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  • 1
    Online Resource
    Online Resource
    Cham :Springer International Publishing AG,
    Keywords: Stochastic control theory. ; Electronic books.
    Type of Medium: Online Resource
    Pages: 1 online resource (598 pages)
    Edition: 1st ed.
    ISBN: 9783030823313
    Series Statement: Probability Theory and Stochastic Modelling Series ; v.101
    DDC: 519.2
    Language: English
    Note: Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Why Stochastic Distributed Parameter Control Systems? -- 1.2 Two Fundamental Issues in Control Theory -- 1.3 Range Inclusion and the Duality Argument -- 1.4 Two Basic Methods in This Book -- 2 Some Preliminaries in Stochastic Calculus -- 2.1 Measures and Probability, Measurable Functions and Random Variables -- 2.2 Integrals and Expectation -- 2.3 Signed/Vector Measures, Conditional Expectation -- 2.3.1 Signed Measures -- 2.3.2 Distribution, Density and Characteristic Functions -- 2.3.3 Vector Measures -- 2.3.4 Conditional Expectation -- 2.4 A Riesz-Type Representation Theorem -- 2.4.1 Proof of the Necessity for a Special Case -- 2.4.2 Proof of the Necessity for the General Case -- 2.4.3 Proof of the Sufficiency -- 2.5 A Sequential Banach-Alaoglu-Type Theorem in the Operator Version -- 2.6 Stochastic Processes -- 2.7 Stopping Times -- 2.8 Martingales -- 2.8.1 Real Valued Martingales -- 2.8.2 Vector-Valued Martingales -- 2.9 Brownian Motions -- 2.9.1 Brownian Motions in Finite Dimensions -- 2.9.2 Construction of Brownian Motions in one Dimension -- 2.9.3 Vector-Valued Brownian Motions -- 2.10 Stochastic Integrals -- 2.10.1 Itô's Integrals w.r.t. Brownian Motions in Finite Dimensions -- 2.10.2 Itô's Integrals w.r.t. Vector-Valued Brownian Motions -- 2.11 Properties of Stochastic Integrals -- 2.11.1 Itô's Formula for Itô's Processes (in a Strong Form) -- 2.11.2 Burkholder-Davis-Gundy Inequality -- 2.11.3 Stochastic Fubini Theorem -- 2.11.4 Itô's Formula for Itô's processes in a Weak Form -- 2.11.5 Martingale Representation Theorem -- 2.12 Notes and Comments -- 3 Stochastic Evolution Equations -- 3.1 Stochastic Evolution Equations in Finite Dimensions -- 3.2 Well-Posedness of Stochastic Evolution Equations -- 3.2.1 Notions of Solutions -- 3.2.2 Well-Posedness in the Sense of Mild Solution. , 3.3 Regularity of Mild Solutions to Stochastic Evolution Equations -- 3.3.1 Burkholder-Davis-Gundy Type Inequality and Time Regularity -- 3.3.2 Space Regularity -- 3.4 Notes and Comments -- 4 Backward Stochastic Evolution Equations -- 4.1 The Case of Finite Dimensions and Natural filtration -- 4.2 The Case of Infinite Dimensions -- 4.2.1 Notions of Solutions -- 4.2.2 Well-Posedness in the Sense of Mild Solution for the Case of Natural Filtration -- 4.3 The Case of General Filtration -- 4.4 The Case of Natural Filtration Revisited -- 4.5 Notes and Comments -- 5 Control Problems for Stochastic Distributed Parameter Systems -- 5.1 An Example of Controlled Stochastic Differential Equations -- 5.2 Control Systems Governed by Stochastic Partial Differential Equations -- 5.3 Some Control Problems for Stochastic Distributed Parameter Systems -- 5.4 Notes and Comments -- 6 Controllability for Stochastic Differential Equations in Finite Dimensions -- 6.1 The Control Systems With Controls in Both Drift and Diffusion Terms -- 6.2 Control System With a Control in the Drift Term -- 6.3 Lack of Robustness for Null/Approximate Controllability -- 6.4 Notes and Comments -- 7 Controllability for Stochastic Linear Evolution Equations -- 7.1 Formulation of the Problems -- 7.2 Well-Posedness of Stochastic Systems With Unbounded Control Operators -- 7.3 Reduction to the Observability of Dual Problems -- 7.4 Explicit Forms of Controls for the Controllability Problems -- 7.5 Relationship Between the Forward and the Backward Controllability -- 7.5.1 The Case of Bounded Control Operators -- 7.5.2 The Case of Unbounded Control Operators -- 7.6 