Search

Hilbert space operator polynomials with self-inversive structure are studied. If the inner numerical radius of an associated polynomial is greater than or equal to one then the spectrum lies on the unit circle and consists of normal approximate characteristic values.

The linear matrix equations A X B − C X D = E , A X − X ⁎ D = E , and A X B − X ⁎ = E are studied. In the case of uniqueness the solutions are expressed in terms of contour integrals.

If f is an endomorphism of a finite dimensional vector space V over a field K then an invariant subspace X ⊆ V is called hyperinvariant (respectively, characteristic) if X is invariant under all endomorphisms (respectively, automorphisms) that commute with f . The characteristic hull of a subset W of V is defined to be the smallest characteristic subspace in V that contains W . It is known that characteristic subspaces that are not hyperinvariant can only exist when | K | = 2 . In this paper we study subspaces X which are the characteristic hull of a single element. In the case where | K | = 2 we derive a necessary and sufficient condition such that X is hyperinvariant.

We deal with consistency of the generalized Sylvester equation over Bezout domains and prove a result on rank minimization which extends Roth’s equivalence theorem.

Let $f$ be an endomorphism of a vector space $V$ over a field $K$. An $f$-invariant subspace $X \subseteq V$ is called hyperinvariant (respectively characteristic) if $X$ is invariant under all endomorphisms (respectively automorphisms) that commute with $f$. If $|K| > 2$ then all characteristic subspaces are hyperinvariant. If $|K| = 2$ then there are endomorphisms $f$ with invariant subspaces that are characteristic but not hyperinvariant. In this paper we give a new proof of a theorem of Shoda, which provides a necessary and sufficient condition for the existence of characteristic non-hyperinvariant subspaces., 18 pages

In this paper we study a class of matrix polynomials with the property that spectral radius and numerical radius coincide. Special attention is paid to the spectrum on the boundary of the numerical range.

An existence result on diagonal solutions of a linear matrix inequality is used to study diagonal Hurwitz and Schur stability and to derive the secant condition for systems with cyclic structure.

Recent pre-clinical research has indicated that chronic treatment with methylphenidate (Ritalin®) in young animals can result in lasting and potentially detrimental alterations in brain function that can persist into adulthood. Chronic methylphenidate-induced neuronal alterations may result in behavior and cognitive deficits that include increases in behavioral responses and impairment in recognition memory. This study compared the cognitive consequences following chronic treatment with two doses (5 and 10 mg/kg) of methylphenidate on recognition and spatial memory in adult male Long-Evans rats using an established oral dosing procedure. The animals were then tested in the Object Recognition test at 14 days post treatment and the Object Placement test at 21 days post treatment. The results indicate that repeated exposure to oral methylphenidate impaired the performance of rats in these tests. The current findings add to recent research demonstrating negative consequences in rats pre-treated with methylphenidate, and extend previous findings to include deficits in spatial recognition memory.

Methylphenidate (MPD) is widely prescribed for the treatment of attention deficit disorders in children and has generally been thought to be free of significant side effects when administered at recommended therapeutic doses. However, recent behavioral research with laboratory rodents has indicated that, like other psychostimulants with which it shares neurotransmitter-modulating properties, chronically administered MPD can bring about lasting and potentially detrimental alterations in brain function. Some of these may involve changes in the neuromodulatory input from noradrenergic and dopaminergic systems that project to the prefrontal cortex and hippocampus, regions with significant roles in several cognitive functions, including those critical to memory formation. To investigate the possibility of cognitive impairment, the effects of a regimen of chronic MPD on the performance of an object recognition task known to rely on the integrity of systems involved in rodent memory was assessed. The drug, at doses of 2, 3 or 5 mg/kg, was delivered twice daily to periadolescent rats via an oral administration technique on either 11 or 21 treatment days. Subsequent to this period, the animals were subjected to an object recognition test at 14, 28, and 42 days after their last MPD treatment. In each of these tests, exploration time for two objects, one novel and one previously encountered (3 h earlier), was assessed. Longer exploration of the novel object was considered evidence of retained memory for the familiar object. It was found that rats exposed to 3 or 5 mg/kg (b.i.d.) on 21 occasions exhibited no significant preference for exploration of the novel object at any of the three post-treatment intervals. This finding was interpreted as evidence of a persisting MPD-induced impairment of recognition memory in these animals.

