Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Coalgebra (13)
- Slice hyperholomorphic functions (9)
- Reproducing kernels (8)
- White noise space (8)
- Modal logic (7)
-
- Wick product (7)
- Realization (6)
- Fock space (5)
- Infinite order differential operators (5)
- Rational functions (5)
- S-resolvent operators (5)
- Schur analysis (5)
- Superoscillations (5)
- Gaussian processes (4)
- Quaternions (4)
- Residuated lattice (4)
- Residuated lattices (4)
- S-spectrum (4)
- Beurling-Lax theorem (3)
- Coalgebraic logic (3)
- Coalgebras (3)
- Convolution algebra (3)
- De Branges Rovnyak spaces (3)
- Display calculus (3)
- Finite embeddability property (3)
- Frame (3)
- Hilbert space (3)
- Hyperholomorphic functions (3)
- Infinite products (3)
- Interpolation (3)
- Publication Year
- Publication
- Publication Type
Articles 1 - 30 of 275
Full-Text Articles in Physical Sciences and Mathematics
Canonical Extensions Of Quantale Enriched Categories, Alexander Kurz
Canonical Extensions Of Quantale Enriched Categories, Alexander Kurz
MPP Research Seminar
No abstract provided.
Generalized Q-Fock Spaces And Structural Identities, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider
Generalized Q-Fock Spaces And Structural Identities, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using đ-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift operators, and their đ-calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative.
On Axially Rational Regular Functions And Schur Analysis In The Clifford-Appell Setting, Daniel Alpay, Fabrizio Colombo, Antonino De Martino, Kamal Diki, Irene Sabadini
On Axially Rational Regular Functions And Schur Analysis In The Clifford-Appell Setting, Daniel Alpay, Fabrizio Colombo, Antonino De Martino, Kamal Diki, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we start the study of Schur analysis for CauchyâFueter regular quaternionic-valued functions, i.e. null solutions of the CauchyâFueter operator in . The novelty of the approach developed in this paper is that we consider axially regular functions, i.e. functions spanned by the so-called Clifford-Appell polynomials. This type of functions arises naturally from two well-known extension results in hypercomplex analysis: the Fueter mapping theorem and the generalized CauchyâKovalevskaya (GCK) extension. These results allow one to obtain axially regular functions starting from analytic functions of one real or complex variable. Precisely, in the Fueter theorem two operators play a âŠ
A Bayesian Approach For Lifetime Modeling And Prediction With Multi-Type Group-Shared Missing Covariates, Hao Zeng, Xuxue Sun, Kuo Wang, Yuxin Wen, Wujun Si, Mingyang Li
A Bayesian Approach For Lifetime Modeling And Prediction With Multi-Type Group-Shared Missing Covariates, Hao Zeng, Xuxue Sun, Kuo Wang, Yuxin Wen, Wujun Si, Mingyang Li
Engineering Faculty Articles and Research
In the field of reliability engineering, covariate information shared among product units within a specific group (e.g., a manufacturing batch, an operating region), such as operating conditions and design settings, exerts substantial influence on product lifetime prediction. The covariates shared within each group may be missing due to sensing limitations and data privacy issues. The missing covariates shared within the same group commonly encompass a variety of attribute types, such as discrete types, continuous types, or mixed types. Existing studies have mainly considered single-type missing covariates at the individual level, and they have failed to thoroughly investigate the influence of âŠ
Regular Functions On The Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Cho
Regular Functions On The Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Cho
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we study the regularity of R-differentiable functions on open connected subsets of the scaled hypercomplex numbers {Ht}tâR by studying the kernels of suitable differential operators {ât}tâR, up to scales in the real field R.
