Other Mathematics Commons^™

The Spectral Theorem For Unitary Operators Based On The S-Spectrum, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

The quaternionic spectral theorem has already been considered in the literature, see e.g. [22], [31], [32], however, except for the finite dimensional case in which the notion of spectrum is associated to an eigenvalue problem, see [21], it is not specified which notion of spectrum underlies the theorem.

In this paper we prove the quaternionic spectral theorem for unitary operators using the S-spectrum. In the case of quaternionic matrices, the S-spectrum coincides with the right-spectrum and so our result recovers the well known theorem for matrices. The notion of S-spectrum is relatively new, see [17], and has been used for …

A New Realization Of Rational Functions, With Applications To Linear Combination Interpolation, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce the following linear combination interpolation problem (LCI): Given N distinct numbers w1,…wN and N+1 complex numbers a1,…,aN and c, find all functions f(z) analytic in a simply connected set (depending on f) containing the points w1,…,wN such that ∑u=1Nauf(wu)=c. To this end we prove a representation theorem for such functions f in terms of an associated polynomial p(z). We first introduce the following two operations, (i) substitution of p, and (ii) multiplication by monomials zj,0≤j

The Prominence Of Affect In Creativity: Expanding The Conception Of Creativity In Mathematical Problem Solving, Eric L. Mann, Scott A. Chamberlin, Amy K. Graefe

Faculty Publications

Constructs such as fluency, flexibility, originality, and elaboration have been accepted as integral components of creativity. In this chapter, the authors discuss affect (Leder GC, Pehkonen E, Törner G (eds), Beliefs: a hidden variable in mathematics education? Kluwer Academic Publishers, Dordrecht, 2002; McLeod DB, J Res Math Educ 25:637–647, 1994; McLeod DB, Adams VM, Affect and mathematical problem solving: a new perspective. Springer, New York, 1989) as it relates to the production of creative outcomes in mathematical problem solving episodes. The saliency of affect in creativity cannot be underestimated, as problem solvers require an appropriate state of mind in order …

The Stationary Phase Method For Real Analytic Geometry, Domenico Napoletani, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

We prove that the existence of isolated solutions of systems of equations of analytical functions on compact real domains in R^p, is equivalent to the convergence of the phase of a suitable complex valued integral I(h) for h→∞. As an application, we then use this result to prove that the problem of establishing the irrationality of the value of an analytic function F(x) at a point x₀ can be rephrased in terms of a similar phase convergence.

The Varieties Of Indispensability Arguments, Marco Panza, Andrea Sereni

MPP Published Research

The indispensability argument (IA) comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and …

In Honor And Memory Of Professor Lajos Takács, Aliakbar M. Haghighi, Sri G. Mohanty

Applications and Applied Mathematics: An International Journal (AAM)

This issue of AAM is dedicated to honoring and remembering Professor Lajos Takács. While wrapping up the manuscript of my book (co-authored by Dr. Dimitar Mishev): Delayed and Network Queues, I went back to celebrate his 1962 book, Introduction to the Theory of Queues, where he gives an example illustrating a waiting time paradox, where the waiting time of a passenger waiting for a bus at a bus stop is infinite, while, in reality, he will wait a finite unit of time before a bus arrive. I sent Professor Takács an e-mail on December 4, 2015, inquiring if he had …

Two-Dimensional 1-Meixner Random Vectors And Their Semi-Quantum Operators, Gabriela Popa, Aurel I Stan

Communications on Stochastic Analysis

No abstract provided.

A Poisson Shot-Noise Process Of Pulses And Its Scaling Limits, Mine Çaglar

Communications on Stochastic Analysis

No abstract provided.

Solving A Class Of Linear Skorokhod Stochastic Differential Equations, Karl-Heinz Fichtner, Steffen Klaere, Volkmar Liebscher

Communications on Stochastic Analysis

No abstract provided.

Large Deviations For Stochastic Tidal Dynamics Equation, Murugan Suvinthra, Sivaguru S Sritharan, Krishnan Balachandran

Communications on Stochastic Analysis

No abstract provided.

On The Lévy-Khinchin Decomposition Of Generating Functionals, Uwe Franz, Malte Gerhold, Andreas Thom

Communications on Stochastic Analysis

No abstract provided.

White Noise Analysis For The Canonical Lévy Process, Rolando D Navarro Jr., Frederi G Viens

Communications on Stochastic Analysis

No abstract provided.

Krylov-Veretennikov Formula For Functionals From The Stopped Wiener Process, Georgii V Riabov

Communications on Stochastic Analysis

No abstract provided.

Doob's Decomposition Theorem For Near-Submartingales, Hui-Hsiung Kuo, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.

Manzanar Murakami As Radical Mathematician, Logan Bishop-Van Horn

Scholarly Undergraduate Research Journal at Clark (SURJ)

In Karen Tei Yamashita’s Tropic of Orange, characters attempt to make meaning of the many complex structures in which they are situated. In his unique meaning-making process, Manzanar Murakami, a homeless Sansei, “conducts” the Los Angeles traffic with a silver baton from atop a highway overpass. In conducting his music, Murakami per- forms complex mathematics, finding meaning in connection by mapping the rhythmic flow of humans, machines, and goods. Through his baton, to the sounds of a beautiful orchestra, he translates precisely the relationships he sees before him. Murakami’s music and Yamashita’s fantastic images constitute a “mathematical realism,” a lens …

Some Quantum Dynamical Semi-Groups With Quantum Stochastic Dilation, Lingaraj Sahu, Preetinder Singh

Communications on Stochastic Analysis

No abstract provided.

Stochastic Dynamics Of Determinantal Processes By Integration By Parts, Laurent Decreusefond, Ian Flint, Nicolas Privault, Giovanni Luca Torrisi

Communications on Stochastic Analysis

No abstract provided.

On The Regularity Of One Parameter Transformation Groups In Barreled Locally Convex Topological Vector Spaces, Maximilian Bock

Communications on Stochastic Analysis

No abstract provided.

Hidden Markov Change Point Estimation, Robert J Elliott, Sebastian Elliott

Communications on Stochastic Analysis

No abstract provided.

Theoretical And Numerical Analysis Of An Optimal Execution Problem With Uncertain Market Impact, Kensuke Ishitani, Takashi Kato

Communications on Stochastic Analysis

No abstract provided.