A solution X of a discrete-time algebraic Riccati equation is called unmixed if the corresponding closed-loop matrix Φ(X) has the property that the common roots of det(sI−Φ(X)) and det(I−sΦ(X)∗) (if any) are on the unit circle. A necessary and sufficient condition is given for existence and uniqueness of an unmixed solution such that the eigenvalues of Φ(X) lie in a prescribed subset of C.

This paper deals with the monotonicity of the optimal, rather than the more usual stabilising, cost of the discrete-time regulator problem. The approach relies on a monotonicity result on Riccati operators and on a formula for the difference of Schur complements.

The existence of a solution of the discrete-time algebraic Riccati equation is established assuming modulus controllability and positive semidefiniteness on the unit circle of the Popov function. As an application a nonstrictly bounded real lemma is obtained.

If two solutions Y⩽Z of the DARE are given then the set of solutions X with Y⩽X⩽Z can be parametrized by invariant subspaces of the closed loop matrix corresponding to Y. The paper extends the geometric theory of Willems from the continuous-time to the discrete-time ARE making the weakest possible assumptions.

Let ℂ n = ℒ ⊕ %plane1D;4B2; be a given direct sum decomposition. We determine the largest number r i such that all subspaces ℳ for which the gap θ between ℒ and %plane1D;4B2; satisfies θ(ℒℳ) have the property dim (ℳ∩%plane1D;4B2;). The problem involves angles between subspaces, i.e. singular values of products of projections.

Integrated bioelectrocatalytically active electrodes are assembled by the deposition of enzymes onto respective electrically contacted affinity matrices and further cross-linking of the enzyme monolayers. A catalyst-NAD(+)-dyad for the binding of the NAD(+)-dependent enzymes and cytochrome-like molecules for the binding of the heme-protein-dependent enzymes are used to construct integrated electrically contacted biocatalytic systems. NAD(+)-dependent lactate dehydrogenase (LDH) is assembled onto a pyrroloquinoline quinone-NAD+ monolayer. The redox-active monolayer is organized via covalent attachment of pyrroloquinoline quinone (PQQ) to a cystamine monolayer associated with a Au-electrode, followed by covalent linkage of N6-(2-aminoethyl)-NAD+ to the monolayer. The interface modified with the PQQ-NAD(+)-dyad provides temporary affinity binding for LDH and allows cross-linking of the enzyme monolayer. The cross-linked LDH is bioelectrocatalytically active towards oxidation of lactate. The bioelectrocatalyzed process involves the PQQ-mediated oxidation of the immobilized NADH. Integrated, electrically contacted bioelectrodes are produced by the affinity binding and further cross-linking of nitrate reductase (NR) (cytochrome-dependent, E.C. 1.9.6.1 from E. coli) or CoII-protoporphyrin IX reconstituted myoglobin (CoII-Mb) atop the microperoxidase-11 (MP-11) monolayer associated with a Au-electrode. The MP-11 monolayer provides an affinity interface for the temporary binding of the enzymes, that allows the cross-linkage of the enzyme molecules. The MP-11 assembly acts as electron transfer mediator for the reduction of the secondary enzyme layer. The integrated bioelectrodes consisting of NR and CoII-Mb show catalytic activities for NO3- reduction and acetylene-dicarboxylic acid hydrogenation, respectively. Two FeIII-protoporphyrin IX units are reconstituted into a four alpha-helix bundle de novo protein assembled as a monolayer on a Au-electrode. Vectorial electron transfer proceeds in the synthetic heme-protein monolayer. Cross-linking of an affinity complex generated between the FeIII-protoporphyrin IX reconstituted de novo protein monolayer and NR yields an integrated, electrically contacted enzyme electrode that stimulates the bioelectrocatalyzed reduction of nitrate.