Pseudo-Differential Operators On The Circle, Bernoulli Polynomials, Roger Gay, Ahmed Sebbar
Pseudo-Differential Operators On The Circle, Bernoulli Polynomials, Roger Gay, Ahmed Sebbar
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show how the classical polylogarithm function Lis (z) and its relatives, the Hurwitz zeta function and the Lerch function are all of a spectral nature, and can explain many properties of the complex powers of the Laplacian on the circle and of the distribution (x +i0)s .We also make a relation with a result of Keiper [Fractional Calculus and its relationship to Riemannâs zeta function, Master of Science, Ohio State University, Mathematics (1975)].
Spacetime Geometry Of Acoustics And Electromagnetism, Lucas Burns, Tatsuya Daniel, Stephon Alexander, Justin Dressel
Spacetime Geometry Of Acoustics And Electromagnetism, Lucas Burns, Tatsuya Daniel, Stephon Alexander, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energyâmomentum 4-vector potential field. Acoustic pressure and velocity fields form an energyâmomentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The âŠ
A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen
A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen
Mathematics, Physics, and Computer Science Faculty Articles and Research
As usual, let RL denote the ring of real-valued continuous functions on a completely regular frame L. Let ÎČL and λL denote the Stone- Äech compactification of L and the Lindelöf coreflection of L, respectively. There is a natural way of associating with each sublocale of ÎČL two ideals of RL, motivated by a similar situation in C(X). In [12], the authors go one step further and associate with each sublocale of λL an ideal of RL in a manner similar to one of the ways one does it for sublocales of ÎČL. The intent in this paper âŠ
Certain Invertible Operator-Block Matrices Induced By C*-Algebras And Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Choo
Certain Invertible Operator-Block Matrices Induced By C*-Algebras And Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Choo
Mathematics, Physics, and Computer Science Faculty Articles and Research
The main purposes of this paper are (i) to enlarge scaled hypercomplex structures to operator-valued cases, where the operators are taken from a C*-subalgebra of an operator algebra on a separable Hilbert space, (ii) to characterize the invertibility conditions on the operator-valued scaled-hypercomplex structures of (i), (iii) to study relations between the invertibility of scaled hypercomplex numbers, and that of operator-valued cases of (ii), and (iv) to confirm our invertibility of (ii) and (iii) are equivalent to the general invertibility of (2Ă2)-block operator matrices.
The General Theory Of Superoscillations And Supershifts In Several Variables, Fabrizio Colombo, Stefano Pinton, Irene Sabadini, Daniele C. Struppa
The General Theory Of Superoscillations And Supershifts In Several Variables, Fabrizio Colombo, Stefano Pinton, Irene Sabadini, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential operators acting on holomorphic functions with growth conditions of exponential type. Additional constraints are required when dealing with infinite order differential operators whose symbol is a function that is holomorphic in some open set, but not necessarily entire. The results proved for superoscillating sequences in several variables are extended to sequences of supershifts in several variables.
Superoscillations And Fock Spaces, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa
Superoscillations And Fock Spaces, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we use techniques in Fock spaces theory and compute how the Segal-Bargmann transform acts on special wave functions obtained by multiplying superoscillating sequences with normalized Hermite functions. It turns out that these special wave functions can be constructed also by computing the approximating sequence of the normalized Hermite functions. First, we start by treating the case when a superoscillating sequence is multiplied by the Gaussian function. Then, we extend these calculations to the case of normalized Hermite functions leading to interesting relations with Weyl operators. In particular, we show that the Segal-Bargmann transform maps superoscillating sequences onto âŠ
Many-Valued Coalgebraic Logic: From Boolean Algebras To Primal Varieties, Alexander Kurz, Wolfgang Poiger
Many-Valued Coalgebraic Logic: From Boolean Algebras To Primal Varieties, Alexander Kurz, Wolfgang Poiger
Engineering Faculty Articles and Research
We study many-valued coalgebraic logics with primal algebras of truth-degrees. We describe a way to lift algebraic semantics of classical coalgebraic logics, given by an endofunctor on the variety of Boolean algebras, to this many-valued setting, and we show that many important properties of the original logic are inherited by its lifting. Then, we deal with the problem of obtaining a concrete axiomatic presentation of the variety of algebras for this lifted logic, given that we know one for the original one. We solve this problem for a class of presentations which behaves well with respect to a lattice structure âŠ
An Extension Of The ComplexâReal (CâR) Calculus To The Bicomplex Setting, With Applications, Daniel Alpay, Kamal Diki, Mihaela Vajiac
An Extension Of The ComplexâReal (CâR) Calculus To The Bicomplex Setting, With Applications, Daniel Alpay, Kamal Diki, Mihaela Vajiac
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we extend notions of complex âââ-calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms.
