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Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2017, Volume 145, Issue 9, pp. 4041 - 4047
The f-vector of a d-dimensional polytope P stores the number of faces of each dimension. When P is a simplicial polytope the Dehn-Sommerville relations... 
F-VECTORS | MATHEMATICS | MATHEMATICS, APPLIED | MCMULLEN CONDITIONS | NUMBERS | THEOREM | SUFFICIENCY | FACES
Journal Article
ISRAEL JOURNAL OF MATHEMATICS, ISSN 0021-2172, 08/2019, Volume 232, Issue 2, pp. 827 - 848
Polytope theory has produced a great number of remarkably simple and complete characterization results for face-number sets or f-vector sets of classes of... 
MATHEMATICS | NUMBER | MCMULLEN CONDITIONS | SUFFICIENCY | FACES | Fuzzy sets | Set theory | Lattice theory | Research | Vector spaces | Mathematical research
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 01/2018, Volume 153, pp. 31 - 45
We characterize homology manifolds with . Specifically, using retriangulations of simplicial complexes, we give a short proof of Nevo and Novinsky's result on... 
Lower bound theorem | [formula omitted]-number | Rigidity theory of frameworks | Retriangulations of complexes | Homology manifolds | number | CONVEX POLYTOPE | THEOREM | SPHERES | ENUMERATION | PSEUDOMANIFOLDS | LOWER-BOUND CONJECTURE | FACES | F-VECTORS | MATHEMATICS | MCMULLEN CONDITIONS | SUFFICIENCY | g2-number
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 05/2019, Volume 292, Issue 5, pp. 1032 - 1042
Recently Lipschitz equivalence of self‐similar sets on R d has been studied extensively in the literature. However for self‐affine sets the problem is more... 
20F65 | self‐affine set | Lipschitz equivalence | 28A80 | McMullen–Bedford set | hyperbolic graph | open set condition | pseudo‐norm | 05C05 | self-affine set | pseudo-norm | MATHEMATICS | DIMENSION | CANTOR SETS | McMullen-Bedford set | GRAPHS
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 4/2016, Volume 55, Issue 3, pp. 497 - 521
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 10/2014, Volume 46, Issue 5, pp. 924 - 942
It is shown that the h ‐vectors of Stanley–Reisner rings of three classes of matroids are pure O ‐sequences. The classes are (a) matroids that are truncations... 
F-VECTORS | MATHEMATICS | MCMULLEN CONDITIONS | NUMBERS | SUFFICIENCY | RESOLUTIONS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2003, Volume 180, Issue 1, pp. 1 - 63
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 2009, Volume 116, Issue 3, pp. 730 - 732
The -theorem proved by Billera, Lee, and Stanley states that a sequence is the -vector of a simplicial polytope if and only if it is an -sequence. For any... 
f-vector | Simplicial polytope | Totally nonnegative matrix | g-theorem | F-VECTORS | MATHEMATICS | MCMULLEN CONDITIONS | SIMPLICIAL POLYTOPES | SUFFICIENCY | Mathematics | Naturvetenskap | Natural Sciences | Matematik | Simplicial polytope; g-theorem; f-vector; Totally nonnegative matrix
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 9/2005, Volume 34, Issue 3, pp. 507 - 521
We use the Billera-Liu algebra to show how the flag f-vectors of several special classes of polytopes fit into the closed convex hull of the flag f-vectors of... 
Computational Mathematics and Numerical Analysis | Convex Hull | Closed Convex Hull | Special Classis | Computational Mathematic | Tight Inequality | Mathematics | Combinatorics | F-VECTORS | MATHEMATICS | HOPF-ALGEBRAS | POSETS | MCMULLEN CONDITIONS | PARTIALLY ORDERED SETS | ENUMERATION | COMPUTER SCIENCE, THEORY & METHODS | SUFFICIENCY | CD-INDEX | Algebra | Polytopes
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 10/2003, Volume 30, Issue 4, pp. 529 - 542
Generalizing a result of Stanley on centrally symmetric polytopes, Adin has derived tight lower bounds for the face numbers of a rational simplical polytope... 
Linear Action | Equivariant Version | Cyclic Group | Lower Bound | Prime Power | Philosophy | F-VECTORS | MATHEMATICS | MCMULLEN CONDITIONS | NUMBERS | SIMPLICIAL POLYTOPES | COMPUTER SCIENCE, THEORY & METHODS | SUFFICIENCY | FACES | Geometry | Mathematical analysis | Algebra
Journal Article
by Kim, N
The Young Researcher, ISSN 2560-9823, 08/2019, Volume 3, Issue 1, pp. 89 - 101
Heart failure is a common but serious condition that affects approximately 5.7 million adults in the United States and costs the economy $30.7 billion each... 
