On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

∗ Partially supported by Grant MM-428/94 of MESC.

Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices

2000 Mathematics Subject Classification: 42C05.

The Direct and Inverse Spectral Problems for some Banded Matrices

2000 Mathematics Subject Classification: 15A29.

Microporous polycaprolactone matrices for drug delivery and tissue engineering:the release behaviour of bioactives having extremes of aqueous solubility

Microporous polycaprolactone (PCL) matrices loaded with hydrophobic steroidal drugs or a hydrophilic drug - pilocarpine hydrochloride - were produced by precipitation casting using solutions of PCL in acetone. The efficiency of steroid incorporation in the final matrix (progesterone (56 %) testosterone (46 %) dexamethasone (80 %)) depended on the nature of the drug initially co-dissolved in the PCL solution. Approximately 90 % w/w of the initial load of progesterone, 85 % testosterone and 50 % dexamethasone was released from the matrices in PBS at 37°C over 8 days. Pilocarpine hydrochloride (PH)-loaded PCL matrices, prepared by dispersion of powder in PCL solution, released 70-90 % of the PH content over 12 days in PBS. Application of the Higuchi model revealed that the kinetics of steroid and PH release were consistent with a Fickian diffusion mechanism with corresponding diffusion coefficients of 5.8 × 10-9 (progesterone), 3.9 × 10 -9 (testosterone), 7.1 × 10-10 (dexamethasone) and 22 × 10-8 cm2/s (pilocarpine hydrochloride). The formulation techniques described are expected to be useful for production of implantable, insertable and topical devices for sustained delivery of a range of bioactive molecules of interest in drug delivery and tissue engineering.

Pairwise comparison matrices and the error-free property of the decision maker

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal.

On Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices

The aim of the paper is to obtain some theoretical and numerical properties of Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices (PRM). In the case of 3 × 3 PRM, a differentiable one-to-one correspondence is given between Saaty’s inconsistency ratio and Koczkodaj’s inconsistency index based on the elements of PRM. In order to make a comparison of Saaty’s and Koczkodaj’s inconsistencies for 4 × 4 pairwise comparison matrices, the average value of the maximal eigenvalues of randomly generated n × n PRM is formulated, the elements aij (i < j) of which were randomly chosen from the ratio scale ... ... with equal probability 1/(2M − 1) and a ji is defined as 1/a ij . By statistical analysis, the empirical distributions of the maximal eigenvalues of the PRM depending on the dimension number are obtained. As the dimension number increases, the shape of distributions gets similar to that of the normal ones. Finally, the inconsistency of asymmetry is dealt with, showing a different type of inconsistency.

Incomplete pairwise comparison matrices and weighting methods

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the property linear order preservation if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.

Elemental analysis of biological matrices by laser ablation high resolution inductively coupled plasma mass spectrometry (LA-HR-ICP-MS) and high resolution inductively coupled plasma mass spectrometry (HR -ICP -MS)

The need for elemental analysis of biological matrices such as bone, teeth, and plant matter for sourcing purposes has emerged within the forensic and geochemical laboratories. Trace elemental analyses for the comparison of materials such as glass by inductively coupled plasma mass spectrometry (ICP-MS) and laser ablation ICP-MS has been shown to offer a high degree of discrimination between different manufacturing sources. Unit resolution ICP-MS instruments may suffer from some polyatomic interferences including 40Ar16O+, 40Ar 16O1H+, and 40Ca 16O+ that affect iron measurement at trace levels. Iron is an important element in the analysis of glass and also of interest for the analysis of several biological matrices. A comparison of the analytical performance of two different ICP-MS systems for iron analysis in glass for determining the method detection limits (MDLs), accuracy, and precision of the measurement is presented. Acid digestion and laser ablation methods are also compared. Iron polyatomic interferences were reduced or resolved by using dynamic reaction cell and high resolution ICP-MS. MDLs as low as 0.03 μg g-1 and 0.14 μg g-1 for laser ablation and solution based analyses respectively were achieved. The use of helium as a carrier gas demonstrated improvement in the detection limits of both iron isotopes (56Fe and 57Fe) in medium resolution for the HR-ICP-MS and with a dynamic reaction cell (DRC) coupled to a quadrupole ICP-MS system. ^ The development and application of robust analytical methods for the quantification of trace elements in biological matrices has lead to a better understanding of the potential utility of these measurements in forensic chemical analyses. Standard reference materials (SRMs) were used in the development of an analytical method using HR-ICP-MS and LA-HR-ICP-MS that was subsequently applied on the analysis of real samples. Bone, teeth and ashed marijuana samples were analyzed with the developed method. ^ Elemental analysis of bone samples from 12 different individuals provided discrimination between individuals, when femur and humerus bones were considered separately. Discrimination of 14 teeth samples based on elemental composition was achieved with the exception of one case where samples from the same individual were not associated with each other. The discrimination of 49 different ashed plant (cannabis) samples was achieved using the developed method. ^