Schur Analysis And Discrete Analytic Functions: Rational Functions And Co-Isometric Realizations, Daniel Alpay, Dan Volok
Schur Analysis And Discrete Analytic Functions: Rational Functions And Co-Isometric Realizations, Daniel Alpay, Dan Volok
Mathematics, Physics, and Computer Science Faculty Articles and Research
We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers.
Discrete Wiener Algebra In The Bicomplex Setting, Spectral Factorization With Symmetry, And Superoscillations, Daniel Alpay, Izchak Lewkowicz, Mihaela Vajiac
Discrete Wiener Algebra In The Bicomplex Setting, Spectral Factorization With Symmetry, And Superoscillations, Daniel Alpay, Izchak Lewkowicz, Mihaela Vajiac
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we present parallel theories on constructing Wiener algebras in the bicomplex setting. With the appropriate symmetry condition, the bicomplex matrix valued case can be seen as a complex valued case and, in this matrix valued case, we make the necessary connection between bicomplex analysis and complex analysis with symmetry. We also write an application to superoscillations in this case.
A Strong-Type FurstenbergâSĂĄrközy Theorem For Sets Of Positive Measure, Polona Durcik, Vjekoslav KovaÄ, Mario StipÄiÄ
A Strong-Type FurstenbergâSĂĄrközy Theorem For Sets Of Positive Measure, Polona Durcik, Vjekoslav KovaÄ, Mario StipÄiÄ
Mathematics, Physics, and Computer Science Faculty Articles and Research
For every ÎČ â (0,â), ÎČ â 1, we prove that a positive measure subset A of the unit square contains a point (x0, y0) such that A nontrivially intersects curves y â y0 = a(x âx0)ÎČ for a whole interval I â (0,â) of parameters a â I . A classical Nikodym set counterexample prevents one to take ÎČ = 1, which is the case of straight lines. Moreover, for a planar set A of positive density, we show that the interval I can be arbitrarily large on the logarithmic scale. These results can âŠ
Operators Induced By Certain Hypercomplex Systems, Daniel Alpay, Ilwoo Choo
Operators Induced By Certain Hypercomplex Systems, Daniel Alpay, Ilwoo Choo
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we consider a family {Ht}tâR of rings of hypercomplex numbers, indexed by the real numbers, which contain both the quaternions and the split-quaternions. We consider natural Hilbert-space representations {(C2, Ït)}tâR of the hypercomplex system {Ht}tâR, and study the realizations Ït(h) of hypercomplex numbers h â Ht, as (2 Ă 2)-matrices acting on C2, for an arbitrarily fixed scale t â R. Algebraic, operator-theoretic, spectral-analytic, and free-probabilistic properties of them are considered.
