Physical Sciences and Mathematics Commons^™

Structured Invariant Subspace And Decomposition Of Systems With Time Delays And Uncertainties, Huan Phan-Van, Keqin Gu

SIUE Faculty Research, Scholarship, and Creative Activity

This article discusses invariant subspaces of a matrix with a given partition structure. The existence of a nontrivial structured invariant subspace is equivalent to the possibility of decomposing the associated system with multiple feedback blocks such that the feedback operators are subject to a given constraint. The formulation is especially useful in the stability analysis of time-delay systems using the Lyapunov-Krasovskii functional approach where computational efficiency is essential in order to achieve accuracy for large scale systems. The set of all structured invariant subspaces are obtained (thus all possible decompositions are obtained as a result) for the coupled differential-difference equations …

First Review Of Equilibrium Landscape Of Ingress/Egress Channels And Gating Residues Of The Cytochrome P450 3a4, Edward Ackad Ph.D, Maria Kontoyianni

SIUE Faculty Research, Scholarship, and Creative Activity

The review document and changes made to "Equilibrium Landscape of Ingress/Egress Channels and Gating Residues of the Cytochrome P450 3A4".

Dataset For Characterization Of ‘Cool’ And ‘Warm’ White Leds, Edward Navarre

SIUE Faculty Research, Scholarship, and Creative Activity

The emission properties of “cool” and “warm” white LEDs were studied. The suitability of pulse-width modulation as a method to control LED brightness was examined. Both types of LED demonstrated emission standard deviation minima at a PWM frequency greater than 2000 Hz. The functional wavelength ranges of the LEDs were approximated using the linearity of brightness as a function of pulse-width modulation duty-cycle and the root mean squared deviation from mean for absorbance measurements. Both LED types demonstrated good stability in absorbance measurements over long operation times. The “warm” LED demonstrated a broader range of wavelengths useful for spectrophotometry. This …

A Geometric Description Of The Set Of Stabilizing Pid Controllers, Keqin Gu, Qian Ma, Huiqing Zhou, Mahzoon Salma, Xingzi Yang

SIUE Faculty Research, Scholarship, and Creative Activity

This article developed a new method to described the set of stabilizing PID control. The method is based on D-parameterization with natural description of the set. It was found that the stability crossing surface is a ruled surface that is completely determined by a curve known as discriminant. The discriminant is divided into sectors at the cusps. Corresponding to the sectors, the stability crossing surface is divided into positive and negative patches. A systematic study is conducted to identify the regions with a fixed number of right half-plane characteristic roots. The crossing directions of characteristic roots for positive patches and …

Extensible Interface For A Compact Spectrophotometer For Teaching Molecular Absorption In The Undergraduate Laboratory, Edward Navarre

SIUE Faculty Research, Scholarship, and Creative Activity

A simple computer interface for controlling a compact spectrograph for use as a spectrophotometer in an undergraduate teaching laboratory was developed. The project was implemented on a Raspberry Pi computer which permits the integration of a light source into the software. The interface was written in Python to facilitate modification by the user and because of its compatibility with several computing platforms. An implementation of the project in Linux on a Raspberry Pi computer is described.

Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the …

Markov Chains And Generalized Wavelet Multiresolutions, Myung-Sin Song, Palle Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We develop some new results for a general class of transfer operators, as they are used in a construction of multi-resolutions. We then proceed to give explicit and concrete applications. We further discuss the need for such a constructive harmonic analysis/dynamical systems approach to fractals.

Removal Of Acid Yellow 25 From Aqueous Solution By Chitin Prepared From Waste Snow Crab Legs, Chin-Chuan Wei, Inoka K. Pathiraja, Emily Fabry, Kyle Schafer, Nick Schimp, Tuo-Ping Hu, Lawrence P. Norcio

SIUE Faculty Research, Scholarship, and Creative Activity

Acid Yellow 25 (AY25) is used in the textile industry for dyeing of natural and synthetic fibers, and is also used as a coloring agent in paints, inks, plastics, and leathers. Effluents from such industries are major sources of water pollution. Hence, it is important to find simple, efficient, and inexpensive ways to remove these dyes from wastewater. Here, we determined the suitability of chitin extracted from waste crab legs as an adsorbent for removing AY25 dye. The adsorption kinetics was modeled using pseudo-first order, pseudo-second order, and intraparticle diffusion equations to determine the rate controlling step. Results showed that …

Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper studies the migration of double imaginary roots of the systems’ characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right halfplane, and the other moves to the left half-plane. When the parameters move into the …

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence …

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters τi, i = 1, 2, . . . , K. The characteristic quasipolynomial of such an equation is a multilinear function of e−τis. It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delay-per-scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between …

