Signal Transceiver Transit Times and Propagation Delay Corrections for Ranging and Georeferencing Applications

The accuracy of ranging measurements depends critically on the knowledge of time delays undergone by signals when retransmitted by a remote transponder and due to propagation effects. A new method determines these delays for every single pulsed signal transmission. It utilizes four ground-based reference stations, synchronized in time and installed at well-known geodesic coordinates and a repeater in space, carried by a satellite, balloon, aircraft, and so forth. Signal transmitted by one of the reference bases is retransmitted by the transponder, received back by the four bases, producing four ranging measurements which are processed to determine uniquely the time delays undergone in every retransmission process. A minimization function is derived comparing repeater's positions referred to at least two groups of three reference bases, providing the signal transit time at the repeater and propagation delays, providing the correct repeater position. The method is applicable to the transponder platform positioning and navigation, time synchronization of remote clocks, and location of targets. The algorithm has been demonstrated by simulations adopting a practical example with the transponder carried by an aircraft moving over bases on the ground.

Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Pseudodifferential analysis in Psi*-algebras on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces

The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

Mutually catalytic branching at infinite rate

The purpose of this doctoral thesis is to prove existence for a mutually catalytic random walk with infinite branching rate on countably many sites. The process is defined as a weak limit of an approximating family of processes. An approximating process is constructed by adding jumps to a deterministic migration on an equidistant time grid. As law of jumps we need to choose the invariant probability measure of the mutually catalytic random walk with a finite branching rate in the recurrent regime. This model was introduced by Dawson and Perkins (1998) and this thesis relies heavily on their work. Due to the properties of this invariant distribution, which is in fact the exit distribution of planar Brownian motion from the first quadrant, it is possible to establish a martingale problem for the weak limit of any convergent sequence of approximating processes. We can prove a duality relation for the solution to the mentioned martingale problem, which goes back to Mytnik (1996) in the case of finite rate branching, and this duality gives rise to weak uniqueness for the solution to the martingale problem. Using standard arguments we can show that this solution is in fact a Feller process and it has the strong Markov property. For the case of only one site we prove that the model we have constructed is the limit of finite rate mutually catalytic branching processes as the branching rate approaches infinity. Therefore, it seems naturalto refer to the above model as an infinite rate branching process. However, a result for convergence on infinitely many sites remains open.

An infinite level atom coupled to a heat bath

Wir untersuchen die Mathematik endlicher, an ein Wärmebad gekoppelter Teilchensysteme. Das Standard-Modell der Quantenelektrodynamik für Temperatur Null liefert einen Hamilton-Operator H, der die Energie von Teilchen beschreibt, welche mit Photonen wechselwirken. Im Heisenbergbild ist die Zeitevolution des physikalischen Systems durch die Wirkung einer Ein-Parameter-Gruppe auf eine Menge von Observablen A gegeben: Diese steht im Zusammenhang mit der Lösung der Schrödinger-Gleichung für H. Um Zustände von A, welche das physikalische System in der Nähe des thermischen Gleichgewichts zur Temperatur T darstellen, zu beschreiben, folgen wir dem Ansatz von Jaksic und Pillet, eine Darstellung von A zu konstruieren. Die Vektoren in dieser Darstellung definieren die Zustände, die Zeitentwicklung wird mit Hilfe des Standard Liouville-Operators L beschrieben. In dieser Doktorarbeit werden folgende Resultate bewiesen bzw. hergeleitet: - die Konstuktion einer Darstellung - die Selbstadjungiertheit des Standard Liouville-Operators - die Existenz eines Gleichgewichtszustandes in dieser Darstellung - der Limes des physikalischen Systems für große Zeiten.

Stochastic dynamics on infinite and finite transport capacity networks: an operatorial approach

Nella tesi viene studiata la dinamica stocastica di particelle non interagenti su network con capacita di trasporto finita. L'argomento viene affrontato introducendo un formalismo operatoriale per il sistema. Dopo averne verificato la consistenza su modelli risolvibili analiticamente, tale formalismo viene impiegato per dimostrare l'emergere di una forza entropica agente sulle particelle, dovuta alle limitazioni dinamiche del network. Inoltre viene proposta una spiegazione qualitativa dell'effetto di attrazione reciproca tra nodi vuoti nel caso di processi sincroni.

Effect of treatment delay on disease severity and need for resuscitation in porcine fecal peritonitis.

Early treatment in sepsis may improve outcome. The aim of this study was to evaluate how the delay in starting resuscitation influences the severity of sepsis and the treatment needed to achieve hemodynamic stability.

Clinical presentation and diagnostic delay in bullous pemphigoid: a prospective nationwide cohort

Prospective systematic analyses of the clinical presentation of bullous pemphigoid (BP) are lacking. Little is known about the time required for its diagnosis. Knowledge of the disease spectrum is important for diagnosis, management and inclusion of patients in therapeutic trials.

