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Articles 10741 - 10770 of 10866
Full-Text Articles in Physical Sciences and Mathematics
Synthesis And Functionalization Of A Triaryldiamine-Base Photoconductive/Photorefractive Composite, And Its Application To Aberrated Image Restoration, Yichen Liang
Doctoral Dissertations
"Organic photorefractive (PR) composites have recently emerged as an important class of materials for applications including high-density data storage, optical communication, and biomedical imaging. In an effort to further improve their performance, this study focused on the utilization of functionalized semiconductor nanocrystals to photosensitize triaryamine (TPD)-based PR composites, as well as the application of TPD-based PR composites in the restoration of aberrated optical information. A novel approach to functionalize CdSe quantum dot (QCdSe) was firstly introduced where the sulfonated triarydiamine (STPD) was used as charge-transporting ligand to passivate QCdSe. TPD-based photoconductive and PR composites were photosensitized with the STPD-passivated QCdSe …
Existence And Classification Of Nonoscillatory Solutions Of Two Dimensional Time Scale Systems, Özkan Özturk
Existence And Classification Of Nonoscillatory Solutions Of Two Dimensional Time Scale Systems, Özkan Özturk
Doctoral Dissertations
"During the past years, there has been an increasing interest in studying oscillation and nonoscillation criteria for dynamic equations and systems on time scales that harmonize the oscillation and nonoscillation theory for the continuous and discrete cases in order to combine them in one comprehensive theory and eliminate obscurity from both.
We not only classify nonoscillatory solutions of dynamic equations and systems on time scales but also guarantee the (non)existence of such solutions by using the Knaster fixed point theorem, Schauder - Tychonoff fixed point theorem, and Schauder fixed point theorem. The approach is based on the sign of nonoscillatory …
Geophysical Imaging Of Karst Features In Missouri, Jeremiah Chukwunonso Obi
Geophysical Imaging Of Karst Features In Missouri, Jeremiah Chukwunonso Obi
Doctoral Dissertations
"Automated electrical resistivity tomography (ERT) supported with multichannel analysis of surface waves (MASW) and boring data were used to map karst related features in Missouri in order to understand karst processes better in Missouri. Previous works on karst in Missouri were mostly surficial mapping of bedrock outcrops and joints, which are not enough to define the internal structure of karst system, since most critical processes in karst occur underground. To understand these processes better, the density, placement and pattern of karst related features like solution-widened joints and voids, as well as top of bedrock were mapped. In the course of …
Fully Differential Study Of Projectile Coherence Effects In Ionization Of Molecular Hydrogen And Atomic Helium, Thusitha Priyantha Arthanayaka
Fully Differential Study Of Projectile Coherence Effects In Ionization Of Molecular Hydrogen And Atomic Helium, Thusitha Priyantha Arthanayaka
Doctoral Dissertations
"It has been well established, that projectile coherent properties are important for the study of atomic fragmentation processes. Recent studies of ionization of molecular hydrogen had demonstrated that measured double differential cross sections (DDCS) are very sensitive to the coherent length of the projectile. These measurements have been performed with varied coherence length of the projectiles by controlling the geometry of the collimating slits, which are placed before the target. Later, fully differential cross sections (FDCS) for a coherent and an incoherent projectile beam has been study for the same collision system and the results confirmed the important role of …
Pointwise And Uniform Convergence Of Fourier Series On Su(2), Donald Forrest Myers
Pointwise And Uniform Convergence Of Fourier Series On Su(2), Donald Forrest Myers
Doctoral Dissertations
"Let f be a Lipschitz function on the special unitary group SU (2). We prove that the Fourier partial sums of f converge to f uniformly on SU (2), thereby extending theorems of Caccioppoli, Mayer, and a special case of Ragozin. Pointwise convergence theorems for the Fourier series of functions on SU (2), due to Liu and Qian, were obtained by Clifford algebra techniques. We obtain similar versions of these theorems using simpler proof techniques: classical harmonic analysis and group theory"--Abstract, page iii.