Minimal spectral factors of spectral density matrices are constructed where poles and zeros lie in prescribed unmixed subsets of the complex plane.

Summary Ecological plant experiments using artificial light sources require careful shaping of the spectral irradiance. This includes the steep UV-absorption characteristics resulting from the filtering of solar radiation by atmosphefic ozone. Borosilicate and soda-lime glass filters screen radiation very similarly to ozone. They have a high mechanical stability and are available in large filter sheets and are, therefore, suited for the simulation of future scenarios of enhanced solar UV-B radiation in large scale vegetation stress experiments. Although such filters meet many requirements of light engineering, there are limitations due to the slope of the UV-edge and due to solarisation effects. Thus, the interpretation of the artifical radiation spectra and their comparison to UV scenarios of decreasing stratospheric ozone need careful discussion. Different methods to classify spectra of artificial UV-radiation are presented, and a new classification by a cut-off wavelength of the UV-edge and its slope is introduced.

Summary Plants have adapted very efficiently to their natural light habitat. Artificial plant illumination, therefore, requires careful design. Not only the quantity of radiation per area or volume (intensity) but also the spectral quality has to match seasonal and diurnal variations of natural global radiation as close as possible. The GSF Research Center has developed a phytotron system especially devoted to plant stress research, where these requirements are of particular importance. The phytotron consists of seven closed chambers (4 walk-in size chambers, two medium and one small sun simulator). Our contribution oudines the basic design of the lighting and presents spectral data. A good approximation of terrestrial global radiation is achieved if several commercially available lamp types are combined and adequate filters are applied to reject unwanted infrared and harmful ultraviolet radiation. A programmable switch control for the individual lamp banks allows a variation of both spectrum and intensity of the illumination. Spectroradiometric measurements show that the maximum level of illumination in the small and in the medium size chambers can compete both in spectral distribution and in intensity with outdoor global radiation for solar elevations up to 60°. The maximum light level available inside the large walk-in chambers reaches an irradiance corresponding to solar elevation of 50°. The UV-B: UV-A: PAR ratio, which mirrors the spectral balance of plant lighting, can be adjusted to values following the diurnal variation of natural global radiation.

The set of solutions of the discrete-time algebraic Riccati equation is described. It is shown that each solution is a combination of a pair of opposite unmixed solutions. There is a one-to-one correspondence between solutions and invariant subspaces of the closed loop matrix associated to an unmixed solution. The results of the paper are a counterpart of the parametrization theory of continuous-time algebraic Riccati equations due to Willems, Coppel and Shayman.

The set of negative-semidefinite solutions of the algebraic Riccati equation A∗X + XA + XBB∗X − C∗C = 0 is studied under the most general hypothesis, namely that (A, B) is stabilizable modulo the undetectable subspace of (A, C). If is a lattice, then is isomorphic to 0 ⊕ S where T0 is the direct sum of copies of the set of nonnegative real numbers and is a closure of which is order isomorphic to a system of well-defined A-invariant subspaces. Necessary and sufficient conditions are given such that (or) is a lattice.

The sets of negative semidefinite solutions T i of two algebraic Riccati equations R i (X)=A ∗ i X+XA i +XB i B ∗ i −C ∗ i C i =(I, X)H i (I, X) ∗ , i=1, 2, are compared under the hypothesis that H1⩽H2. If X+1 and X+2 are the greatest solutions in T 1 and T 2 respectively, then X+1⩽X+2. A more general result will be proved which allows the comparison of other solutions of T 1 and T 2 besides the extremal ones and which in the case of stabilizability leads to a Galois connection between T 1 and T 2. The comparison results are based on one hand on a decomposition of the equations R i (X)=0 into Lyapunov matrix equations and genuine Riccati equations which induce a corresponding decomposition of the solutions in T i, and the other hand on a parametrization of the Riccati components by Ai-invariant subspaces.

