Integral Equations and Operator Theory, ISSN 0378-620X, 7/2015, Volume 82, Issue 4, pp. 469 - 518

A self-adjoint operator A in a Kreĭn space ( $${\mathcal{K}, [\cdot , \cdot]}$$ K , [ · , · ] ) is called partially fundamentally reducible if there exist a...

Kreĭn space | Primary 47B50 | fundamentally reducible operator | similar to a self-adjoint operator | Mathematics | symmetric operator | Secondary 46C20 | 47B25 | Analysis | boundary triple | Self-adjoint extension | Weyl function | coupling of operators

Kreĭn space | Primary 47B50 | fundamentally reducible operator | similar to a self-adjoint operator | Mathematics | symmetric operator | Secondary 46C20 | 47B25 | Analysis | boundary triple | Self-adjoint extension | Weyl function | coupling of operators

Journal Article

The College Mathematics Journal, ISSN 0746-8342, 11/2014, Volume 45, Issue 5, pp. 391 - 392

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 12/2013, Volume 77, Issue 4, pp. 533 - 557

We consider a regular indefinite Sturm–Liouville eigenvalue problem −f′′ + q f = λ r f on [a, b] subject to general self-adjoint boundary conditions and with a...

Primary 34B09 | Secondary 34B24 | 26D10 | HELP inequality | Analysis | regular critical point | Mathematics | Indefinite Sturm–Liouville problem | 47B50 | 34L10 | Riesz basis | Indefinite Sturm-Liouville problem | MATHEMATICS | LITTLEWOOD | SIMILARITY PROBLEM | HARDY | OPERATORS

Primary 34B09 | Secondary 34B24 | 26D10 | HELP inequality | Analysis | regular critical point | Mathematics | Indefinite Sturm–Liouville problem | 47B50 | 34L10 | Riesz basis | Indefinite Sturm-Liouville problem | MATHEMATICS | LITTLEWOOD | SIMILARITY PROBLEM | HARDY | OPERATORS

Journal Article

The American Mathematical Monthly, ISSN 0002-9890, 01/2015, Volume 122, Issue 1, p. 36

Journal Article

Elemente der Mathematik, ISSN 0013-6018, 2014, Volume 69, Issue 1, pp. 33 - 39

Journal Article

The American Mathematical Monthly, ISSN 0002-9890, 02/2015, Volume 122, Issue 1, pp. 36 - 42

The standard theorem for stochastic matrices with positive entries is generalized to matrices with no sign restriction on the entries. The condition that...

Integers | Mathematical theorems | Linear algebra | Eigenvalues | Markov chains | Matrices | Mathematical vectors | ARTICLES | MATHEMATICS

Integers | Mathematical theorems | Linear algebra | Eigenvalues | Markov chains | Matrices | Mathematical vectors | ARTICLES | MATHEMATICS

Journal Article

American Mathematical Monthly, ISSN 0002-9890, 2013, Volume 120, Issue 9, pp. 841 - 846

We prove a generalization of the well-known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection...

MATHEMATICS | Triangle | Theorems (Mathematics) | Analysis

MATHEMATICS | Triangle | Theorems (Mathematics) | Analysis

Journal Article

Journal of Geometry, ISSN 0047-2468, 12/2012, Volume 103, Issue 3, pp. 375 - 408

For a given triangle T and a real number ρ we define Ceva’s triangle $${\mathcal{C}_{\rho}(T)}$$ to be the triangle formed by three cevians each joining a...

reflection matrix | shape function | 15B05 | generalized median triangle | Mathematics | similarity of triangles | 51F15 | Geometry | 51N20 | 15A24 | 51M04 | 51M15 | left-circulant matrix | 20H15 | Cevian | median triangle | group structure on $${\mathbb{R}} | Brocard angle | Shape function | Group structure on ℝ | Left-circulant matrix | Generalized median triangle | Median triangle | Reflection matrix | Similarity of triangles

reflection matrix | shape function | 15B05 | generalized median triangle | Mathematics | similarity of triangles | 51F15 | Geometry | 51N20 | 15A24 | 51M04 | 51M15 | left-circulant matrix | 20H15 | Cevian | median triangle | group structure on $${\mathbb{R}} | Brocard angle | Shape function | Group structure on ℝ | Left-circulant matrix | Generalized median triangle | Median triangle | Reflection matrix | Similarity of triangles

Journal Article

Constructive Approximation, ISSN 0176-4276, 2010, Volume 32, Issue 3, pp. 523 - 541

Let T = alpha I-0 + alpha D-1 + ... + alpha D-n" , where D is the differentiation operator and alpha(0) not equal 0, and let f be a square-free polynomial with...