Methodology Investigations For Shear Wave Splitting Analysis, Fansheng Kong
Methodology Investigations For Shear Wave Splitting Analysis, Fansheng Kong
Doctoral Dissertations
"Over the past several decades, shear wave splitting analyses have been increasingly utilized to delineate mantle structure and probe mantle dynamics. However, the reported splitting parameters (fast polarization orientations and splitting times) are frequently inconsistent among different studies, partially due to the different techniques used to estimate the splitting parameters. Here the study conduct research on methodology investigations for shear wave splitting analysis, which are composed of two sub-topics, i.e., a systematic comparison of the transverse minimization (TM) and the splitting intensity (SI) techniques and applicability of the multiple-event stacking technique (MES). Numerical experiments are conducted using both synthetic and …
Models Of Leader Elections And Their Applications, Stephen Curtis Jackson
Models Of Leader Elections And Their Applications, Stephen Curtis Jackson
Doctoral Dissertations
"New research about cyber-physical systems is rapidly changing the way we think about critical infrastructures such as the power grid. Changing requirements for the generation, storage, and availability of power are all driving the development of the smart-grid. Many smart-grid projects disperse power generation across a wide area and control devices with a distributed system. However, in a distributed system, the state of processes is hard to determine due to isolation of memory. By using information flow security models, we reason about a process's beliefs of the system state in a distributed system. Information flow analysis aided in the creation …
Liposomal Delivery Of Pde5 Inhibitors And Ut-15c To Human Erythrocytes, Elizabeth Anne Bowles
Liposomal Delivery Of Pde5 Inhibitors And Ut-15c To Human Erythrocytes, Elizabeth Anne Bowles
Doctoral Dissertations
"Previous studies have shown that the controlled release of adenosine triphosphate (ATP) from human erythrocytes is an important mechanism for the regulation of vascular caliber. However, erythrocytes from patients with pulmonary arterial hypertension (PAH) fail to release ATP in response to the physiological stimuli of exposure to low oxygen tension or mechanical deformation of a magnitude these cells would encounter in the pulmonary circulation. This defect could be a significant contributor to the increased pulmonary vascular resistance (PVR) that is the cause of the pathological increase in vascular pressures in humans with PAH.
One important approach to the treatment of …
Spectroscopic And Spectro-Astrometric Analysis Of T Tauri Stars, Logan Ryan Brown
Spectroscopic And Spectro-Astrometric Analysis Of T Tauri Stars, Logan Ryan Brown
Doctoral Dissertations
"To understand our own solar origins, we must investigate the composition of the protoplanetary disk from which the solar system formed. To infer this, we study analogs to the early solar system called T Tauri stars. These objects are low-mass, pre-main sequence stars surrounded by circumstellar disks of material from which planets are believed to form. We present high-resolution, near-infrared spectroscopic data for the T Tauri stars DR Tau and AA Tau using NIRSPEC at the Keck II telescope. For DR Tau, a spectro-astrometric analysis was performed, obtaining sub-seeing spatial information on water emission. Alongside a disk model, we constrained …
Unconventional Phase Transitions In Random Systems, Hatem Nuri Barghathi
Unconventional Phase Transitions In Random Systems, Hatem Nuri Barghathi
Doctoral Dissertations
"In this thesis we study the effects of different types of disorder and quasiperiodic modulations on quantum, classical and nonequilibrium phase transitions. After a brief introduction, we examine the effect of topological disorder on phase transitions and explain a host of violations of the Harris and Imry-Ma criteria that predict the fate of disordered phase transitions. We identify a class of random and quasiperiodic lattices in which a topological constraint introduces strong anticorrelations leading to modifications of the Harris and Imry-Ma criteria for such lattices. We investigate whether or not the Imry-Ma criterion, that predicts that random field disorder destroys …
Polyacrylamide And Its Derivatives For Oil Recovery, Zun Chen
Polyacrylamide And Its Derivatives For Oil Recovery, Zun Chen
Doctoral Dissertations
"Polyacrylamide is an umbrella term used to describe the homo-polymer of acrylamide and the copolymer of acrylamide with a small amount of other monomers. Owing to their superior property on increasing viscosity and gelling ability in the presence of crosslinkers, polyacrylamides has become the primarily selection for polymer flooding and gel treatment agent in enhanced oil recovery. Recent developments, performance, applications and limitations of polyacrylamides and its derivatives, including copolymers and hydrogels for enhancing oil recovery are reviewed.