This note deals with the consistency of complex matrix equations AX − YB = C and AX − XB = C under the constraints Y = X ∗ and X = X ∗ .

In a study of drug-drug conditioning, chlordiazepoxide (CDP) was administered to rats 30 min before chlorpromazine (CPZ) every 3–4 days for 5 weeks. Thereafter, CDP was tested for its ability to a) increase animals' exploration of the normally avoided “exposed” arms of a plus-maze (a screening method for anxiolytic substances) and b) protect against induced by pentylenetetrazol (PTZ). The CDP-CPZ conditioning procedure potentiated the usual increase in open-arm activity seen in CDP-injected rats but attenuated the anti-PTZ effect. When injected with CDP 60 min prior to PTZ, rats with a previous history of CDP-CPZ pairing had shorter latencies to seizures onset and showed a greater likelihood of progression to the most severe behavioral indices of a maximal seizure relative to control subjects with a history of backward drug pairings (CPZ-CDP) or pairings of CDP with isotonic saline.

The Maqarin area, northern Jordan, hosts some unusual, hyperalkaline (pH= 12.5) groundwaters discharging from thermally metamorphosed bituminous marls which formed through spontaneous, in situ combustion of the bitumen. The groundwaters have evolved geochemically through hydration, recarbonation and sulphatization of high temperature minerals. Mineralogical relations of the carbonate phases were examined by XRD and cathodoluminescence in conjunction with a detailed investigation of stable isotope ratios by Nd-YAG laser microsampling. Carbon-13 contents trace the sequence of alteration reactions, involving high temperature decarbonation of host biomic marl, followed by in situ recarbonation of secondary calcium hydroxide and calcium-silicate-hydrates (CSH). Carbonation took place shortly after thermal metamorphism, when non-saturated conditions allowed an atmosphere rich in CO2 from adjacent combustion zones to access reaction sites. Low δ18OCaCO3 values suggest that the earliest phase of recarbonation took place by reaction with hydroxide at elevated temperatures while later phases formed at cooler temperatures. Variable14 activities show that soil CO2 was a component of the later recarbonating atmosphere. Once saturated conditions prevailed in the alteration zone, recarbonation ended and alteration evolved to hydroxide and sulphate dissolution reactions. The recarbonation reactions are a field-scale analogue of recarbonation and14C attenuation in cementitious barriers for radioactive waste repositories.

Yohimbine HCl, an antagonist at alpha 2-noradrenaline receptors with putative panicogenic effects in human subjects, was administered to Swiss-Webster mice at doses of 0.5, 1.0, and 2.0 mg/kg. Animals were then tested in two defense test batteries. Yohimbine produced increases in flight from an approaching/contacting human and potentiated animals' reactions to dorsal contact. During a 5-min exposure to a cat (separated from the mouse by a wire-mesh screen) and the 15-min period thereafter, yohimbine produced a dose-dependent pattern of changes in defensive behaviors that included increases in locomotion, transits from one segment of the test chamber to another, fore- and hindpaw wall climbing, screen climbing and hanging, and roof pushing. Crouching (relative immobility while in a hunched-back posture) was notably decreased at all doses. During the postcat period, two different response patterns, "high-escape" and "low-escape," characterized in part by high and low frequencies of wall climbing, were observed in cat-exposed groups. In yohimbine-injected mice, the low-escape behavior pattern also included a tendency to avoid the segment of the test chamber closest to the cat compartment. Both patterns differed from the crouching and immobility generally exhibited by vehicle-injected, cat-exposed controls. It was suggested that yohimbine effected these behavioral changes by either potentiating neural mechanisms mediating flight or inhibiting mechanisms mediating freezing. This model may have some utility for the investigation of panicogenic and antipanic compounds and may contribute insights into the etiology of panic disorder.