A HörmanderâFock Space, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa
A HörmanderâFock Space, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In a recent paper we used a basic decomposition property of polyanalytic functions of order 2 in one complex variable to characterize solutions of the classical â-problem for given analytic and polyanalytic data. Our approach suggested the study of a special reproducing kernel Hilbert space that we call the Hörmander-Fock space that will be further investigated in this paper. The main properties of this space are encoded in a specific moment sequence denoted by η= (ηn)nâ„0 leading to a special entire function E(z) that is used to express the kernel function of the Hörmander-Fock space. We âŠ
Formula 101 Using 2022 Formula One Season Data To Understand The Race Results, Christopher Garcia, Oliver Lopez
Formula 101 Using 2022 Formula One Season Data To Understand The Race Results, Christopher Garcia, Oliver Lopez
Student Scholar Symposium Abstracts and Posters
The reason why I am interested in Formula One is that my friend showed me what Formula One was all about. It became interesting to see the action of the sport, including the battles the drivers have during the race and how fast they go through a corner. Also, when qualifying comes around, they push their car to the absolute limit to gain a few seconds off their opponents. The drivers only in the top 10 receive points from the winner getting 25 points, the last driver in the top 10 getting 1 point, and those below the top ten âŠ
Commutators On Fock Spaces, Daniel Alpay, Paula Cerejeiras, Uwe KĂ€hler, Trevor Kling
Commutators On Fock Spaces, Daniel Alpay, Paula Cerejeiras, Uwe KĂ€hler, Trevor Kling
Mathematics, Physics, and Computer Science Faculty Articles and Research
Given a weighted â2 space with weights associated with an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of GelfondâLeontiev derivatives. This general class of operators includes many known examples, such as classic fractional derivatives and Dunkl operators. This allows us to establish a general framework, which goes beyond the classic WeylâHeisenberg algebra. Concrete examples for its application are provided.
HörmanderâS L2 -Method, â-Problem And Polyanalytic Function Theory In One Complex Variable, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa
HörmanderâS L2 -Method, â-Problem And Polyanalytic Function Theory In One Complex Variable, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we consider the classical â-problem in the case of one complex variable both for analytic and polyanalytic data. We apply the decomposition property of polyanalytic functions in order to construct particular solutions of this problem and obtain new Hörmander type estimates using suitable powers of the Cauchy-Riemann operator. We also compute particular solutions of the â-problem for specific polyanalytic data such as the ItĂŽ complex Hermite polynomials and polyanalytic Fock kernels.
The Structure Of Locally Integral Involutive Po-Monoids And Semirings, José Gil-Férez, Peter Jipsen, Siddhartha Lodhia
The Structure Of Locally Integral Involutive Po-Monoids And Semirings, José Gil-Férez, Peter Jipsen, Siddhartha Lodhia
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show that every locally integral involutive partially ordered monoid (ipo-monoid) A = (A,â©œ, ·, 1,âŒ,â), and in particular every locally integral involutive semiring, decomposes in a unique way into a family {Ap : p â A+} of integral ipo-monoids, which we call its integral components. In the semiring case, the integral components are semirings. Moreover, we show that there is a family of monoid homomorphisms Ί = {Ïpq : Ap â Aq : p â©œ q}, indexed on the positive cone (A+,â©œ), so that the structure of A can be recovered as a glueing R ΊAp of its integral âŠ
Completeness Of Nominal Props, Samuel Balco, Alexander Kurz
Completeness Of Nominal Props, Samuel Balco, Alexander Kurz
Engineering Faculty Articles and Research
We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This leads us to define nominal PROPs and nominal monoidal theories. We show that the categories of ordinary PROPs and nominal PROPs are equivalent. This equivalence is then extended to symmetric monoidal theories and nominal monoidal theories, which allows us to transfer completeness results between ordinary and nominal calculi for string diagrams.
Music: Numbers In Motion, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa
Music: Numbers In Motion, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
Music develops and appears as we allow numbers to acquire a dynamical aspect and create, through their growth, the various keys that permit the richness of the musical texture. This idea was simply adumbrated in Platoâs work, but its importance to his philosophical worldview cannot be underestimated. In this paper we begin by discussing what is probably the first written record of an attempt to create a good temperament and then follow the Pythagoreans approach, whose problems forced musicians, over the next several centuries up to the Renaissance and early modern times, to come up with many different variations.
The Merchant And The Mathematician: Commerce And Accounting, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa
The Merchant And The Mathematician: Commerce And Accounting, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article we describe the invention of double-entry bookkeeping (or partita doppiaas it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved.