Brown Capuchins (Cebus apella) Exhibit Self-Control on a Delay of Gratification Food Exchange Task When Food Options Differ Qualitatively

Self-control allows an individual to obtain a more preferred outcome by forgoing an immediate interest. Self-control is an advanced cognitive process because it involves the ability to weigh the costs and benefits of impulsive versus restrained behavior, determine the consequences of such behavior, and make decisions based on the most advantageous course of action. Self-control has been thoroughly explored in Old World primates, but less so in New World monkeys. There are many ways to test self-control abilities in non-human primates, including exchange tasks in which an animal must forgo an immediate, less preferred reward to receive a delayed, more preferred reward. I examined the self-control abilities of six capuchin monkeys using a task in which a monkey was given a less preferred food and was required to wait a delay interval to trade the fully intact less preferred food for a qualitatively higher, more preferred food. Partially eaten pieces of the less preferred food were not rewarded, and delay intervals increased on an individual basis based on performance. All six monkeys were successful in inhibiting impulsivity and trading a less preferred food for a more preferred food at the end of a delay interval. The maximum duration each subject postponed gratification instead of responding impulsively was considered their delay tolerance. This study was the first to show that monkeys could inhibit impulsivity in a delay of gratification food exchange task in which the immediate and delayed food options differed qualitatively and a partially eaten less preferred food was not rewarded with the more preferred food at the end of a delay interval. These results show that New World monkeys possess advanced cognitive abilities similar to those of Old World primates.

Executive functions of children born very preterm--deficit or delay?

This cross-sectional study examined the performance of children born very preterm and/or at very low birth weight (VPT/VLBW) and same-aged term-born controls in three core executive functions: inhibition, working memory, and shifting. Children were divided into two age groups according to the median (young, 8.00-9.86 years; old, 9.87-12.99 years). The aims of the study were to investigate whether (a) VPT/VLBW children of both age groups performed poorer than controls (deficit hypothesis) or caught up with increasing age (delay hypothesis) and (b) whether VPT/VLBW children displayed a similar pattern of performance increase in executive functions with advancing age compared with the controls. Fifty-six VPT/VLBW children born in the cohort of 1998-2003 and 41 healthy-term-born controls were recruited. All children completed tests of inhibition (Color-Word Interference Task, Delis-Kaplan Executive Function System (D-KEFS)), working memory (Digit Span Backwards, HAWIK-IV), and shifting (Trail Making Test, Number-Letter Sequencing, D-KEFS). Results revealed that young VPT/VLBW children performed significantly poorer than the young controls in inhibition, working memory, and shifting, whereas old VPT/VLBW children performed similar to the old controls across all three executive functions. Furthermore, the frequencies of impairment in inhibition, working memory and shifting were higher in the young VPT/VLBW group compared with the young control group, whereas frequencies of impairment were equal in the old groups. In both VPT/VLBW children and controls, the highest increase in executive performance across the ages of 8 to 12 years was observed in shifting, followed by working memory, and inhibition.

GH mutant (R77C) in a pedigree presenting with the delay of growth and pubertal development: structural analysis of the mutant and evaluation of the biological activity

A heterozygous missense mutation in the GH-1 gene converting codon 77 from arginine (R) to cysteine (C), which was previously reported to have some GH antagonistic effect, was identified in a Syrian family. The index patient, a boy, was referred for assessment of his short stature (-2.5 SDS) at the age of 6 years. His mother and grandfather were also carrying the same mutation, but did not differ in adult height from the other unaffected family members. Hormonal examination in all affected subjects revealed increased basal GH, low IGF-I concentrations, and subnormal IGF-I response in generation test leading to the diagnosis of partial GH insensitivity. However, GH receptor gene (GHR) sequencing demonstrated no abnormalities. As other family members carrying the GH-R77C form showed similar alterations at the hormonal level, but presented with normal final height, no GH therapy was given to the boy, but he was followed through his pubertal development which was delayed. At the age of 20 years he reached his final height, which was normal within his parental target height. Functional characterization of the GH-R77C, assessed through activation of Jak2/Stat5 pathway, revealed no differences in the bioactivity between wild-type-GH (wt-GH) and GH-R77C. Detailed structural analysis indicated that the structure of GH-R77C, in terms of disulfide bond formation, is almost identical to that of the wt-GH despite the introduced mutation (Cys77). Previous studies from our group demonstrated a reduced capability of GH-R77C to induce GHR/GH-binding protein (GHBP) gene transcription rate when compared with wt-GH. Therefore, reduced GHR/GHBP expression might well be the possible cause for the partial GH insensitivity found in our patients. In addition, this group of patients deserve further attention because they could represent a distinct clinical entity underlining that an altered GH peptide may also have a direct impact on GHR/GHBP gene expression causing partial GH insensitivity. This might be responsible for the delay of growth and pubertal development. Finally, we clearly demonstrate that GH-R77C is not invariably associated with short stature, but that great care needs to be taken in ascribing growth failure to various heterozygous mutations affecting the GH-IGF axis and that careful functional studies are mandatory.