# Marilyn Breen

#98,612

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Mathematician

## Marilyn Breen's AcademicInfluence.com Rankings

Marilyn Breenmathematics Degrees

Mathematics

#5351

World Rank

#7534

Historical Rank

Measure Theory

#3503

World Rank

#4132

Historical Rank

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Mathematics

## Marilyn Breen's Degrees

- PhD Mathematics Princeton University
- Masters Mathematics Stanford University
- Bachelors Mathematics University of California, Berkeley

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## Why Is Marilyn Breen Influential?

(Suggest an Edit or Addition)According to Wikipedia, Marilyn Janet Breen is a professor of mathematics at the University of Oklahoma. Her research involves geometry, including visibility and orthogonal polygons. Life and work Breen graduated in 1966 from Agnes Scott College, and received her Ph.D. from Clemson University in 1970 under the supervision of William Ray Hare Jr. She joined the Oklahoma faculty in 1971 and was promoted to full professor in 1982.

## Marilyn Breen's Published Works

### Published Works

- An improved Krasnosel'skii-type theorem for orthogonal polygons which are starshaped via staircase paths (1994) (31)
- General decomposition theorems form-convex sets in the plane (1976) (30)
- Staircasek-kernels for orthogonal polygons (1992) (26)
- Puncture of the trachea during catheterization of the subclavian vein. (1989) (23)
- The dimension of the kernel of a planar set. (1979) (22)
- A Krasnosel′skiĭ-type theorem for points of local nonconvexity (1982) (19)
- Primitive radon partitions for cyclic polytopes (1973) (18)
- Clear visibility and the dimension of kernels of starshaped sets (1982) (17)
- Starshaped unions and nonempty intersections of convex sets in (1990) (16)
- Improved Krasnosel'skii theorems for the dimension of the kernel of a starshaped set (1986) (14)
- Clear visibility, starshaped sets, and finitely starlike sets (1982) (14)
- A Krasnosel'skii theorem for staircase paths in orthogonal polygons (1994) (14)
- k-Dimensional intersections of convex sets and convex kernels (1981) (13)
- A Krasnosel'skiĭ-type theorem for unions of two starshaped sets in the plane. (1985) (13)
- A Helly-type theorem for countable intersections of starshaped sets (2005) (12)
- Staircase kernels in orthogonal polygons (1992) (11)
- CLEAR VISIBILITY AND UNIONS OF TWO STARSHAPED SETS IN THE PLANE (1984) (11)
- Determining a polytope by Radon partitions (1972) (11)
- A decomposition theorem form-convex sets (1976) (10)
- A Helly theorem for intersections of orthogonally starshaped sets (2003) (10)
- A characterization theorem for certain unions of two starshaped sets in R2 (1987) (10)
- KRASNOSEL'SKII‐TYPE THEOREMS (1985) (10)
- A characterization theorem for bounded starshaped sets in the plane (1985) (9)
- Points of local nonconvexity, clear visibility, and starshaped sets in Rd (1983) (9)
- Decomposition theorems for $3$-convex subsets of the plane. (1974) (8)
- Points of local nonconvexity and sets which are almost starshaped (1982) (8)
- A Decomposition Theorem for m-Convex Sets in Rd (1976) (8)
- The dimension of the kernel in an intersection of starshaped sets (2003) (8)
- A Helly-Type Theorem for Intersections of Compact Connected Sets in the Plane (1998) (8)
- Points of Local Nonconvexity and Finite Unions of Convex Sets (1975) (8)
- A Krasnosel’skii-type theorem for paths of bounded length (1997) (8)
- Characterizing Certain Staircase Convex Sets in R d (2010) (7)
- Tilings whose members have finitely many neighbors (1985) (6)
- Characterizing certain staircase convex sets in . (2010) (6)
- UNIONS OF TWO STARSHAPED SETS IN R 2 (1987) (6)
- A Krasnosel'skii-type theorem for nonclosed sets in the plane (1982) (6)
- A Helly-type theorem for simple polygons (1996) (5)
- Generating a staircase starshaped set from a minimal collection of its subsets (2011) (5)
- Some Krasnosel'skii numbers for finitely starlike sets in the plane (1988) (5)
- Unions of orthogonally convex or orthogonally starshaped polygons (1994) (5)
- The combinatorial structure of (m, n)-convex sets (1973) (5)
- A Weak Krasnosel'skii Theorem in R d (1988) (5)
- A quantitative version of Krasnosel'skiĭ 's theorem in ${\bf R}^{2}$. (1980) (5)
- An example concerning unions of two starshaped sets in the plane (1974) (5)