Electrochemical Investigation Of The Kinetics Of Chloride Substitution Upon Reduction Of [Ru(Porphyrin)(No)Cl] Complexes In Thf., Jeremy R. Zink, E G. Abucayon, Anthony R. Ramuglia, Arghavan Fadamin, James E. Eilers, George B. Richter-Addo, Michael J. Shaw

SIUE Faculty Research, Scholarship, and Creative Activity

The electrochemistry of several ruthenium porphyrin nitrosyl chloride complexes [Ru(por)(NO)Cl] have been examined in tetrahydrofuran. The complexes undergo 1-electron irreversible reductions which result in the diffusion-limited substitutions of the chloride ligands for THF. This chloride metathesis is reversible in the presence of added NBu₄Cl, and equilibrium constants and rate constants for chloride loss have been estimated. These parameters correlate with the NO stretching frequencies of the parent complexes, with more electron-donating porphyrin ligands favouring chloride loss from the reduced complexes. The [Ru(por)(NO)(THF)] products of the reductions can be detected by IR, EPR and visible spectroscopies. These species undergo …

Infinite-Dimensional Measure Spaces And Frame Analysis, Palle Jorgensen, Myung-Sin Song

SIUE Faculty Research, Scholarship, and Creative Activity

We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs. infinite dimensions. For the case of infinite-dimensional Hilbert space ℋ, we study three cases of measures. We first show that, for ℋ infinite dimensional, one must resort to infinite dimensional measure spaces which properly contain ℋ. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.

Kadison's Pythagorean Theorem And Essential Codimension, Jireh Loreaux, Victor Kaftal

SIUE Faculty Research, Scholarship, and Creative Activity

Kadison’s Pythagorean theorem (Proc Natl Acad Sci USA, 99(7):4178–4184, 2002; Proc Natl Acad Sci USA 99(8):5217–5222, 2002) provides a characterization of the diagonals of projections with a subtle integrality condition. Arveson (Proc Natl Acad Sci USA 104(4):1152–1158, 2007), Kaftal, Ng, Zhang (J Funct Anal 257(8):2497–2529, 2009), and Argerami (Integral Equ Oper Theory 82(1):33–49, 2015) all provide different proofs of that integrality condition. In this paper we interpret the integrality condition in terms of the essential codimension of a pair of projections introduced by Brown et al. (Proceedings of a conference on operator theory, Lecture notes …

Synthesis, Structural Characterization And Catalytic Activity Of Indenyl Complexes Of Ruthenium Bearing Fluorinated Phosphine Ligands, Matthew J. Stark, Michael J. Shaw, Arghavan Fadamin, Nigam P. Rath, Eike B. Bauer

SIUE Faculty Research, Scholarship, and Creative Activity

The synthesis, characterization and catalytic activity of new ruthenium complexes of fluorinated triarylphosphines is described. The new ruthenium complexes [RuCl(ind)(PPh₃){P(p-C₆H₄CF₃)₃}] and [RuCl(ind)(PPh₃){P(3,5-C₆H₃(CF₃)₂)₃}] were synthesized in 57% and 24% isolated yield, respectively, by thermal ligand exchange of [RuCl(ind)(PPh₃)₂], where ind = indenyl ligand η⁵-C₉H₇⁻. The electronic and steric properties of the new complexes were studied through analysis of the X-ray structures and through cyclic voltammetry. The …

Over Or Under: Hydride Attack At The Metal Versus The Coordinated Nitrosyl Ligand In Ferric Nitrosyl Porphyrins., E G. Abucayon, R L. Khade, D R. Powell, Michael J. Shaw, Y Yang, G B. Richter-Addo

SIUE Faculty Research, Scholarship, and Creative Activity

Hydride attack at a ferric heme–NO to give an Fe–HNO intermediate is a key step in the global N--‐cycle. We demonstrate differential reactivity when six--‐ and five--‐coordinate ferric heme--‐NO models react with hydride. Although Fe–HNO formation is thermodynamically favored from this reaction, Fe–H formation is kinetically favored for the 5C case.

Decline In Methylmercury In Museum-Preserved Bivalves From San Francisco Bay, California, Allison C. Luengen, Heather M. Foslund, Ben K. Greenfield

SIUE Faculty Research, Scholarship, and Creative Activity

There are ongoing efforts to manage mercury and nutrient pollution in San Francisco Bay (California, USA), but historical data on biological responses are limited. We used bivalves preserved in formalin or ethanol from museum collections to investigate long-term trends in methylmercury (MeHg) concentrations and carbon and ni- trogen isotopic signatures. In the southern reach of the estuary, South Bay, MeHg in the Asian date mussel (Musculista senhousia) significantly declined over the study duration (1970 to 2012). Mean MeHg concentrations were highest (218 ng/g dry weight, dw) in 1975 and declined 3.8-fold (to 57 ng/g dw) by 2012. This …