A water-free suspension system was developed to synthesize PAMs and PAMs-microgel. Products are dry particle powder and ready to disperse in water. …
Seismic Anisotropy And Mantle Dynamics Beneath The Central And Western United States, Bin Yang
Seismic Anisotropy And Mantle Dynamics Beneath The Central And Western United States, Bin Yang
Doctoral Dissertations
"Various tectonic features and the recent availability of high-quality broadband seismic data from the USArray and other seismic stations in the central and western United States (CWUS) provide a distinct opportunity to test different anisotropy-forming mechanisms. For the first part of the study, a total of 4138 pairs of well-defined shear wave splitting (SWS) parameters observed at 445 stations on the northern Great Plains show systematic spatial variations of anisotropic characteristics. Azimuthally invariant fast orientations subparallel to the absolute plate motion (APM) direction are observed at most of the stations on the Superior Craton and the southern Yavapai province, indicating …
Properties Of Amorphous Transparent Conducting And Semiconducting Oxides From First Principles, Rabi Khanal
Properties Of Amorphous Transparent Conducting And Semiconducting Oxides From First Principles, Rabi Khanal
Doctoral Dissertations
"Amorphous transparent conducting and semiconducting oxides possess properties superior or comparable to their crystalline counterparts. The structure-property relationship in amorphous oxides is not nearly as well understood as in the case of the crystalline transparent conducting oxides. We have employedab initio molecular dynamics and a liquid quench approach to simulate amorphous oxide structures and performed density functional-based calculations to study the electronic properties of several amorphous conducting and semiconducting oxides with various cation compositions.
The effect of amorphization in oxides was investigated by taking indium oxide as a progenitor of the system. From the thorough study it was confirmed …
New Polyanion-Based Cathode Materials For Alkali-Ion Batteries, Hooman Yaghoobnejad Asl
New Polyanion-Based Cathode Materials For Alkali-Ion Batteries, Hooman Yaghoobnejad Asl
Doctoral Dissertations
"A number of new materials have been discovered through exploratory synthesis with the aim to be studied as the positive electrode (cathode) in Li-ion and Na-ion batteries. The focus has been set on the ease of synthesis, cost and availability of active ingredients in the battery, and decent cycle-life performance through a combination of iron and several polyanionic ligands. An emphasis has been placed also on phosphite (HPO32-) as a polyanionic ligand, mainly due to the fact that it has not been studied seriously before as a polyanion for cathode materials. The concept of mixed polyanions, for …
Identifying Shallow Subsurface Stratigraphy And Voids Using Dispersive Characteristics Of Electromagnetic And Surface Waves, Payman Hajiani
Identifying Shallow Subsurface Stratigraphy And Voids Using Dispersive Characteristics Of Electromagnetic And Surface Waves, Payman Hajiani
Doctoral Dissertations
"This dissertation presents the results of three manuscripts on spectral analysis of electromagnetic and seismic surface waves to detect subsurface stratigraphy and voids. In the first manuscript, a new technique was developed by utilizing spectral analysis of surface waves to detect subsurface openings. This technique applied the concept of group delay to evaluate the effects of subsurface voids on the phase shift domain. Seismic data sets were acquired at different sites where the shape, size, and depth of the void varied. In all surveys, the time delay technique precisely identified the locations of the subsurface openings. The second manuscript presents …
Seismic Reflection, Well Log, And Gravity Analysis Of The Thrace Basin, Northwestern Turkey, Murat Kuvanc
Seismic Reflection, Well Log, And Gravity Analysis Of The Thrace Basin, Northwestern Turkey, Murat Kuvanc
Graduate Theses/Dissertations