Notes and Comments -- 8 Exact Controllability for Stochastic Transport Equations -- 8.1 Formulation of the Problem and the Main Result -- 8.2 Hidden Regularity and a Weighted Identity. , 8.3 Observability Estimate for Backward Stochastic Transport Equations -- 8.4 Notes and Comments -- 9 Controllability and Observability of Stochastic Parabolic Systems -- 9.1 Formulation of the Problems -- 9.2 Controllability of a Class of Stochastic Parabolic Systems -- 9.2.1 Preliminaries -- 9.2.2 Proof of the Null Controllability -- 9.2.3 Proof of the Approximate Controllability -- 9.3 Controllability of a Class of Stochastic Parabolic Systems by one Control -- 9.3.1 Proof of the Null Controllability Result -- 9.3.2 Proof of the Negative Null Controllability Result -- 9.4 Carleman Estimate for a Stochastic Parabolic-Like Operator -- 9.5 Observability Estimate for Stochastic Parabolic Equations -- 9.5.1 Global Carleman Estimate for Stochastic Parabolic Equations, I -- 9.5.2 Global Carleman Estimate for Stochastic Parabolic Equations, II -- 9.5.3 Proof of the Observability Result -- 9.6 Null and Approximate Controllability of Stochastic Parabolic Equations -- 9.6.1 Global Carleman Estimate for Backward Stochastic Parabolic Equations -- 9.6.2 Proof of the Observability Estimate for Backward Stochastic Parabolic Equations -- 9.7 Notes and Comments -- 10 Exact Controllability for a Refined Stochastic Wave Equation -- 10.1 Formulation of the Problem -- 10.2 Well-Posedness of Stochastic Wave Equations With Boundary Controls -- 10.3 Main Controllability Results -- 10.4 A Reduction of the Exact Controllability Problem -- 10.5 A Fundamental Identity for Stochastic Hyperbolic-Like Operators -- 10.6 Observability Estimate for the Stochastic Wave Equation -- 10.7 Notes and Comments -- 11 Exact Controllability for Stochastic Schrödinger Equations -- 11.1 Formulation of the Problem and the Main Result -- 11.2 Well-Posedness of the Control System -- 11.3 A Fundamental Identity for Stochastic Schrödinger-Like Operators. , 11.4 Observability Estimate for Backward Stochastic Schrödinger Equations -- 11.5 Notes and Comments -- 12 Pontryagin-Type Stochastic Maximum Principle and Beyond -- 12.1 Formulation of the Optimal Control Problem -- 12.2 The Case of Finite Dimensions -- 12.3 Necessary Condition for Optimal Controls for Convex Control Regions -- 12.4 Operator-Valued Backward Stochastic Evolution Equations -- 12.4.1 Notions of Solutions -- 12.4.2 Preliminaries -- 12.4.3 Proof of the Uniqueness Results -- 12.4.4 Well-Posedness Result for a Special Case -- 12.4.5 Proof of the Existence and Stability for the General Case -- 12.4.6 A Regularity Result -- 12.5 Pontryagin-Type Maximum Principle -- 12.6 Sufficient Condition for Optimal Controls -- 12.6.1 Clarke's Generalized Gradient -- 12.6.2 A Sufficient Condition for Optimal Controls -- 12.7 Second Order Necessary Condition for Optimal Controls -- 12.8 Notes and Comments -- 13 Linear Quadratic Optimal Control Problems -- 13.1 Formulation of the Problem -- 13.2 Optimal Feedback for Deterministic LQ Problem in Finite Dimensions -- 13.3 Optimal Feedback for Stochastic LQ Problem in Finite Dimensions -- 13.3.1 Differences Between Deterministic and Stochastic LQ Problems in Finite Dimensions -- 13.3.2 Characterization of Optimal Feedbacks for Stochastic LQ Problems in Finite Dimensions -- 13.4 Finiteness and Solvability of Problem (SLQ) -- 13.5 Pontryagin-Type Maximum Principle for Problem (SLQ) -- 13.6 Transposition Solutions to Operator-Valued Backward Stochastic Riccati Equations -- 13.7 Existence of Optimal Feedback Operator for Problem (SLQ) -- 13.8 Global Solvability of Operator-Valued Backward Stochastic Riccati Equations -- 13.8.1 Some Preliminary Results -- 13.8.2 Proof of the Main Solvability Result -- 13.9 Some Examples -- 13.9.1 LQ Problems for Stochastic Wave Equations. , 13.9.2 LQ problems for Stochastic Schrödinger Equations -- 13.10 Notes and Comments -- References -- Index.