A polynomial approach is described to deal with problems of the following type. Given two companion matrices A and Z , when does there exist a nonsingular matrix S such that S -1 AS is upper triangular and S -1 ZS is lower triangular, and the eigenvalues of A and Z appear in the main diagonals of S -1 AS and S -1 ZS in a prescribed ordering? Such problems are related to complete minimal factorizations in systems theory.

Difference equations of the form X(t) = F ∗ (t)X(t − 1)F(t) − F ∗ (t)X(t − 1)G(t)[I + G ∗ (t)X(t − 1)G(t) −1 G ∗ (t)X(t − 1)F(t) + Q(t) and their associated Hermitian matrices H(t) = ( F Q F ∗ −GG ∗ )(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to the discrete-time LQ optimal control problem is given.

Criticism of extrapolation from single-species laboratory toxicity tests to the real environment initiated the search of new test protocols. One way to bridge the gap between the ecological and industrial point of view in the regulatory process is the development of multispecies tests based on the microcosm idea. During the last few years, practical knowledge has demonstrated that such tests are an attempt to make some kind of connection between a precisely controlled laboratory experiment and an observational field study whereby the greatest value of the microcosmology is attributed to the study of ecosystem-level functions. The first paper of the series presents the description of a terrestrial multispecies assemblage developed for screening purposes within the regulatory framework, discusses the problems of methodology, species selection, test protocol, and selection of test parameters, and demonstrates the construction of the multispecies assemblage. The test system itself is based on a section of agro-ecosystems and combines a hierarchical approach at the community, population, species and cellular level. Indicator organisms tested include members of the invertebrate groups nematodes, enchytraeids, and arthropods. The plant species is incorporated in the testing protocol, too but to a lesser extend. Methods applied include histoenzymology, histopathology, morphology, and ecological parameters characterizing population dynamics and community structure. The test protocol combines the elucidation of the mode of action of the test chemical to the biochemical apparatus of the cell with the ecological effects and enables the demonstration of cause-effect relationships.

The effects of solvent pH on spectral properties and fluorescence decay kinetics were investigated in order to characterize the microenvironment of meso-tetraphenylporphine tetrasulphonate (TPPS4) taken up by cells. Steady-state absorption and fluorescence spectra of TPPS4 in buffer solutions of different pH were used to identify a ring protonated species at pH less than or equal to 4. This dictation could also be distinguished from the unprotonated form by its altered fluorescence decay time (3.5 vs. 11.4 ns). In addition, time-resolved spectroscopy gave some evidence of a monocationic species existing at pH 6-9. This was concluded from the occurrence of another component with a decay time of 5 ns. Measurements of the spectral and kinetic properties of the fluorescence emission of single epithelial cells (RR1022) incubated with TPPS4 indicated that the sensitizer was mainly localized in a microenvironment with a pH of 5, a value which occurs intracellularly only within lysosomes. Cells kept in the dark exhibited the characteristic spectra of both the dication and the neutral form. The fluorescence decay showed two components with decay times of 2.6 ns and 10.6 ns. Irradiation of the cells changed the decay times to 4.6 ns and 13.4 ns and the dication fluorescence emission peak vanished, which is in accordance with the results obtained from buffer solutions at pH greater than or equal to 6. Therefore, we deduce that the photodynamic action leads to a rupture of the lysosomes and that the sensitizer is released into the surrounding cytoplasm.

