SelectedWorks - Branko Ćurgus

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Selected Works of Branko Ćurgus

Professor, Department of Mathematics

Math: a lifetime of free entertainment.
Research areas: Analysis - Differential equations, operator theory

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About Branko Ćurgus

Math: a lifetime of free entertainment.
Research areas: Analysis - Differential equations, operator theory

Present	Professor, Department of Mathematics, Western Washington University ‐ Department of Mathematics
Institution Organization Position Type Position Title Time Period to Options Current Position Affiliate my profile with this Institution

Differential equations, operator theory and Operator theory

Math 204 - Introduction to Linear Algebra
Math 225 - Multivariable Calculus and Geometry. II
Math 226 - Limits and infinite series
Math 307 - Mathematical Computing
Math 309 - Discrete mathematics
Math 430/530 - Fourier Series and Applications to Partial Differential Equations
Math 504 - Abstract linear algebra

Phone: (510)650-3484
Office: BH 178
Alternate email: curgus@gmail.com

Email:

Articles (41)

Partially Fundamentally Reducible Operators in Krein Spaces

Integral Equations and Operator Theory (2015)

Branko Ćurgus and Vladimir Derkach

A self-adjoint operator A in a Kreĭn space (K,[⋅,⋅]) is called partially fundamentally reducible if there exist a fundamental decomposition ...

Somewhat Stochastic Matrices

American Mathematical Monthly (2015)

Branko Ćurgus and Robert I. Jewett

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

A Proof of the Main Theorem on Bezoutians

Elemente der Mathematik (2014)

Branko Ćurgus and Aad Dijksma

We give a self-contained proof that the nullity of the Bezoutian matrix associated with a pair of polynomials f and ...

A Squeeze for Two Common Sequences that Converge to e

College Mathematics Journal (2014)

In this note, we give a direct proof that {Sn} and {Pn} converge to the same limit. The main tool ...

Ceva's Triangle Inequalities

Mathematical Inequalities and Applications (2014)

Branko Ćurgus and Árpád Bényi

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

Outer Median Triangles

Mathematics Magazine (2014)

Árpád Bényi and Branko Ćurgus

We define the notions of outer medians and outer median triangles. We show that outer median triangles enjoy similar properties ...

The Riesz Basis Property of an Indefinite Sturm-Liouville Problem with ...

Integral Equations and Operator Theory (2013)

Branko Ćurgus, Andreas Fleige and Aleksey Kostenko

We consider a regular indefinite Sturm–Liouville eigenvalue problem −f′′ + q f = λ r f on [a, b] subject ...

A Generalization of Routh's Triangle Theorem

American Mathematical Monthly (2013)

Árpád Bényi and Branko Ćurgus

On the Reproducing Kernel of a Pontryagin Space of Vector ...

Linear Algebra and its Applications (2012)

Branko Ćurgus and Aad Dijksma

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

Triangles and Groups via Cevians

Journal of Geometry (2012)

Árpád Bényi and Branko Ćurgus

For a given triangle T and a real number ρ we define Ceva’s triangle Cρ(T) to be the triangle formed ...

Stability of Roots of Polynomials Under Linear Combinations of Derivatives

Constructive Approximation (2010)

Branko Ćurgus and Vania Mascioni

Let T=α 0 I+α 1 D+⋅⋅⋅+α n D n , where D is the differentiation operator and α0≠0 , and ...

Riesz Bases of Root Vectors of Indefinite Sturm-Liouville Problems with ...

Integral Equations and Operator Theory (2009)

Paul Binding and Branko Ćurgus

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

Perturbations of Roots under Linear Transformations of Polynomials

Constructive Approximation (2007)

Branko Ćurgus and Vania Mascioni

Let Pn be the complex vector space of all polynomials of degree at most n. We give several characterizations of ...

Root Preserving Transformations of Polynomials

Mathematics Magazine (2007)

Branko Ćurgus and Vania Mascioni

Consider the real vector space P2 of all polynomials of degree at most 2. High-school students study the roots of ...

An Unexpected Limit of Expected Values

Expositiones Mathematicae (2007)

Branko Ćurgus and Robert I. Jewett

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

On a convex Operator for Finite Sets

Discrete Applied Mathematics (2007)

Branko Ćurgus and Krzysztof Kołodziejczyk

Let S be a finite set with m elements in a real linear space and let be a set of ...

An Exceptional Exponential Function

The College Mathematics Journal (2006)

We show that there is a link between a standard calculus problem of finding the best view of a painting ...

Roots and Polynomials as Homeomorphic Spaces

Expositiones Mathematicae (2006)

Branko Ćurgus and Vania Mascioni

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

A Contraction of the Lucas Polygon

Proceedings of the American Mathematical Society (2004)

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

A Counterexample in Sturm-Liouville Completeness Theory

Proceedings of the Royal Society of Edinburgh (2004)

Paul Binding and Branko Ćurgus

We give an example of an indefinite weight Sturm-Lionville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions ...

Numbers in the Sky(viewing Sculpture)

Isamu Noguchi and Skyviewing Sculpture : Proceedings of Symposia and Special Lectures (2004)

The following is my personal exploration of Noguchi’s sculpture inspired by what I do most of the time: math, or ...

Standard Symmetric Operators in Pontryagin Spaces: A Generalized von Neumann ...

Journal of Functional Analysis (2003)

Branko Ćurgus, Tomas Azizov and Aad Dijksma

Certain meromorphic matrix valued functions on ℂ/ℝ , the so-called boundary coefficients, are characterized in terms of a standard symmetric ...

Continuous Embeddings, Completions and Complementation in Krein Spaces

Radovi Matematički (2003)

Branko Ćurgus and H. Langer

Let the Krein space (A,[. , . ]A) be continuously embedded in the Krein space (K,[.,.]K ). A unique self-adjoint ...

On the Location of Critical Points of Polynomials

Proceedings of the American Mathematical Society (2003)

Branko Ćurgus and Vania Mascioni

Given a polynomial p of degree n ≥ 2 and with at least two distinct roots let Z(p) = {z ...

Form Domains and Eigenfunction Expansions for Differential Equations with Eigenparameter ...

Canadian Journal of Mathematics (2002)

Branko Ćurgus and Paul Binding

Form domains are characterized for regular 2n-th order differential equations subject to general self-adjoint boundary conditions depending affinely on the ...