The Thrace basin is located between the Paleogene the Istranca and Rhdope massifs in the northwestern part of Turkey. Sediments in the Thrace basin accumulated during the early Eocene to the late Miocene, and the basin includes normal and strike-slip faults that were mainly formed in the Miocene. The hydrocarbon potential of the Thrace basin has been investigated by analyzing seismic reflection, well log, and gravity data since the 1930s; the basin has a huge gas reservoir potential and contains the first gas production field in Turkey. To determine the geologic and geophysics features of a portion of the basin …
The Effects Of Blended Learning On Critical Thinking In A High School Earth Science Class, Renee Nicole Borglum
The Effects Of Blended Learning On Critical Thinking In A High School Earth Science Class, Renee Nicole Borglum
Dissertations and Theses @ UNI
This study analyzed the effects of differing levels of technology use in a high school Earth Science class on student performance on the Classroom Test of Scientific Reasoning (CTSR). Blended learning manipulates the combination of hands-on activities, classroom discussions, online discussions, interactive simulations and a variety of assessments that engage, instruct and assess student learning. Critical thinking is the set of skills and dispositions that foster problem solving, reasoning ability and selfregulation. The increasing use of technology in the classroom and fluctuation of content standards prompted this research. The results have implications for the classroom teacher of a wide range …
พอลิเมอร์ผสมของพอลิแล็กทิกแอซิดและเซลลูโลสแอซีเทตจากผักตบชวา, กรองกาญจน์ อมตาริยกุล
พอลิเมอร์ผสมของพอลิแล็กทิกแอซิดและเซลลูโลสแอซีเทตจากผักตบชวา, กรองกาญจน์ อมตาริยกุล
Chulalongkorn University Theses and Dissertations (Chula ETD)
เซลลูโลสอะซิเทดถูกสังเคราะห์โดยใช้เซลลูโลสผักตบชวาเป็นวัตถุดิบ ซึ่งส่วนที่ใช้จะเป็นส่วนของก้านขั้นตอนแรกนำเส้นใยผักตบชวาไปกำจัดสิ่งสกปรกก้านแห้งและตามมาด้วยการฟอกสีไฮโปคลอไรเซลลูโลสให้เป็นสีขาวสีขาวแล้ว หลังจากนั้นเตรียมเซลลูโลสเจลโดยใช้โซเดียมไฮดรอกไซด์ / ยูเรีย / น้ำ (7:12:81 โดยน้ำหนัก) จากนั้นนำมาผสม ปริมาณของไวนิลอะซิเตทโดยมีอัตราส่วนต่างกันคือ 3.0, 5.0, 7.0, 9.0, 11.0% โดยน้ำหนักของเซลลูโลส หลังจากนั้นส่วนผสมที่ถูกเก็บไว้ในตู้แช่แข็งเป็นเวลา 6 ชั่วโมงเพื่อให้เกิดปฏิกิริยาแอซิทิเลชันสมบูรณ์ เซลลูโลสอะซิเตทมีความสามารถในการปรับปรุงคุณสมบัติของพอลิแล็กทิกแอซิดโดยการเปลี่ยนเป็นผลึกที่สมบัติเชิงกลและสมบัติทางความร้อน จุดมุ่งหมายของการศึกษาครั้งนี้คือการสังเคราะห์ เซลลูโลสแอซิเทดจากผักตบชวาโดยใช้พอลิไวนิลอะซิเตตสารช่วยเพิมความเข้ากันได้ (Compatiblizer) จากนั้นพอลิแล็กทิกแอซิด / เซลลูโลสอะซิเทดนำไปผสมกันโดยใช้เครื่องอัดรีดเกลียว หลังจากนั้นนำไปวิเคราะผล ดังนี้ วิเคราะห์หมู่ฟังก์ชันโดยใช้ฟูเรียทรานสฟอร์มสเปกโตรสโคปี (FTIR) วิเคราห์ความเป็นผลึกด้วยเครื่องเอกซ์เรย์ดิฟแฟรกโทรมิเตอร์(XRD) และ วิเคราะห์สัณฐานวิทยาด้วยกล้องจุลทรรศน์อิเล็กตรอนแบบส่องกราด(SEM) พบว่าพอลิแล็กทิกแอซิด / เซลลูโลสอะซิเตทโดยความเข้มข้นที่เหมาะสมที่สุดของเซลลูโลสอะซิเตทสำหรับการผสมกับพอลิแล็กทิกแอซิด เป็น 11% โดยน้ำหนักและสัดส่วนของพอลิแล็กทิกแอซิด/เซลลูโลสแอซิเทดคือ 95 : 5
Higher Order Z-Ideals In Commutative Rings, Themba Dube, Oghenetega Ighedo
Higher Order Z-Ideals In Commutative Rings, Themba Dube, Oghenetega Ighedo
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study ideals that resemble z-ideals in commutative rings with identity. For each positive integer n, we say an ideal of a commutative ring A is a zn-ideal in case it has the property that if a and b belong to the same maximal ideals of A, and an ϵ I , then bn is also in I. The set of all zn-ideals of A is denoted by A --> ʒn (A). This gives an ascending chain ʒ(A) < ʒ2(A) < ʒ3(A) <… of collections of ideals, starting with the collection of z-ideals. ……>
No Return To Classical Reality, David Jennings, Matthew S. Leifer
No Return To Classical Reality, David Jennings, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