Ideals Of Functions With Compact Support In The Integer-Valued Case, Themba Dube, Oghenetega Ighedo, Batsile Tlharesakgosi
Ideals Of Functions With Compact Support In The Integer-Valued Case, Themba Dube, Oghenetega Ighedo, Batsile Tlharesakgosi
Mathematics, Physics, and Computer Science Faculty Articles and Research
For a zero-dimensional Hausdorff space X, denote, as usual, by C(X, â€) the ring of continuous integer-valued functions on X. If f â C(X, â€), denote by Z(f) the set of all points of X that are mapped to 0 by f. The set CK(X; â€) = {f â C(X; â€) | clX(X \ Z(f)) is compact} is the integer-valued analogue of the ideal of functions with compact support in C(X). By first working in the category of locales and then interpreting âŠ
An Approach To The Gaussian Rbf Kernels Via Fock Spaces, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini
An Approach To The Gaussian Rbf Kernels Via Fock Spaces, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
We use methods from the Fock space and SegalâBargmann theories to prove several results on the Gaussian RBF kernel in complex analysis. The latter is one of the most used kernels in modern machine learning kernel methods and in support vector machine classification algorithms. Complex analysis techniques allow us to consider several notions linked to the radial basis function (RBF) kernels, such as the feature space and the feature map, using the so-called SegalâBargmann transform. We also show how the RBF kernels can be related to some of the most used operators in quantum mechanics and time frequency analysis; specifically, âŠ
An Uncountable Ergodic Roth Theorem And Applications, Polona Durcik, Rachel Greenfeld, Annina Iseli, Asgar Jamneshan, José Madrid
An Uncountable Ergodic Roth Theorem And Applications, Polona Durcik, Rachel Greenfeld, Annina Iseli, Asgar Jamneshan, José Madrid
Mathematics, Physics, and Computer Science Faculty Articles and Research
We establish an uncountable amenable ergodic Roth theorem, in which the acting group is not assumed to be countable and the space need not be separable. This generalizes a previous result of Bergelson, McCutcheon and Zhang, and complements a result of Zorin- Kranich. We establish the following two additional results: First, a combinatorial application about triangular patterns in certain subsets of the Cartesian square of arbitrary amenable groups, extending a result of Bergelson, McCutcheon and Zhang for countable amenable groups. Second, a uniformity aspect in the double recurrence theorem for Î-systems for arbitrary uniformly amenable groups Î. Our uncountable Roth âŠ
A Question Of Fundamental Methodology: Reply To Mikhail Katz And His Coauthors, Tom Archibald, Richard T. W. Arthur, Giovanni Ferraro, Jeremy Gray, Douglas Jesseph, Jesper LĂŒtzen, Marco Panza, David Rabouin, Gert Schubring
A Question Of Fundamental Methodology: Reply To Mikhail Katz And His Coauthors, Tom Archibald, Richard T. W. Arthur, Giovanni Ferraro, Jeremy Gray, Douglas Jesseph, Jesper LĂŒtzen, Marco Panza, David Rabouin, Gert Schubring
Philosophy Faculty Articles and Research
This paper is a response by several historians of mathematics to a series of papers published from 2012 onwards by Mikhail Katz and various co-authors, the latest of which was recently published in the Mathematical Intelligencer, âTwo-Track Depictions of Leibnizâs Fictionsâ (Katz, Kuhlemann, Sherry, Ugaglia, and van Atten, 2021). At issue is a question of fundamental methodology. These authors take for granted that non-standard analysis provides the correct framework for historical interpretation of the calculus, and castigate rival interpretations as having had a deleterious effect on the philosophy, practice, and applications of mathematics. Rather than make this case by reasoned âŠ
On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The aim of this paper is to study a class of superoscillatory functions in several variables, removing some restrictions on the functions that we introduced in a previous paper. Since the tools that we used with our approach are not common knowledge we will give detailed proof for the case of two variables. The results proved for superoscillatory functions in several variables can be further extended to supershifts in several variables.