s / Osteoarthritis and Cartilage 21 (2013) S63–S312 S193 proton slice sequence as shown in Figure 2 (second row). Here, cartilage boundaries are extracted automatically using the enhanced information in cartilage. Conclusions: Direct measurement of sodium concentration in AC enables early OA detectionwhile extracted cartilage boundaries in fused images may enable reconstruction of 3D models of articular cartilage that can be used to measure accurate cartilage thickness on load wearing sites as well as in different zones. This study confirms that use of dual tuned knee coil will enable the combined assessment of cartilage physiology and morphology for early detection of OA. Figure 2. Physiological and morphological measurements: First row-sodium signal intensity extraction in cartilage, Second row-fusion of sodium image with proton and cartilage boundary extraction. 366 7 TESLA SODIUM (23NA) IMAGING FOR THE ASSESSMENT OF PATELLAR CARTILAGE DAMAGE AFTER PATELLA-DISLOCATION: PRELIMINARY RESULTS H. Widhalm y, M. Brix y, S. Apprich y, G. Welsch z, S. Zbyn y, G. Vekszler y, M. Hambock y, M. Weber y, S. Domayer y, J. Hofstatter y, R. Windhager y, S. Trattnig y. yMed. Univ. of Vienna, Vienna, Austria; zUniv. Hosp. Erlangen, Erlangen, Germany Purpose: As OA is resulting in total joint replacement, it is of high interest to detect early changes of the articular cartilage. In the last decade, great afford has been made to develop biochemical MRI techniques, in order to determine the composition of articular cartilage. One of these techniques is Sodium imaging which directly correlates with the quantitative occurrence of glycosaminoglycans (GAG). Loss of GAG is known as the earliest change of cartilage degeneration before other changes occur. The purpose of this study was to evaluate the feasibility of 23Na (sodium) MR imaging, for the detection of OA at the patella cartilage in patients after patella-dislocation and to compare the results to healthy volunteers and cadaver samples. Methods: Nine patients after patella-dislocation, mean age 26.4 years ( 5.6), nine healthy volunteers, with a mean age of 26.1 years ( 5.0) and 5 cadaveric samples (mean age 75.8 7.4 years), were enrolled in this study. All measurements were performed on a 7T MR whole body system (Magnetom, Siemens Healthcare, Erlangen, Germany) using a twenty-eight-channel transmit/receive knee array coil (Quality Electrodynamics LLC, Cleveland, OH, US) and a 15-channel 23Na-only transmit/receive knee coil (Quality Electrodynamics LLC, Cleveland, OH, US). For morphological imaging a 2D-PDw-TSEfs-sequence (TR/TE 1⁄4 4390/26 ms; FOV 1⁄4 159*130 mm2, 20 slices; matrix size 1⁄4 448*366; resolution1⁄4 0.36*0.36*3.0 mm3; flip angle1⁄4 130; bandwidth1⁄4 245 Hz/ pixel) and a T1w-3D-GRE sequence (TR/TE 1⁄4 8.3/3.57 ms; FOV 1⁄4 185*156 mm2, 224 slices; matrix size 1⁄4 384*324; resolution 1⁄4 0.48*0.48*0.48 mm3; flip angle 1⁄4 8; bandwidth 1⁄4 450 Hz/pixel) were performed. Axial sodium images were derived from an optimized 3D GRE-sequence (TR/TE 1⁄4 17.0/8.34 ms; FOV 1⁄4 190*190 mm2, 32 slices; matrix size 1⁄4 64*128; resolution 1⁄4 1.48*1.48*3.0 mm3; bandwidth of 80 Hz/pix; 13 averages; 50 degree flip angle). Morphological cartilage grading was performed and sodium SNR values were calculated. Mean global sodium-values and SNR were compared between patients and volunteers and cartilage defect grades using an analysis of variance. In cadaver samples, the patella was divided into medial and lateral and from each side, 5 contiguous cartilage samples were analyzed with a GAG assay (Blyscan B3000 GAGAssay) for GAG content quantification. These values were compared with SNR values. Results: The mean SNR in sodium images for cartilage was 13.5 2.5 in patients and 14.8 3.7 in volunteers (p1⁄4 0.014). ANOVA-analysis yielded a marked decrease of the sodium-SNR with increasing grade of cartilage lesions (0.002). SNR values according to the number of patella dislocations also showed significantly different values (P1⁄4 0.010). The mean SNR in sodium images for cadaver samples was 27.4 8.4 on the medial side of the patella and 30.6 8.2. on the lateral side. The mean GAG values were 3.9 1.1 %GAG wet weight on the medial side and 3.9 11 %GAG wet weight on the lateral side. The results between sodium SNR and the biochemical assay demonstrated a statistical significant correlation (r1⁄40.563; p