A Möbius Arithmetic Incidence Function. Notes on Number Theory and Discrete Mathematics, 21(3), 27-34.
  • Schwab, E. D., (2015). Möbius monoids and their connection to inverse monoids. Semigroup Forum, Springer, 90(3), 694-720.
  • Schwab, E. D., Schwab, E., (2015). On Inverse Categories with Splitting Idempotents. Archivum Mathematicum, 51(1), 13-25.
  • Schwab, E. D., Bede, B. (2014). A Note on a Broken Dirichlet Convolution. Notes on Number Theory and Discrete Mathematics, 20(2), 65-73.
  • Schwab, E. D., (2013). Dirichlet Convolution, Bicyclic Semigroup and the Breaking Process. Int. Journal of Number Theory, 9(8), 1961-1972.
  • Schwab, E. D., (2013). Inverse Semigroups Generated by Group Congruences. The Möbius Function. Algebra and Discrete Mathematics, 16(1), 116-126.
  • Schwab, E. D., (2013). The Reduced Clifford Category of the Kachel Semigroup on n Letters. Journal of Algebra and its Applications, 12(1), 1250134 1-9.
  • Schwab, E. D., (2013). Lawvere intervals and the Möbius function of a Möbius category. Discrete Mathematics and Applications, 22 (2012)(5-6), 545-554.
  • Schwab, E. D., (2013). The Free Monogenic Inverse Semigroup and the Bicyclic Multplication. Annales des Sciences Mathematique du Quebec, 36 ( 2012)(1), 235 - 243.
  • Schwab, E., Schwab, E. D., (2012). Quantum Logic, Dagger Kernel Categories and Inverse Baer*-Categories. Order / Springer, 29(3), 405-417.
  • Schwab, E. D., (2011). Binary Matrices as Morphisms of a Triangular Category. Journal of Combinatorics and Number Theory., 3(2), 113–122.
  • Stoianov, G.*, Schwab, E. D., (2011). A Dirichlet Analogue of the Free Monogenic Inverse Semigroup via Mobius Inversion. Rocky Mountain Journal of Mathematics, 41(5), 1701 - 1710.
  • Macedo, A.*, Schwab, E. D., (2011). Maximal elements and their group-like set. Annals. Computer Science Series, Tibiscus University, 9(1), 107-114.
  • Schwab, E. D., (2010). On Fibonacci and Thue-Morse Words. Journal of Automata, Languages and Combinatorics, vol.15(no.3/4), 285-295.
  • Schwab, E. D., (2010). Generalized Arithmetical Functions of Three Variables. Int. Journal of Number Theory, vol.6(no.7), 1689-1699.
  • Schwab, E. D., (2010). On Incidence Algebras of Combinatorial Inverse Monoids. Communications in Algebra, vol.38(no.5), 1778-1789.
  • Schwab, E. D., (2010). The Möbius Category of a Combinatorial Inverse Monoid with Zero. Annales des Sciences Mathématiques du Québec, vol.33 (2009)(no.1), 93-113.
  • Schwab, E. D., (2009). A partial order on bipartite graphs with n vertices. Annals. Computer Science Series, Tibiscus, 7(1), 315-324.
  • Bede, B., Nobuhara, H., Rudas, I.J., Schwab, E. D., (2009). Approximation by Shepard type pseudo-linear operators and applications to Image Processing. Int. Journal of Approx. Reasoning, Elsevier, 50, 21-36.
  • Haukkanen, P., Schwab, E. D., (2008). A unique factorization in commutative Möbius monoids. Int. Journal of Number Theory, World Scientific, 4(4), 549-561.
  • Popescu, L., Schwab, E. D., Mendez, O., (2008). Inner Separation Structures for Topological Spaces. Balcan Journal of Geometry and its Appl, 13(2), 59-65.
  • Schwab, E. D., (2008). Strictly Increasing Sequences of Integers and the Möbius Inversion Formula. JP J. of Algebra, Number Th.& Appl., Pushpa Publishing House, 11(1), 59-65.
  • Schwab, E. D., (2008). The Möbius Category of a Semilattice of Groups. Italian Journal of Pure and Appl. Math, 24, 121-134.
  • Schwab, E. D., Romero E.*, (2006). On the Combinatorial Inverse Monoid IO3. Anale Univ. Tibiscus, vol.4 (no 1), 213-227.
  • Romero, E.*, Schwab, E. D., (2005). Abstract Möbius-Division Categories are Reduced Standard Division Categories of Combinatorial Inverse Monoids. Anale Univ. Tibiscus, vol.3(tome 1), 21-29.
  • Schwab, E. D., (2004). Characterizations of Lambek-Carlitz Type. Archivum Mathematicum, 40(3), 295-300.
  • Schwab, E. D., (2004). Möbius Categories as Reduced Standard Division Categories of Combinatorial Inverse Monoids. Semigroup Forum, Springer-Verlag, 69, 30-40.