Elemental Analysis of Biological Matrices by Laser Ablation High Resolution Inductively Coupled Plasma Mass Spectrometry (LA-HR-ICP-MS) and High Resolution Inductively Coupled Plasma Mass Spectrometry (HR-ICP-MS)

The need for elemental analysis of biological matrices such as bone, teeth, and plant matter for sourcing purposes has emerged within the forensic and geochemical laboratories. Trace elemental analyses for the comparison of aterials such as glass by inductively coupled plasma mass spectrometry (ICP-MS) and laser ablation ICP-MS has been shown to offer a high degree of discrimination between different manufacturing sources. Unit resolution ICP-MS instruments may suffer from some polyatomic interferences including 40Ar16O+, 40Ar16O1H+, and 40Ca16O+ that affect iron measurement at trace levels. Iron is an important element in the analysis of glass and also of interest for the analysis of several biological matrices. A comparison of the nalytical performance of two different ICP-MS systems for iron analysis in glass for determining the method detection limits (MDLs), accuracy, and precision of the measurement is presented. Acid digestion and laser ablation methods are also compared. Iron polyatomic interferences were reduced or resolved by using dynamic reaction cell and high resolution ICP-MS. MDLs as low as 0.03 ìg g-1 and 0.14 ìg g-1 for laser ablation and solution based analyses respectively were achieved. The use of helium as a carrier gas demonstrated improvement in the detection limits of both iron isotopes (56Fe and 57Fe) in medium resolution for the HR-ICP-MS and with a dynamic reaction cell (DRC) coupled to a quadrupole ICP-MS system. The development and application of robust analytical methods for the quantification of trace elements in biological matrices has lead to a better understanding of the potential utility of these measurements in forensic chemical analyses. Standard reference materials (SRMs) were used in the development of an analytical method using HR-ICP-MS and LA-HR-ICP-MS that was subsequently applied on the analysis of real samples. Bone, teeth and ashed marijuana samples were analyzed with the developed method. Elemental analysis of bone samples from 12 different individuals provided discrimination between individuals, when femur and humerus bones were considered separately. Discrimination of 14 teeth samples based on elemental composition was achieved with the exception of one case where samples from the same individual were not associated with each other. The discrimination of 49 different ashed plant (cannabis)samples was achieved using the developed method.

Superregular matrices and applications to convolutional codes

The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matrix is superregular if all of its minors that are not trivially zero are nonzero. Given a a×b, a ≥ b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients, has at least a−b + 1 nonzero entries. Secondly, we make use of this result to construct convolutional codes that attain the maximum possible distance for some fixed parameters of the code, namely, the rate and the Forney indices. These results answer some open questions on distances and constructions of convolutional codes posted in the literature.

The analysis and detection of new psychoactive substances in biological matrices

New psychoactive substances (NPSs) have appeared on the recreational drug market at an unprecedented rate in recent years. Many are not new drugs but failed products of the pharmaceutical industry. The speed and variety of drugs entering the market poses a new complex challenge for the forensic toxicology community. The detection of these substances in biological matrices can be difficult as the exact compounds of interest may not be known. Many NPS are sold under the same brand name and therefore users themselves may not know what substances they have ingested. The majority of analytical methods for the detection of NPSs tend to focus on a specific class of compounds rather than a wide variety. In response to this, a robust and sensitive method was developed for the analysis of various NPS by solid phase extraction (SPE) with gas chromatography mass spectrometry (GCMS). Sample preparation and derivatisation were optimised testing a range of SPE cartridges and derivatising agents, as well as derivatisation incubation time and temperature. The final gas chromatography mass spectrometry method was validated in accordance with SWGTOX 2013 guidelines over a wide concentration range for both blood and urine for 23 and 25 analytes respectively. This included the validation of 8 NBOMe compounds in blood and 10 NBOMe compounds in urine. This GC-MS method was then applied to 8 authentic samples with concentrations compared to those originally identified by NMS laboratories. The rapid influx of NPSs has resulted in the re-analysis of samples and thus, the stability of these substances is crucial information. The stability of mephedrone was investigated, examining the effect that storage temperatures and preservatives had on analyte stability daily for 1 week and then weekly for 10 weeks. Several laboratories identified NPSs use through the cross-reactivity of these substances with existing screening protocols such as ELISA. The application of Immunalysis ketamine, methamphetamine and amphetamine ELISA kits for the detection of NPS was evaluated. The aim of this work was to determine if any cross-reactivity from NPS substances was observed, and to determine whether these existing kits would identify NPS use within biological samples. The cross- reactivity of methoxetamine, 3-MeO-PCE and 3-MeO-PCP for different commercially point of care test (POCT) was also assessed for urine. One of the newest groups of compounds to appear on the NPS market is the NBOMe series. These drugs pose a serious threat to public health due to their high potency, with fatalities already reported in the literature. These compounds are falsely marketed as LSD which increases the chance of adverse effects due to the potency differences between these 2 substances. A liquid chromatography tandem mass spectrometry (LC-MS/MS) method was validated in accordance with SWGTOX 2013 guidelines for the detection for 25B, 25C and 25I-NBOMe in urine and hair. Long-Evans rats were administered 25B-, 25C- and 25I-NBOMe at doses ranging from 30-300 µg/kg over a period of 10 days. Tail flick tests were then carried out on the rats in order to determine whether any analgesic effects were observed as a result of dosing. Rats were also shaved prior to their first dose and reshaved after the 10-day period. Hair was separated by colour (black and white) and analysed using the validated LC-MS/MS method, assessing the impact hair colour has on the incorporation of these drugs. Urine was collected from the rats, analysed using the validated LC-MS/MS method and screened for potential metabolites using both LC-MS/MS and quadrupole time of flight (QToF) instrumentation.