Delay-Independent Stability Analysis Of Linear Time-Delay Systems Based On Frequency, Xianwei Li, Huijun Gao, Keqin Gu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper studies strong delay-independent stability of linear time-invariant systems. It is known that delay-independent stability of time-delay systems is equivalent to some frequency-dependent linear matrix inequalities. To reduce or eliminate conservatism of stability criteria, the frequency domain is discretized into several sub-intervals, and piecewise constant Lyapunov matrices are employed to analyze the frequency-dependent stability condition. Applying the generalized Kalman–Yakubovich–Popov lemma, new necessary and sufficient criteria are then obtained for strong delay-independent stability of systems with a single delay. The effectiveness of the proposed method is illustrated by a numerical example.

Synthesis, Structural Characterization And Catalytic Activity Of Indenyl Tris-N-Pyrrolyl Phosphine Complexes Of Ruthenium, Matthew J. Stark, Michael J. Shaw, Nigam P. Rath, Eike B. Bauer

SIUE Faculty Research, Scholarship, and Creative Activity

The synthesis, characterization and catalytic activity of new ruthenium complexes of the tris-N-pyrrolyl phosphine ligand P(pyr)3 is described. The new ruthenium complexes [RuCl(ind)(PPh3){P(pyr)3}] and [RuCl(ind){P(pyr)3}2] (ind = indenyl ligand η5-C9H7−) were synthesized in 73% and 63% isolated yield, respectively, by thermal ligand exchange of [RuCl(ind)(PPh3)2] with P(pyr)3. The electronic and steric properties of the new complexes were studied through analysis of the X-Ray structures and through cyclic voltammetry. The new complexes [RuCl(ind)(PPh3){P(pyr)3}] and [RuCl(ind){P(pyr)3}2] and the known complex [RuCl(ind)(PPh3)2}] differed only slightly in their steric properties, as seen from the comparable bond lengths and angles around the ruthenium …

Preparation, Characterization, Electrochemistry, And Infrared Spectroelectrochemistry Of Ruthenium Nitrosyl Porphyrins Containing Η1-O Bonded Axial Carboxylates, Dennis Awasabisah, Nan Xu, Krishna P. Sharmah-Gautam, Douglas R. Powell, Michael J. Shaw, George B. Richter-Addo

SIUE Faculty Research, Scholarship, and Creative Activity

The synthesis, characterization and redox behavior of eight low-spin nitrosyl carboxylate compounds (por)Ru(NO)(η¹-OC(=O)R) (por = T(p-OMe)PP: R = Me (1), i-Pr (2), t-Bu (3), p-C₆H₄NO₂ (4), Fc (5), CF₃ (8); por = TTP: R = Fc (6)) and (T(p-OMe)PP)Ru(NO)(OC₆HF₄) (7) are reported. The compounds are moderately stable in air as solids. Their IR (KBr) spectral data show ʋNO's in the 1839-1861 range cm^-1. The X-ray crystal structures of compounds 1 …

Rapid Access To Conformationally-Constrained Oxatricycles Via Ugi-Smiles Couplings, Bree Richey, Katelynn M. Mason, Michael S. Meyers, Sarah Luesse

SIUE Faculty Research, Scholarship, and Creative Activity

Use of allylamine and substituted 2-furaldehydes as components in Ugi-Smiles couplings of 2-nitrophenol provide ready access to N-aryl epoxyisoindolines. These adducts form via a dual event involving the Ugi-Smiles multicomponent reaction and an intramolecular Diels-Alder cycloaddition with the furan ring.

Zeon Roots, Lisa M. Dollar, G. Stacey Staples

SIUE Faculty Research, Scholarship, and Creative Activity

Zeon algebras can be thought of as commutative analogues of fermion algebras, and they can be constructed as subalgebras within Clifford algebras of appropriate signature. Their inherent combinatorial properties make them useful for applications in graph enumeration problems and evaluating functions defined on partitions. In this paper, kth roots of invertible zeon elements are considered. More specifically, conditions for existence of roots are established, numbers of existing roots are determined, and computational methods for constructing roots are developed. Recursive and closed formulas are presented, and specific low-dimensional examples are computed with Mathematica. Interestingly, Stirling numbers of the first kind appear …

Zeons, Orthozeons, And Graph Colorings, G. Stacey Staples, Tiffany Stellhorn

SIUE Faculty Research, Scholarship, and Creative Activity

No abstract provided.

