2015, ISBN 9781783482696, xiv, 266

Book

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

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

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

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

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

We show that for every simplicial polytope an inscribed simplicial polytope exists that has the same dimension, number of vertices, number of edges, and number...

Computational Mathematics and Numerical Analysis | Inscribed polytope | g -theorem | Delaunay triangulation | Mathematics | f -vector | Combinatorics | f-vector | g-theorem | NUMBER | CONVEX POLYHEDRA | INSCRIBABILITY | PROOF | FACES | HYPERBOLIC 3-SPACE | MATHEMATICS | MCMULLEN CONDITIONS | IDEAL POLYHEDRA | COMPUTER SCIENCE, THEORY & METHODS | SUFFICIENCY | Geometry | Polytopes | Theoretical mathematics | Computational geometry | Construction | Graph theory

Computational Mathematics and Numerical Analysis | Inscribed polytope | g -theorem | Delaunay triangulation | Mathematics | f -vector | Combinatorics | f-vector | g-theorem | NUMBER | CONVEX POLYHEDRA | INSCRIBABILITY | PROOF | FACES | HYPERBOLIC 3-SPACE | MATHEMATICS | MCMULLEN CONDITIONS | IDEAL POLYHEDRA | COMPUTER SCIENCE, THEORY & METHODS | SUFFICIENCY | Geometry | Polytopes | Theoretical mathematics | Computational geometry | Construction | Graph theory

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

F-VECTORS | MATHEMATICS | MCMULLEN CONDITIONS | NUMBERS | SUFFICIENCY | RESOLUTIONS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2003, Volume 180, Issue 1, pp. 1 - 63

An SI-sequence is a finite sequence of positive integers which is symmetric, unimodal and satisfies a certain growth condition. These are known to correspond...

Compressed algebra | Graded Betti numbers | Gorenstein ideal | Gorenstein liaison | Weak Lefschetz property | SI-sequence | Hilbert function | Arithmetically Gorenstein subscheme | Simplicial polytopes | arithmetically Gorenstein subscheme | PROJECTIVE-SPACE | graded Betti numbers | FREE RESOLUTIONS | compressed algebra | MONOMIAL IDEALS | COMPRESSED ALGEBRAS | F-VECTORS | MATHEMATICS | weak Lefschetz property | simplicial polytopes | MCMULLEN CONDITIONS | LIAISON CLASS | CONVEX POLYTOPES | ARTIN-ALGEBRAS

Compressed algebra | Graded Betti numbers | Gorenstein ideal | Gorenstein liaison | Weak Lefschetz property | SI-sequence | Hilbert function | Arithmetically Gorenstein subscheme | Simplicial polytopes | arithmetically Gorenstein subscheme | PROJECTIVE-SPACE | graded Betti numbers | FREE RESOLUTIONS | compressed algebra | MONOMIAL IDEALS | COMPRESSED ALGEBRAS | F-VECTORS | MATHEMATICS | weak Lefschetz property | simplicial polytopes | MCMULLEN CONDITIONS | LIAISON CLASS | CONVEX POLYTOPES | ARTIN-ALGEBRAS

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

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

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

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

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

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

1889, United States congressional serial set, Volume serial set no. 2612, 175

Customs Service | United States | Executive Department Publications | Tariffs and duties | Witnesses and testimony | Misconduct in government and politics | Fraud | Imports | Customs agents | McMullen, Lewis | Burt, James | Customs appraisal | Foreign trade | Government investigations | Sugar trade | Weights and measures | Dreyfous, Joseph A | Sherer Brothers | Sugar

eBook

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

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

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

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

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

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

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

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

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.