Minimum root separation | Roots of polynomials | Linear operators | MATHEMATICS | Derivatives (Financial instruments)

Minimum root separation | Roots of polynomials | Linear operators | MATHEMATICS | Derivatives (Financial instruments)

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2007, Volume 155, Issue 13, pp. 1774 - 1792

Let S be a finite set with m elements in a real linear space and let J S be a set of m intervals in R . We introduce a convex operator co ( S , J S ) which...

Polytope | Convexity | Homothety | Lucas polygon | Minimal family | Irreducible family | MATHEMATICS, APPLIED | minimal family | lucas polygon | homothety | irreducible family | convexity | polytope

Polytope | Convexity | Homothety | Lucas polygon | Minimal family | Irreducible family | MATHEMATICS, APPLIED | minimal family | lucas polygon | homothety | irreducible family | convexity | polytope

Journal Article

Mathematical Inequalities and Applications, ISSN 1331-4343, 2014, Volume 17, Issue 2, pp. 591 - 609

We characterize triples of cevians which form a triangle independent of the triangle where they are constructed. This problem is equivalent to solving a...

Cone preserving matrices | Triangle inequality | Triangle inequality for cevians | Common invariant cone | MATHEMATICS | cone preserving matrices | triangle inequality for cevians | common invariant cone

Cone preserving matrices | Triangle inequality | Triangle inequality for cevians | Common invariant cone | MATHEMATICS | cone preserving matrices | triangle inequality for cevians | common invariant cone

Journal Article

The College Mathematics Journal, ISSN 0746-8342, 11/2006, Volume 37, Issue 5, pp. 344 - 354

We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential...

Line graphs | Tangents | Mathematical theorems | Golden mean | Triangles | Art galleries | Linear transformations | Exponential functions | Mathematical functions | College mathematics | College Mathematics | Mathematics Instruction | Visual Arts | Problem Solving | Mathematical Concepts | Calculus | Teaching Methods | Functions, Exponential | Analysis | Mathematical problems

Line graphs | Tangents | Mathematical theorems | Golden mean | Triangles | Art galleries | Linear transformations | Exponential functions | Mathematical functions | College mathematics | College Mathematics | Mathematics Instruction | Visual Arts | Problem Solving | Mathematical Concepts | Calculus | Teaching Methods | Functions, Exponential | Analysis | Mathematical problems

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 04/2009, Volume 63, Issue 4, pp. 473 - 499

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions affinely dependent on the eigenparameter. We give sufficient...

eigenvalue dependent boundary conditions | Analysis | Indefinite Sturm-Liouville problem | Krein space | Mathematics | Primary 34B10 | Secondary 34B09, 47B25, 47B50 | Riesz basis | definitizable operator | Definitizable operator | Eigenvalue dependent boundary conditions | MATHEMATICS | EIGENFUNCTION-EXPANSIONS | ORDINARY DIFFERENTIAL-OPERATORS

eigenvalue dependent boundary conditions | Analysis | Indefinite Sturm-Liouville problem | Krein space | Mathematics | Primary 34B10 | Secondary 34B09, 47B25, 47B50 | Riesz basis | definitizable operator | Definitizable operator | Eigenvalue dependent boundary conditions | MATHEMATICS | EIGENFUNCTION-EXPANSIONS | ORDINARY DIFFERENTIAL-OPERATORS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 03/2012, Volume 436, Issue 5, pp. 1312 - 1343

We give necessary and sufficient conditions under which the reproducing kernel of a Pontryagin space of d×1 vector polynomials is determined by a generalized...