Talking Through The Problems: A Study Of Discourse In Peer-Led Small Groups, Michelle D. Repice, R. Keith Sawyer, Mark C. Hogrebe, Patrick L. Brown, Sarah Luesse, Daniel J. Gealy, Regina F. Frey

SIUE Faculty Research, Scholarship, and Creative Activity

Increasingly, studies are investigating the factors that influence student discourse in science courses, and specifically the mechanisms and discourse processes within small groups, to better understand the learning that takes place as students work together. This paper contributes to a growing body of research by analyzing how students engage in conversation and work together to solve problems in a peer-led small-group setting. This qualitative study evaluates video of Peer-Led Team Learning (PLTL) sessions in general chemistry, with attention to both the activity structures and the function of discourse as students undertook different types of problems across one semester. Our findings …

Climate Change And Interpersonal Violence: A "Global" Estimate And Regional Inequities, Dennis Mares, Kenneth W. Moffett

SIUE Faculty Research, Scholarship, and Creative Activity

This study estimates the predicted impact of climate change on levels of violence in a sample of 57 countries. We sample western and non-western countries and perform a multilevel ARFIMA regression to examine if warmer temperatures are associated with higher levels of homicide. Our results indicate that each degree Celsius increase in annual temperatures is associated with a nearly 6% average increase in homicides. Regional variation in this predicted effect is detected, for example, with no apparent effects in former Soviet countries and far stronger effects found in Africa. This variation indicates that climate change may acutely increase violence in …

Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We give a number of explicit matrix-algorithms for analysis/synthesis

in multi-phase filtering; i.e., the operation on discrete-time signals which

allow a separation into frequency-band components, one for each of the

ranges of bands, say N , starting with low-pass, and then corresponding

filtering in the other band-ranges. If there are N bands, the individual

filters will be combined into a single matrix action; so a representation of

the combined operation on all N bands by an N x N matrix, where the

corresponding matrix-entries are periodic functions; or their extensions to

functions of a complex variable. Hence our setting entails …

Reproducing Kernel Hilbert Space Vs. Frame Estimates, Palle E. T. Jorgensen, Myung-Sin Song

SIUE Faculty Research, Scholarship, and Creative Activity

We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn Hinto a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω . We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. We further give an explicit formula for the kernel, and for the corresponding isometric isomorphism. Applications are given to Hilbert spaces associated to families of Gaussian processes.

The Exchanged Ef-Hands In Calmodulin And Troponin C Chimeras Impair The Ca2+-Induced Hydrophobicity And Alter The Interaction With Orai1: A Spectroscopic, Thermodynamic And Kinetic Study, Drake Jensen, Nicole Reynolds, Ya-Ping Yang, Shubha Shakya, Zhi-Qiang Wang, Dennis J. Stuehr, Chin-Chuan Wei

Chemistry Faculty Research, Scholarship, and Creative Activity

Background

Calmodulin (CaM) plays an important role in Ca²⁺-dependent signal transduction. Ca²⁺ binding to CaM triggers a conformational change, forming a hydrophobic patch that is important for target protein recognition. CaM regulates a Ca²⁺-dependent inactivation process in store-operated Ca²⁺entry, by interacting Orai1. To understand the relationship between Ca²⁺-induced hydrophobicity and CaM/Orai interaction, chimera proteins constructed by exchanging EF-hands of CaM with those of Troponin C (TnC) are used as an informative probe to better understand the functionality of each EF-hand.

Results

ANS was used to assess the context of the induced …

Kravchuk Polynomials And Induced/Reduced Operators On Clifford Algebras, G. Stacey Staples

SIUE Faculty Research, Scholarship, and Creative Activity

Kravchuk polynomials arise as orthogonal polynomials with respect to the binomial distribution and have numerous applications in harmonic analysis, statistics, coding theory, and quantum probability. The relationship between Kravchuk polynomials and Clifford algebras is multifaceted. In this paper, Kravchuk polynomials are discovered as traces of conjugation operators in Clifford algebras, and appear in Clifford Berezin integrals of Clifford polynomials. Regarding Kravchuk matrices as linear operators on a vector space V, the action induced on the Clifford algebra over V is equivalent to blade conjugation, i.e., reflections across sets of orthogonal hyperplanes. Such operators also have a natural interpretation in …

Operator Calculus Algorithms For Multi-Constrained Paths, Jamila Ben Slimane, Rene' Schott, Ye Qiong Song, G. Stacey Staples, Evangelia Tsiontsiou

SIUE Faculty Research, Scholarship, and Creative Activity

Classical approaches to multi-constrained routing problems generally require construction of trees and the use of heuristics to prevent combinatorial explosion. Introduced here is the notion of constrained path algebras and their application to multi-constrained path problems. The inherent combinatorial properties of these algebras make them useful for routing problems by implicitly pruning the underlying tree structures. Operator calculus (OC) methods are generalized to multiple non-additive constraints in order to develop algorithms for the multi constrained path problem and multi constrained optimization problem. Theoretical underpinnings are developed first, then algorithms are presented. These algorithms demonstrate the tremendous simplicity, flexibility and speed …