contractile function Introduction Heart failure is a serious condition that affects approximately 5.7 million adults in the United States and costs the economy $30.7 billion each year (Division for Heart Disease and Stroke Prevention | 2017). Although a myriad of treatment options have emerged in recent years for the treatment of heart failure | systolic heart failure is the most common form of heart failure and occurs when the muscle of the left ventricle of the heart loses its ability to contract | 2012). The reasons for this reduced pumping of blood lie in cardiac enlargement | which helps to classify the certain type of heart failure. Those possessing heart failure with reduced ejection fraction have 40% and below of the blood in the left ventricle of the heart pumped out to the rest of the body | 2007). More specifically | which is below the normal ejection fraction of more than 55% (Pai et. al | leading to a loss in vital functions | it is rather recommended by Becher | 2016). It occurs when the heart is not pumping enough blood to meet all of the body’s needs | myosin ATPase activity | contractile function | a promising approach to the development of an effective intervention of heart failure lies in a dipeptide that has been reasoned to increase cardiac contractility (Black et. al | or the enlargement of the heart | Blankenberg | 2004). This is due to the fact that even though current treatment options are effective to some extent in serving as a base-line treatment | systolic heart failure | myosin | and when heart muscles become too stiff to properly contract (McMullen and Jennings | 2015). With this | carnosine | and Westermann from the World Journal of Cardiology that future treatments focus on “augmentation of heart rate in order to increase cardiac output | such as the use of Beta blockers or Angiotensin-converting enzyme (ACE) inhibitors | preventing enough oxygen and blood from circulating throughout the body (“Heart Failure Signs and Symptoms | and can affect both left and right sides of the heart (Nic | there is yet to be an established and definite treatment for this condition (McConaghy & Smith
Journal Article
ARIZ STATE LAND DEP WATER-RESOURCES REP NO 40, JULY 1969. 31 P, 9 FIG, 4 TAB, 2 REF, APPEND, 07/1969
PUMPING OF GROUNDWATER IN MCMULLEN VALLEY, ARIZONA IS CONCENTRATED MAINLY IN TWO AREAS - THE SALOME-WENDEN AREA, WHICH IS NEAR THE OUTLET OF THE VALLEY, AND... 
ARIZONA | WATER SUPPLY | AQUIFERS | WATER YIELD | MCMULLEN VALLEY(ARIZ) | ALLUVIUM | WATER QUALITY | IRRIGATION WATER | DATA COLLECTIONS | HYDROLOGIC DATA | GROUNDWATER | WATER LEVEL FLUCTUATIONS
Journal Article
Mathematics of Operations Research, ISSN 0364-765X, 08/1986, Volume 11, Issue 3, pp. 451 - 464
Assume P * is a simple, convex, d -polytope with facets, and F * is a simple, convex d '-polytope with ' facets, where 0 d ' d – 1. If F * is in fact a face of... 
triangulated sphere | 0-sequence | polyhedron | polytope pair | McMullen's conditions | vector | linear programming | simplicial complex | upper bound theorem | polytope | Polytopes | Integers | Mathematical theorems | Hyperplanes | Polyhedrons | Discrete mathematics | Grants | Combinatorics | Vertices | Linear programming | Models | Combinatorial analysis
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 6/2016, Volume 283, Issue 1, pp. 39 - 58
For a self-affine measure on a Bedford–McMullen carpet we prove that its quantization dimension of order $$r>0$$ r > 0 exists and determine its exact value.... 
Self-affine measures | Multifractal formalism | 94A15 | 28A75 | Quantization dimension | 28A80 | Mathematics, general | Mathematics | Quantization coefficient | Bedford–McMullen carpets | PROBABILITY-MEASURES | GENERAL SIERPINSKI CARPETS | DISTRIBUTIONS | MATHEMATICS | FRACTALS | HAUSDORFF | DIMENSION | SETS | Bedford-McMullen carpets | Rugs | Carpets
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 07/2017, Volume 37, Issue 7, pp. 3567 - 3585
The goal of this paper is to study the family of singular perturbations of Blaschke products given by B-a,B- lambda(z) = z(3) z-a/1-az +lambda/z(2). We focus... 
Singular perturbations | Blaschke products | Connectivity of Fatou components | Holomorphic dynamics | McMullen-like Julia sets | MATHEMATICS | singular perturbations | MATHEMATICS, APPLIED | connectivity of Fatou components | PERTURBED RATIONAL MAPS | DYNAMICS | MCMULLEN MAPS | FAMILY
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 2016, Volume 65, Issue 3, pp. 833 - 865
We study the doubling property of measures on self-affine carpets of Bedford and McMullen. Let M be the family of such carpets, and let S is an element of M be... 
Self-affine measure | Self-affine carpet of Bedford-McMullen | Doubling property | HAUSDORFF DIMENSION | MATHEMATICS | self-affine measure | FRACTALS | doubling property
Journal Article
Nonlinearity, ISSN 0951-7715, 03/2010, Volume 23, Issue 3, pp. 495 - 512
The well-known self-affine Sierpinski carpets, first studied by McMullen and Bedford independently, are constructed geometrically by repeating a single action... 
HAUSDORFF DIMENSION | FRACTALS | MATHEMATICS, APPLIED | BEDFORD | MCMULLEN | SETS | PHYSICS, MATHEMATICAL | Dimensional measurements | Nonlinearity | Construction | Carpets | Mathematical analysis
Journal Article
Fractals, ISSN 0218-348X, 2013, Volume 21, Issue 3-4, pp. 1350022 - 1-1350022-11
Let sets E and F be McMullen sets with the same number of rectangles in each line. We show that E and F are Lipschitz equivalent if they are dust-like or they... 
Fractal | Lipschitz Equivalence | McMullen Set | Self-Affine | HAUSDORFF DIMENSION | FRACTALS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SELF-SIMILAR SETS | CONFORMAL SETS | MULTIDISCIPLINARY SCIENCES | CANTOR SETS | GENERAL SIERPINSKI CARPETS | Separation | Horizontal | Equivalence | Rectangles | Fractal analysis | Blocking | Fractals
Journal Article
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