- AnRdanalogue of Valentine’s theorem on 3-convex sets (1976) (5)
- Characterizing compact unions of two starshaped sets inRd (1989) (5)
- Finitely starlike sets whose F-stars have positive measure (1989) (5)
- Clear visibility and sets which are almost starshaped (1984) (5)
- A characterization theorem for tilings having countably many singular points (1983) (4)
- Some tilings of the plane whose singular points form a perfect set (1983) (4)
- The dimension of the kernel in finite and infinite intersections of starshaped sets (2004) (4)
- An intersection property for starshaped sets in the plane (1991) (4)
- Illumination by translates of convex sets (1992) (4)
- A Helly-type theorem for the dimension of the kernel of a starshaped set (1979) (4)
- Sets in Rd having (d − 2)-dimensional kernels (1978) (4)
- j-partitions for visible shorelines (1988) (4)
- Planar compact sets whose intersections are starshaped via orthogonally convex paths (2008) (4)
- Staircase two-guard kernels of orthogonal polygons (2001) (4)
- Generating the kernel of a staircase starshaped set from certain staircase convex subsets (2012) (4)
- SETS WITH (d - 2)-DIMENSIONAL KERNELS (1978) (4)
- Decompositions for nonclosed planar m-convex sets (1977) (3)
- Increasing unions of starlike sets (1987) (3)
- A helly-number fork-almost-neighborly sets (1972) (3)
- A Krasnosel’skii-type theorem for an enlarged class of orthogonal polytopes (2017) (3)
- Generating a staircase starshaped set and its kernel in $${{\mathbb R}^3}$$ from certain staircase convex subsets (2012) (3)
- Dimensions of staircase kernels in orthogonal polygons (1994) (3)
- An n + 1 Member Decomposition for Sets Whose Lnc Points Form n Convex Sets (1975) (3)
- (D-2)-Extreme Points and a Helly-Type Theorem for Starshaped Sets (1980) (3)
- Helly-type Theorems for Infinite and for Finite Intersections of Sets Starshaped via Staircase Paths (2008) (3)
- Admissible kernels for starshaped sets (1981) (3)
- Visible shorelines inRd (1989) (3)
- An improved Krasnosel'skii theorem for nonclosed sets in the plane (1983) (3)
- A Helly Theorem For Intersections Of Sets Starshaped Via Staircase n-Paths (2006) (3)
- $k$-partitions and a characterization for compact unions of $k$ starshaped sets (1988) (3)
- ℒ2 sets which are almost starshaped (1977) (3)
- A Determination of the Combinatorial Type of a Polytope by Radon Partitions (1970) (3)
- A quantitative Krasnosel'skii theorem in Rd (1982) (2)
- Families of planar sets having starlike union (1999) (2)
- Suitable families of boxes and kernels of staircase starshaped sets in $${\mathbb{R}^d}$$Rd (2014) (2)
- Maximal visibility and unions of orthogonally starshaped sets (2005) (2)
- A Helly-type theorem for intersections of orthogonally starshaped sets in $$\mathbb R^d$$Rd (2014) (2)
- Determining starshaped sets and unions of starshaped sets by their sections (1987) (2)
- Simply connected orthogonal polygons as unions of two orthogonally starshaped sets (2005) (2)
- Unions of three starshaped sets in R2 (1989) (2)
- Some tilings of the plane whose singular points are uncountable and unbounded (1984) (2)
- Intersections of Sets Starshaped Via Paths of Bounded Length (2003) (2)
- Illumination for Unions of Boxes in R d (1992) (2)
- Essential and inessential points of local nonconvexity (1972) (2)
- A Krasnosel'skii theorem for nonclosed sets in Rd (1986) (2)
- A Krasnosel’skii-type result for planar sets starshaped via orthogonally convex paths (2007) (2)
- Intersecting unions of maximal convex sets (1973) (2)
- Sets with convex closure which are unions of two starshaped sets and families of segments which have a 2-partition (1986) (2)
- A family of examples showing that no Krasnosel’skii number exists for orthogonal polygons starshaped via staircase n-paths (2009) (2)
- Intersections and Unions of Orthogonal Polygons Starshaped Via Staircase n-Paths (2006) (2)
- Intersections of staircase convex sets in $${\mathbb {R}}^3$$ R 3 and (2021) (1)
- A Krasnosel'skii theorem for open finitely starlike sets in R3 (1991) (1)
- A bound for decompositions of $m$-convex sets whose LNC points lie in a hyperplane (1977) (1)
- Intersections of staircase convex sets in R 3 and R d (2021) (1)
- Staircase kernels for orthogonald-polytopes (1996) (1)
- A Krasnosel’skii theorem for orthogonal polygons starshaped via staircase (n + 1)-paths (2010) (1)
