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Articles 1 - 7 of 7
Full-Text Articles in Other Mathematics
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 š¯‘˛-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 š¯‘˛-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 Cauchyā€“Fueter regular quaternionic-valued functions, i.e. null solutions of the Cauchyā€“Fueter 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 Cauchyā€“Kovalevskaya (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 ā€¦
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 ā€¦
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 Riemannā€™s 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 energyā€“momentum 4-vector potential field. Acoustic pressure and velocity fields form an energyā€“momentum 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 ā€¦
New Effective Transformational Computational Methods, Jun Zhang, Ruzong Fan, Fangyang Shen, Junyi Tu
New Effective Transformational Computational Methods, Jun Zhang, Ruzong Fan, Fangyang Shen, Junyi Tu
Publications and Research
Mathematics serves as a fundamental intelligent theoretic basis for computation, and mathematical analysis is very useful to develop computational methods to solve various problems in science and engineering. Integral transforms such as Laplace Transform have been playing an important role in computational methods. In this paper, we will introduce Sumudu Transform in a new computational approach, in which effective computational methods will be developed and implemented. Such computational methods are straightforward to understand, but powerful to incorporate into computational science to solve different problems automatically. We will provide computational analysis and essentiality by surveying and summarizing some related recent works, ā€¦
Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And Well-Being Through Hybrid Mathematical Modeling, Maggie Renee Sullens
Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And Well-Being Through Hybrid Mathematical Modeling, Maggie Renee Sullens
Faculty Publications and Other Works -- Mathematics
This dissertation defense presentation highlights the power of hybrid mathematical modeling and addresses crucial issues such as:
1ļø¸. The Impact of Industry Collapse on Community Mental Health: A Complex Contagion ODE Model.
2ļø¸. Budget Allocation and Illegal Fishing: A Game Theoretic Model.
3ļø¸. Reactive Scope Model with an Energy Budget and Multiple Mediators: An ODE Model
The overarching theme of Hybrid Mathematical Modeling beautifully captures the essence of this work, demonstrating its potential to unravel ecological issues while addressing the intricate interactions between humans and the environment.