  • Schwab, E. D., (2004). The Möbius Category of Some Combinatorial Inverse Semigroups. Semigroup Forum, Springer-Verlag, 69, 41-50.
  • Schwab, E. D., (2003). On Triangular Categories. Houston Journal of Mathematics, 29(1), 25-40.
  • Schwab, E. H., Schwab, E. D., (2002). The Inverse Baer-Category of a Chain, Radovi Matematicki, 11, 7-11.
  • Silberberg, G., Schwab, E. D., (2001). The Valuated Ring of the Arithmetical Functions as a Power Series Ring. Archivum Matematicum, vol.37(no.1), 77-80.
  • Silberberg, G., Schwab, E. D., (2000). A Note on Some Discrete Valuation Rings of Arithmetical Functions. Archivum Matematicum, vol.36(no.2), 103-109.
  • Schwab, E. D., Silberberg, G.,(1999). Bemerkungen mit bezug auf die Anzahl der zyklischen Untergruppen von gegebener Ordnung im Falle einer endlichen Gruppe. Bul. St.of Univ. “Politehnica” - Timisoara, 44 (58) (1), 1-6.
  • Schwab, E. D., (1999). Characterization of A-Multiplicative Functions via the Haukkanen's Functions,. Journal of Natural Sciences and Mathematics, vol. 39 (no.1), 1-5.
  • Schwab, E. D., (1998). Complete Multiplicativity and Complete Additivity in Möbius Categories. Italian Journal of Pure and Applied Math., 3, 37-48.
  • Schwab, E. D., Silberberg, G., (1998). Uber die Anzahl der zyklischen Untergruppen gegebener Ordnung im Falle einer endlichen Gruppe. Nieuw Archief voor Wiskunde, (IV), vol.16 (no.3), 143-151.
  • Schwab, E. D., Silberberg, G., (1997). Aplicatii ale teoriei numerelor in studiul grupurilor finite (Applications of Number Theory in the Study of Finite Groups). Seminar Arghiriade / Univ.of Timisoara, 28, 1-22.
  • Schwab, E. D., Schwab, E., (1996). Multiplicativite dans les Categories de Möbius. Bull. for Appl Math./Budapest, 147-164.
  • Schwab, E. D., (1996). Regular Convolutions and A-Additive Arithmetical Functions. Pure Math and Appl., vol.7 (no.1-2), 183-190.
  • Schwab, E. D., (1995). Dirichlet Product and Completely Additive Arithmetical Functions. Nieuw Archief voor Wiskunde, Vierde serie Deel/Amsterdam, vol.13 (no.2), 187-193.
  • Schwab, E. D., (1994). On a Completely Additive Incidence Functions. Pure Math. and Appl., vol.5 (no.2), 201-204.
  • Schwab, E. D., (1994). On Completely Multiplicative Incidence Functions in Triangular Categories, Analele Univ. Oradea, vol 4, 30-32.
  • Schwab, E. D., (1993). On Regular Convolutions, Analele Univ. Oradea.vol 3, 16-21.
  • Schwab, E. D., (1993). Multiplicative and Additive Elements in the Ring of Formal Power Series, Pure Math and Appl.,vol 4, (no.3), 339-346.
  • Schwab, E. D., (1992). Completely Additive Incidence Functions , Analele Univ. Oradea.vol 2, 124-127.
  • Schwab, E. D., (1991). Completely Additive and Discriminative Convolutions, Analele Univ. Oradea.vol 1, 143-148.
  • Schwab, E. D., Schwab, E., (1990). Total Additivity and Summation Function. Seminar Arghiriade/Univ. of Timisoara, 25, 1-7.
  • Schwab, E. D., Toth, L., (1990). On Some Elementary Number Theoretic Inequalities Involving the Dirichlet Convolution. Seminar Arghiriade/Univ. of Timisoara, 24, 1-5.
  • Schwab, E. D., (1989). Asupra functiei de sumare a unei functii aritmetice (On the Summation Function of an Arithmetic Function). G.M./Bucharest, 9, 321-325.
  • Schwab, E. D., Schwab, E.,(1989). Elements multiplicatifs d’une algebre incidente. Seminar Arghiriade / Univ.of Timisoara, 18, 1-27.
  • Schwab, E. D., Schwab, E., (1988). Arithmetic Convolution. Applications in Combinatorics. Seminar Arghiriade / Univ.of Timisoara, 17, 1-8.
  • Schwab, E. D., (1988). Egy szamelmeleti fuggveny osszegezo fuggvenyerol, (On the Summation Function of an Arithmetic Function). Matematikai Lapok 11-12, 426-429.
  • Schwab, E. D., Schwab, E.,(1988). Produsul Dirichlet al functiilor aritmetice (The Dirichlet Product of Arithmetic Functions). G.M. Metod/Bucharest, 3, 120-124.