At a fundamental level, the classical picture of the world is dead, and has been dead now for almost a century. Pinning down exactly which quantum phenomena are responsible for this has proved to be a tricky and controversial question, but a lot of progress has been made in the past few decades. We now have a range of precise statements showing that whatever the ultimate laws of Nature are, they cannot be classical. In this article, we review results on the fundamental phenomena of quantum theory that cannot be understood in classical terms. We proceed by rst granting quite …
Measurement Of The Yb I 1S0-1P1 Transition Frequency At 399 Nm Using An Optical Frequency Comb, Michaela Kleinert, M. E. Gold Dahl, Scott D. Bergeson
Measurement Of The Yb I 1S0-1P1 Transition Frequency At 399 Nm Using An Optical Frequency Comb, Michaela Kleinert, M. E. Gold Dahl, Scott D. Bergeson
Faculty Publications
We determine the frequency of the Yb I 1S0-1P1 transition at 399 nm using an optical frequency comb. Although this transition was measured previously using an optical transfer cavity [D. Das et al., Phys, Rev. A 72, 032506 (2005)], recent work has uncovered significant errors in that method. We compare our result of 751 526 533.49 ± 0.33 MHz for the 174Yb isotope with those from the literature and discuss observed differences. We verify the correctness of our method by measuring the frequencies of well-known transitions in Rb and Cs, and by …
Enabling Method To Design Versatile Biomaterial Systems From Colloidal Building Blocks, Shalini Saxena, L. Andrew Lyon
Enabling Method To Design Versatile Biomaterial Systems From Colloidal Building Blocks, Shalini Saxena, L. Andrew Lyon
Biology, Chemistry, and Environmental Sciences Faculty Articles and Research
Development of materials with fine spatial control over topographical, mechanical, or chemical features has been investigated for a variety of applications. Here we present a method to fabricate an array of polyelectrolyte constructs including two-dimensionally and three-dimensionally patterned assemblies using both compressible and incompressible colloidal building blocks. This method eliminates prior constraints associated with specific chemistries, and can be used to develop modular, multi-component, patterned assemblies. In particular, development of constructs were investigated using microgels, which are colloidally stable hydrogel microparticles, polystyrene (PS) beads, and PS-microgel core-shell building blocks in conjunction with the polycation poly(ethyleneimine) (PEI). The topography, mechanical properties, …
Success Stories And Emerging Themes In Conservation Physiology, Christine L. Madliger, Steven J. Cooke, Erica J. Crespi, Jennifer L. Funk, Kevin R. Hultine, Kathleen E. Hunt, Jason R. Rohr, Brent J. Sinclair, Cory D. Suski, Craig K. R. Willis, Oliver P. Love
Success Stories And Emerging Themes In Conservation Physiology, Christine L. Madliger, Steven J. Cooke, Erica J. Crespi, Jennifer L. Funk, Kevin R. Hultine, Kathleen E. Hunt, Jason R. Rohr, Brent J. Sinclair, Cory D. Suski, Craig K. R. Willis, Oliver P. Love
Biology, Chemistry, and Environmental Sciences Faculty Articles and Research
The potential benefits of physiology for conservation are well established and include greater specificity of management techniques, determination of cause–effect relationships, increased sensitivity of health and disturbance monitoring and greater capacity for predicting future change. While descriptions of the specific avenues in which conservation and physiology can be integrated are readily available and important to the continuing expansion of the discipline of ‘conservation physiology’, to date there has been no assessment of how the field has specifically contributed to conservation success. However, the goal of conservation physiology is to foster conservation solutions and it is therefore important to assess whether …
Growth Conditions For Uniqueness Of Smooth Positive Solutions To An Elliptic Model, Joon Hyuk Kang
Growth Conditions For Uniqueness Of Smooth Positive Solutions To An Elliptic Model, Joon Hyuk Kang
Faculty Publications
The uniqueness of positive solution to the elliptic model
∆u + u[a + g(u, v)] = 0 in Ω, ∆v + v[a + h(u, v)] = 0 in Ω, u = v = 0 on ∂Ω,
were investigated.