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  • 2
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 99 (1995), S. 1768-1775 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 8239-8251 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Fluorene–Arn complexes formed in a pulsed supersonic jet have been studied in their S1 state using two color REMPI spectroscopy with mass resolved detection. The appearance and shifts of the S1 origins relative to the fluorene monomer are measured for cluster sizes up to n=30. The shifts and appearance of these bands are used to identify multiple conformations at low n and have indicated a shift from two sided clustering by Ar at low n to primarily one sided clustering at large n. The ionic ground state of the smaller clusters (n≤6) are studied using mass analyzed threshold ionization (MATI) spectroscopy. The change of the ionization potentials as a function of cluster size has been determined. In the case of the fluorene–Ar4 cluster, the MATI spectrum of two separate cluster conformations was measured, revealing significantly different ionization potentials. Vibrational dynamics has been studied in several smaller clusters (n≤3) by measuring MATI and ZEKE spectra when pumping vibronic transitions in the fluorene chromophore. Significantly enhanced coupling of the chromophore to van der Waals modes is observed in going from n=1 to n=3. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1460-9568
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Medicine
    Notes: Using indirect immunofluorescence, neuropeptide Y Y1 receptor (Y1 receptor)-like immunoreactivity (LI) was localized close to the plasmalemma of small neurons in lumbar dorsal root ganglia (DRGs) and neurons in the inner lamina II of the lumbar spinal cord of the rat. Using confocal microscopy, colocalization of Y1 receptor-LI and transferrin receptor-LI, a marker for endosomes and coated vesicles, was observed in dot-like structures along the plasmalemma. Under the electron microscope, Y1 receptor-LI was localized in coated vesicles and endosomes, in the membrane of tubular cisternae, sometimes connected to multivesicular bodies, and in the plasmalemma. These complex distribution patterns may reflect receptor turnover and internalization processes. In the lamina II of the spinal dorsal horn, Y1 receptor-LI was localized in the plasmalemma of neurons without any apparent association with paramembrane structures, as described above for the DRG neurons. Many dendrites were Y1 receptor-positive, and some of them made synaptic contacts with unstained axonal terminals. In general, Y1 receptor-LI was localized in the membrane outside the postsynaptic density. Double-immunofluorescence staining showed that most Y1 receptor-immunoreactive neurons in lamina II contained somatostatin-LI. Both in DRG and dorsal horn neurons, the Y1 receptor thus seems to represent a postjunctional/postsynaptic receptor.