A lower bound for the energy of symmetric matrices and graphs

The energy of a symmetric matrix is the sum of the absolute values of its eigenvalues. We introduce a lower bound for the energy of a symmetric partitioned matrix into blocks. This bound is related to the spectrum of its quotient matrix. Furthermore, we study necessary conditions for the equality. Applications to the energy of the generalized composition of a family of arbitrary graphs are obtained. A lower bound for the energy of a graph with a bridge is given. Some computational experiments are presented in order to show that, in some cases, the obtained lower bound is incomparable with the well known lower bound $2\sqrt{m}$, where $m$ is the number of edges of the graph.

Euclidean Distance Between Haar Orthogonal and Gaussian Matrices

In this work, we study a version of the general question of how well a Haar-distributed orthogonal matrix can be approximated by a random Gaussian matrix. Here, we consider a Gaussian random matrix (Formula presented.) of order n and apply to it the Gram–Schmidt orthonormalization procedure by columns to obtain a Haar-distributed orthogonal matrix (Formula presented.). If (Formula presented.) denotes the vector formed by the first m-coordinates of the ith row of (Formula presented.) and (Formula presented.), our main result shows that the Euclidean norm of (Formula presented.) converges exponentially fast to (Formula presented.), up to negligible terms. To show the extent of this result, we use it to study the convergence of the supremum norm (Formula presented.) and we find a coupling that improves by a factor (Formula presented.) the recently proved best known upper bound on (Formula presented.). Our main result also has applications in Quantum Information Theory.

IMPROVED SAMPLE INTRODUCTION SYSTEMS FOR INDUCTIVELY COUPLED PLASMA OPTICAL EMISSION SPECTROMETRY AND THEIR APPLICATION TO THE ANALYSIS OF SIMPLE AND COMPLEX MATRICES

The objective of this thesis is to explore new and improved methods for greater sample introduction efficiency and enhanced analytical performance with inductively coupled plasma optical emission spectrometry (ICP-OES). Three projects are discussed in which the capabilities and applications of ICP-OES are expanded: 1. In the first project, a conventional ultrasonic nebuliser was modified to replace the heater/condenser with an infrared heated pre-evaporation tube. In continuation from previous works with pre-evaporation, the current work investigated the effects of heating with infrared block and rope heaters on two different ICP-OES instruments. Comparisons were made between several methods and setups in which temperatures were varied. By monitoring changes to sensitivity, detection limit, precision, and robustness, and analyzing two certified reference materials, a method with improved sample introduction efficiency and comparable analytical performance to a previous method was established. 2. The second project involved improvements to a previous work in which a multimode sample introduction system (MSIS) was modified by inserting a pre-evaporation tube between the MSIS and torch. The new work focused on applying an infrared heated ceramic rope for pre-evaporation. This research was conducted in all three MSIS modes (nebulisation mode, hydride generation mode, and dual mode) and on two different ICP-OES instruments, and comparisons were made between conventional setups in terms of sensitivity, detection limit, precision, and robustness. By tracking both hydride-forming and non-hydride forming elements, the effects of heating in combination with hydride generation were probed. Finally, optimal methods were validated by analysis of two certified reference materials. 3. A final project was completed in collaboration with ZincNyx Energy Solutions. This project sought to develop a method for the overall analysis of a 12 M KOH zincate fuel, which is used in green energy backup systems. By employing various techniques including flow injection analysis and standard additions, a final procedure was formulated for the verification of K concentration, as well as the measurement of additives (Al, Fe, Mg, In, Si), corrosion products (such C from CO₃²¯), and Zn particles both in and filtered from solution. Furthermore, the effects of exposing the potassium zincate electrolyte fuel to air were assessed.