Accommodating Retrocausality With Free Will, Yakir Aharonov, Eliahu Cohen, Tomer Shushi
Accommodating Retrocausality With Free Will, Yakir Aharonov, Eliahu Cohen, Tomer Shushi
Mathematics, Physics, and Computer Science Faculty Articles and Research
Retrocausal models of quantum mechanics add further weight to the conflict between causality and the possible existence of free will. We analyze a simple closed causal loop ensuing from the interaction between two systems with opposing thermodynamic time arrows, such that each system can forecast future events for the other. The loop is avoided by the fact that the choice to abort an event thus forecasted leads to the destruction of the forecaster's past. Physical law therefore enables prophecy of future events only as long as this prophecy is not revealed to a free agent who can otherwise render it …
Regional Variations Of Optimal Sowing Dates Of Maize For The Southwestern U.S., Boksoon Myoung, Seung Hee Kim, Jinwon Kim, Menas Kafatos
Regional Variations Of Optimal Sowing Dates Of Maize For The Southwestern U.S., Boksoon Myoung, Seung Hee Kim, Jinwon Kim, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
Sowing date (SD) is sensitive to regional climate characteristics; thus, it is critical to systematically examine the effects of SD on crop yields for various temperature regimes. We performed a sensitivity study of SD for maize in the southwestern U.S. using the regionally extended version of the Agricultural Production Systems sIMulator (APSIM) model. The model was run utilizing North American Regional Reanalysis at a 32 km resolution from 1991 to 2011, with an irrigation threshold at 95% of the soil water-holding capacity. Two types of SD optimizations maximizing yield potential (Yp), varying spatially or interannually, revealed that the optimal SD …
Sensitivity Of Maize Yield Potential To Regional Climate In The Southwestern U.S., Seung Hee Kim, Boksoon Myoung, David Stack, Jinwon Kim, Menas Kafatos
Sensitivity Of Maize Yield Potential To Regional Climate In The Southwestern U.S., Seung Hee Kim, Boksoon Myoung, David Stack, Jinwon Kim, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
The sensitivity of maize yields to the regional climate in the Southwestern U.S. (SWUS) has been investigated by using the Agricultural Production Systems sIMulator (APSIM) model in conjunction with meteorological forcings [daily maximum and minimum temperature (Tmax and Tmin), precipitation, and radiation] from the North American Regional Reanalysis (NARR) dataset. Sensitivity experiments showed that potential crop production responded nonlinearly to variations in Tmax, Tmin, and downwelling solar radiation at the surface. Mean annual yield potential (Yp) was changed by -3.0 and 1.79 Mg ha-1 for the +1 and -1 standard deviations (σ) of Tmax variation for entire the SWUS. The …
The Spectral Theorem For Quaternionic Unbounded Normal Operators Based On The S-Spectrum, Daniel Alpay, Fabrizio Colombo, David P. Kimsey
The Spectral Theorem For Quaternionic Unbounded Normal Operators Based On The S-Spectrum, Daniel Alpay, Fabrizio Colombo, David P. Kimsey
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The fact that the correct notion of …
Characterizations Of Rectangular (Para)-Unitary Rational Functions, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
Characterizations Of Rectangular (Para)-Unitary Rational Functions, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
Mathematics, Physics, and Computer Science Faculty Articles and Research
We here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle:
(i) through the realization matrix of Schur stable systems,
(ii) the Blaschke-Potapov product, which is then employed to introduce an easy-to-use description of all these functions with dimensions and McMillan degree as parameters,
(iii) through the (not necessarily reducible) Matrix Fraction Description (MFD).
In cases (ii) and (iii) the poles of the rational functions involved may be anywhere in the complex plane, but the unit circle (including both zero and infinity). A special attention is devoted to exploring the gap between the …
The H∞ Functional Calculus Based On The S-Spectrum For Quaternionic Operators And For N-Tuples Of Noncommuting Operators, Daniel Alpay, Fabrizio Colombo, Tao Qian, Irene Sabadini, Tao Qian
The H∞ Functional Calculus Based On The S-Spectrum For Quaternionic Operators And For N-Tuples Of Noncommuting Operators, Daniel Alpay, Fabrizio Colombo, Tao Qian, Irene Sabadini, Tao Qian
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we extend the H∞ functional calculus to quaternionic operators and to n-tuples of noncommuting operators using the theory of slice hyperholomorphic functions and the associated functional calculus, called S-functional calculus. The S-functional calculus has two versions one for quaternionic-valued functions and one for Clifford algebra-valued functions and can be considered the Riesz-Dunford functional calculus based on slice hyperholomorphicity because it shares with it the most important properties.
The S-functional calculus is based on the notion of S-spectrum which, in the case of quaternionic normal operators on a Hilbert space, is also the notion of spectrum that appears …