Reproducing kernel | Forney indices | Defect number | Q-function | Symmetric operator | Self-adjoint extension | Polynomials | Pontryagin space | Smith normal form | Generalized Nevanlinna pair | HILBERT-SPACES | INTERPOLATION | MATRIX POLYNOMIALS | IIX | OPERATORS | MATHEMATICS, APPLIED

Reproducing kernel | Forney indices | Defect number | Q-function | Symmetric operator | Self-adjoint extension | Polynomials | Pontryagin space | Smith normal form | Generalized Nevanlinna pair | HILBERT-SPACES | INTERPOLATION | MATRIX POLYNOMIALS | IIX | OPERATORS | MATHEMATICS, APPLIED

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2004, Volume 132, Issue 10, pp. 2973 - 2981

The celebrated Gauss-Lucas theorem states that all the roots of the derivative of a complex non-constant polynomial p lie in the convex hull of the roots of p,...

Polynomials | Mathematical inequalities | Mathematical theorems | Coefficients | Critical points | Polygons | Roots of polynomials | Gauss-Lucas theorem | Critical points of polynomials | critical points of polynomials | MATHEMATICS | MATHEMATICS, APPLIED | roots of polynomials

Polynomials | Mathematical inequalities | Mathematical theorems | Coefficients | Critical points | Polygons | Roots of polynomials | Gauss-Lucas theorem | Critical points of polynomials | critical points of polynomials | MATHEMATICS | MATHEMATICS, APPLIED | roots of polynomials

Journal Article

Expositiones Mathematicae, ISSN 0723-0869, 2006, Volume 24, Issue 1, pp. 81 - 95

We provide a unified, elementary, topological approach to the classical results stating the continuity of the complex roots of a polynomial with respect to its...

Roots of polynomials | Homeomorphism | Continuity | MATHEMATICS | continuity | roots of polynomials | homeomorphism

Roots of polynomials | Homeomorphism | Continuity | MATHEMATICS | continuity | roots of polynomials | homeomorphism

Journal Article

Expositiones Mathematicae, ISSN 0723-0869, 2007, Volume 25, Issue 1, pp. 1 - 20

Let t ⩾ 0 . Select numbers randomly from the interval [ 0 , 1 ] until the sum is greater than t. Let α ( t ) be the expected number of selections. We prove...

Random walks | Sums of independent random variables | Linear delay differential equations | Asymptotic behavior | MATHEMATICS | random walks | sums of independent random variables | asymptotic behavior | linear delay differential equations

Random walks | Sums of independent random variables | Linear delay differential equations | Asymptotic behavior | MATHEMATICS | random walks | sums of independent random variables | asymptotic behavior | linear delay differential equations

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2003, Volume 131, Issue 1, pp. 253 - 264

Given a polynomial p of degree n \geq 2 and with at least two distinct roots let Z(p) = \{z : p(z) = 0\}. For a fixed root \alpha \in Z(p) we define the...

Circles | Mathematical theorems | Critical points | Triangles | Polynomials | Mathematics | Fall lines | Degrees of polynomials | Parallel lines | Symmetry | Separation of roots | Roots of polynomials | Critical points of polynomials | critical points of polynomials | separation of roots | MATHEMATICS | MATHEMATICS, APPLIED | roots of polynomials

Circles | Mathematical theorems | Critical points | Triangles | Polynomials | Mathematics | Fall lines | Degrees of polynomials | Parallel lines | Symmetry | Separation of roots | Roots of polynomials | Critical points of polynomials | critical points of polynomials | separation of roots | MATHEMATICS | MATHEMATICS, APPLIED | roots of polynomials

Journal Article

The College Mathematics Journal, ISSN 0746-8342, 11/2014, Volume 45, Issue 5, pp. 391 - 392

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2002, Volume 184, Issue 2, pp. 526 - 548

Necessary and sufficient conditions and also simple sufficient conditions are given for the self-adjoint operators associated with the second-order linear...

discrete spectrum | Sturm–Liouville operator | compact embedding | Liouville operator | Sturm | Sturm-Liouville operator | Discrete spectrum | Compact embedding | MATHEMATICS

discrete spectrum | Sturm–Liouville operator | compact embedding | Liouville operator | Sturm | Sturm-Liouville operator | Discrete spectrum | Compact embedding | MATHEMATICS

Journal Article

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