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  • 6
    ISSN: 1460-9568
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Medicine
    Notes: Using monoiodinated peptide YY (PYY) and galanin as radioligands, and neuropeptide Y (NPY) fragments, the distribution of NPY binding sites and its subtypes Y1 and Y2, and of galanin binding sites, was investigated in rat and monkey lumbar (L) 4 and L5 dorsal root ganglia (DRG) and spinal cord before and after a unilateral sciatic nerve cut, ligation or crush. Receptor autoradiography revealed that [125I]PYY bound to some DRG neurons and a few nerve fibres in normal rat DRG, and most of these neurons were small. NPY binding sites were observed in laminae I–IV and X of the rat dorsal horn and in the lateral spinal nucleus, with the highest density in laminae 1–11. [125I]NPY binding was most strongly attenuated by NPY13–36, a Y2 agonist, and partially inhibited by [Leu31,Pro34]NPY, a Y1 agonist, in both rat DRG and the dorsal horn of the spinal cord. These findings suggest that Y2 receptors are the main NPY receptors in rat DRG and dorsal horn, but also that Y1 receptors exist. After sciatic nerve cut, PYY binding markedly increased in nerve fibres and neurons in DRG, especially in large neuron profiles, and in laminae III-IV of the dorsal horn, as well as in nerve fibres in dorsal roots and the sciatic nerve. Incubation with NPY13–36 completely abolished PYY binding, which was also reduced by [Leu,31 Pro34] NPY. However, the increase in PYY binding seen in laminae I–IV of the ipsilateral dorsal horn after axotomy was not observed after coincubation with [Leu31, Pro34] NPY. NPY binding sites were seen in a few neurons in monkey DRG and in laminae I-II, X and IX of the monkey spinal cord. The intensity of PYY binding in laminae I-II of the dorsal horn was decreased after axotomy. Galanin receptor binding sites were not observed in rat DRG, but were observed in the superficial dorsal horn of the spinal cord, mainly in laminae I-II. Axotomy had no effect on galanin binding in rat DRG and dorsal horn. However, galanin receptor binding was observed in many neurons in monkey L4 and L5 DRG and in laminae I–IV and X of monkey L4 and L5 spinal cord, with the highest intensity in laminae I-II. No marked effect of axotomy was observed on the distribution and intensity of galanin binding in monkey DRG or spinal cord. The present results indicate that after axotomy the synthesis of NPY receptors is increased in rat DRG neurons, especially in large neurons, and is transported to the laminae I–IV of the ipsilateral dorsal horn and into the sciatic nerve. No such up-regulation of the NPY receptor occurred in monkey DRG after axotomy. The Y2 receptor seems to be the main NPY receptor in DRG and the dorsal horn of the rat and monkey spinal cord, but Y1 receptors also exist. The increase in NPY binding sites in laminae I–IV of the dorsal horn after axotomy partly represents Y1 receptors. In contrast to the rat, galanin binding sites could be identified in monkey lumbar DRG. No effect of axotomy on the distribution of galanin binding sites in rat or monkey DRG and dorsal horn was detected, suggesting their presence on local dorsal horn neurons (or central afferents).
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  • 7
    ISSN: 1546-1718
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Medicine
    Notes: [Auszug] We used illegitimate transcription in lymphoblastoid cell lines6 to obtain laminin α2 chain mRNA from probands of consanguineous laminin α2 and non-consanguineous chain-deficient families for mutation analysis by RT-PCR. Twenty-four pairs of overlapping primers (see Methods) were ...
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  • 8
    ISSN: 1432-198X
    Keywords: Key words:  In situ hybridization assay ; Hepatitis B virus DNA ; Hepatitis B virus antigen ; Hepatitis B virus-associated glomerulonephritis ; Cytokines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract. Renal tissues from 43 of 49 children with hepatitis B virus-associated glomerulonephritis (HBV-GN) were examined for HBV DNA by in situ hybridization (ISH) assay within the last 10 years. HBV DNA was identified in 41 of the 43 cases (95.3%). HBV DNA was distributed generally in the nucleus and cytoplasm of epithelial cells and mesangial cells of glomeruli, and epithelial cells of renal tubules. HBV DNA also existed simultaneously in renal interstitial tissues in some of these cases. The positive results from HBV DNA ISH correlated well with HBV antigen assays. The analyses implied that the more extensive the existence of HBV DNA in the nephron unit and interstitial tissue, the more severe the clinical manifestation. The duration of proteinuria in cases with HBV DNA in renal tubules was much longer than in those with no HBV DNA in renal tubules. The persistence of the HBV genome or genes in the kidney could lead to the expression of viral antigens in renal tissues and might cause cellular pathological alteration. This would support utilization of antiviral therapy, such as cytokines, in the treatment of HBV-GN.