- A Krasnosel’skii-type theorem for certain orthogonal polytopes starshaped via k-staircase paths (2020) (1)
- A characterization of the kernel of a closed set (1975) (1)
- Helly-type theorems for intersections of sets starshaped via orthogonally convex paths (2012) (1)
- Sets of Locally Maximal Visibility and Finite Unions of Starshaped Sets (2000) (1)
- Convexity and related combinatorial geometry : proceedings of the second University of Oklahoma conference (1982) (1)
- Krasnosel'skii numbers for bounded finitely starlike sets inRd (1990) (1)
- Analogues of Horn’s theorem for finite unions of starshaped sets in ℝd (2009) (1)
- Intersections Of Sets Expressible As Unions Of k Starshaped Sets (2016) (1)
- Visible shorelines containing at least k vertices (2000) (1)
- Dual Helly-Type Theorems For Unions Of Sets Starshaped Via Staircase Paths (2013) (1)
- Krasnosel'skii-type theorems for dent edges in orthogonal polygons (1994) (1)
- Staircase convex results for a certain class of orthogonal polytopes (2015) (1)
- Intersections of m-Convex Sets (1975) (1)
- Generating a staircase starshaped set and its kernel in R 3 from certain staircase convex subsets (2012) (1)
- A helly number for unions of two boxes in R2 (1985) (1)
- The dimension of the kernel in planar sets which are starshaped via $\alpha $-paths (1998) (0)
- A Staircase Illumination Theorem for Orthogonal Polygons (2007) (0)
- A Helly-type theorem for intersections of certain orthogonal polytopes starshaped via k-staircase paths (2020) (0)
- Staircase convex results for a certain class of orthogonal polytopes (2014) (0)
- Intersectional properties concerning planarm-convex sets (1980) (0)
- Illumination for unions of boxes in (1992) (0)
- Staircase Visibility And Krasnosel'skii-Type Results For Planar Compact Sets (2011) (0)
- A Helly theorem for an enlarged class of orthogonally starshaped sets in $$\mathbb {R}^d$$Rd (2018) (0)
- Intersecting unions of convex sets in ⁿ (1975) (0)
- A weak Krasnosel\cprime skiĭ\ theorem in ${\bf R}\sp d$ (1988) (0)
- Measures of F-Stars in Finitely Starlike Sets (1990) (0)
- Helly-Type Theorems for Countable Intersections of Planar Sets Starshaped via Polygonal k-Paths (2010) (0)
- Unions of Sets Starshaped via Staircase Paths or via Paths of Bounded Length (1999) (0)
- A Decomposition Theorem for Simply Connected Orthogonal Polygons (2003) (0)
- A visible shoreline theorem for staircase paths (2009) (0)
- Design and synthesis of novel isoquinoline monoamineoxidase inhibitors (2003) (0)
- Results and Problems in Combinatorial Geometry. By Boltjansky and Gohberg. Cambridge University Press, New York, 1985. 108 pp. (2016) (0)
- A Decomposition for Sets Having a Segment Convexity Property (1980) (0)
- Visible shoreline results for staircase paths in ℝd (2014) (0)
- Visible shorelines for unions of islands (2011) (0)
- Intersecting families of convex cover order two (1976) (0)
- A Krasnoselskii Theorem for Permissible Paths Whose Edges Are Parallel to Three Given Vectors in the Plane (2001) (0)
- Intersecting families of convex cover order m (1976) (0)
- Radon and Carathéodory type theorems for staircase convexity (2023) (0)
- CLEAR VISmmiTY AND THE DIMENSION OF KERNELS OF STARSHAPED SETS (2010) (0)
- Generating the kernel of a staircase starshaped set from certain staircase convex subsets (2012) (0)
- Results and Problems in Combinatorial Geometry. By Boltjansky and Gohberg (1987) (0)
- A weak Krasnosel′skiĭ theorem in ^{} (1988) (0)
- Helly-type theorems for appropriate colorings of visibility sets (2002) (0)
- A visible shoreline result for 3-convex islands (2012) (0)
- Sets Expressible as Unions of Staircase n-Convex Polygons (2011) (0)
- A Helly-type theorem for intersections of orthogonally starshaped sets in Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docum (2014) (0)
- Helly-type theorems for intersections of sets starshaped via orthogonally convex paths (2012) (0)
- LNC points for m-convex sets (1981) (0)
- Krasnoselskii numbers and non simply connected orthogonal polygons (2000) (0)
- A better decomposition theorem for simply connected m-convex sets (1978) (0)
- A decomposition theorem for chi1-convex sets (1982) (0)
- An m-convexity property for complementary pairs in the plane (1980) (0)
- Sets which can be extended to $m$-convex sets (1977) (0)
- A Decomposition for Simple Polygons (2003) (0)

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