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  • 9
    ISSN: 1432-1106
    Keywords: Galanin ; Neuropeptide Y ; Vasoactive intestinal polypeptide ; Plasticity ; Axotomy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Using immunohistochemistry and in situ hybridization, the expression of galanin (GAL)/galanin message associated peptide (GMAP)-, neuropeptide Y (NPY)-, vasoactive intestinal polypeptide (VIP)/peptide histidine isoleucine (PHI)- and nitric oxide synthase (NOS)-like immunoreactivities and mRNAs, and NPY receptor mRNA was studied in normal trigeminal and nodose ganglia and 14 and 42 days after peripheral axotomy. In normal trigeminal ganglia about 11% of the counted neuron profiles contained GAL mRNA, 4% NOS mRNA, 5% NPY mRNA, 7% VIP mRNA, and 19% NPY receptor mRNA. Peptide mRNA- and NPY receptor mRNA-positive neuron profiles were small in size. Fourteen days after axotomy a marked increase in the number of GAL mRNA- (34% of counted neuron profiles), NPY mRNA- (54%) and VIP mRNA- (31%) positive neuron profiles, and a moderate increase in the number of NOS mRNA- (22%) positive neuron profiles were observed in the ipsilateral trigeminal ganglia. The GAL/GMAP, VIP- and NOS-positive profiles were mainly small, the NPY-positive ones mostly large. NPY receptor mRNA was expressed in some large neurons. In normal nodose ganglia, about 3% of the counted neuron profiles contained GAL mRNA, 3% NPY mRNA, 17% NOS mRNA and less than 1% VIP mRNA. Fourteen days after peripheral axotomy, a marked increase in the number of GAL mRNA- (78% of counted neuron profiles), NOS mRNA- (37%) and VIP- (46%) mRNA-positive neuron profiles was seen in the ipsilateral nodose ganglia. The number of NPY-positive (23%) neurons was moderately increased, mainly in small neuron profiles. There were no NPY receptor mRNA-positive neurons, either in normal nodose ganglia or in nodose ganglia ipsilateral to the axotomy. In contralateral nodose ganglia the number of GAL- and NPY-positive neuron profiles was slightly increased, and VIP cells showed a moderate increase. Immunohistochemical analysis revealed parallel changes in expression of peptides and NOS in both trigeminal and nodose ganglia, demonstrating that the changes in mRNA levels are translated into protein. Finally, although not quantified, similar upregulations of peptide and NOS mRNA levels were observed in both ganglia 42 days after nerve injury provided that regeneration was not allowed, suggesting that the changes are long lasting. The present results show that the effect of axotomy on peptide and NOS expression in the trigeminal and nodose ganglia is similar to that previously shown for lumbar dorsal root ganglia. However, no mRNA for the NPY Y1 receptor could be detected in the vagal system. In general the mechanism(s) for and the purpose(s) of the messenger regulation in response to axotomy may be similar in these different sensory systems (dorsal root, trigeminal and nodose ganglia).
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  • 10
    ISSN: 1572-901X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The ion-exchange between the transition metal monosubstituted heteropolyoxometalate anion [SiW11O39-Co(H2O)]6− and the anionic clay Zn2Al(OH)6NO3· xH2O by the action of ultrasound gave the heteropolyanion-pillared layered double hydroxide Zn2Al-(OH)6[SiW11O39Co(H2O)]1/6·4H2O within 7 min. The product was characterized by powder X-ray diffraction, i.r. spectroscopy and elemental analysis. The results show that the gallery height of the complex is 1.00±0.02 nm and the heteropolyanion [SiW11O39-Co(H2O)]6− entering the layer retains the integrity of the Keggin structure. Experimentally, the atomic ratio of each element in the formula is Zn:Al = 2.1:0.95 and Si:W:Co = 0.96:10.90:0.98.
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