Monodromy calculations for some differential equations

In vielen Teilgebieten der Mathematik ist es w"{u}nschenswert, die Monodromiegruppe einer homogenen linearen Differenzialgleichung zu verstehen. Es sind nur wenige analytische Methoden zur Berechnung dieser Gruppe bekannt, daher entwickeln wir im ersten Teil dieser Arbeit eine numerische Methode zur Approximation ihrer Erzeuger.rnIm zweiten Abschnitt fassen wir die Grundlagen der Theorie der Uniformisierung Riemannscher Fl"achen und die der arithmetischen Fuchsschen Gruppen zusammen. Auss erdem erkl"aren wir, wie unsere numerische Methode bei der Bestimmung von uniformisierenden Differenzialgleichungen dienlich sein kann. F"ur arithmetische Fuchssche Gruppen mit zwei Erzeugern erhalten wir lokale Daten und freie Parameter von Lam'{e} Gleichungen, welche die zugeh"origen Riemannschen Fl"achen uniformisieren. rnIm dritten Teil geben wir einen kurzen Abriss zur homologischen Spiegelsymmetrie und f"uhren die $widehat{Gamma}$-Klasse ein. Wir erkl"aren wie diese genutzt werden kann, um eine Hodge-theoretische Version der Spiegelsymmetrie f"ur torische Varit"aten zu beweisen. Daraus gewinnen wir Vermutungen "uber die Monodromiegruppe $M$ von Picard-Fuchs Gleichungen von gewissen Familien $f:mathcal{X}rightarrow bbp^1$ von $n$-dimensionalen Calabi-Yau Variet"aten. Diese besagen erstens, dass bez"uglich einer nat"urlichen Basis die Monodromiematrizen in $M$ Eintr"age aus dem K"orper $bbq(zeta(2j+1)/(2 pi i)^{2j+1},j=1,ldots,lfloor (n-1)/2 rfloor)$ haben. Und zweitens, dass sich topologische Invarianten des Spiegelpartners einer generischen Faser von $f:mathcal{X}rightarrow bbp^1$ aus einem speziellen Element von $M$ rekonstruieren lassen. Schliess lich benutzen wir die im ersten Teil entwickelten Methoden zur Verifizierung dieser Vermutungen, vornehmlich in Hinblick auf Dimension drei. Dar"uber hinaus erstellen wir eine Liste von Kandidaten topologischer Invarianten von vermutlich existierenden dreidimensionalen Calabi-Yau Variet"aten mit $h^{1,1}=1$.

Noise Figure Measurement of Differential Amplifiers Using non-Ideal Baluns

This paper analyzes the noise and gain measurement of microwave differential amplifiers using two passive baluns. A general model of the baluns is considered, including potential losses and phase/amplitude unbalances. This analysis allows de-embedding the actual gain and noise performance of the isolated amplifier by using single-ended measurements of the cascaded system and baluns. Finally, measured results from two amplifier prototypes are used to validate the theoretical principles.

A De-Embedding Method to Characterize Differential

This paper analyses the noise and gain measurement of microwave differential amplifiers using two passive baluns. A model of the baluns that includes potential losses and unbalances has been considered. This analysis allows to de-embed the actual performance of the differential device from the single-ended measurements of the two-port cascaded system and the baluns. The method has been validated with measured results from a fully-differential amplifier prototype.

Phase shift keyed systems based on a gain switched laser transmitter

Return-to-Zero (RZ) and Non-Return-to-Zero (NRZ) Differential Phase Shift Keyed (DPSK) systems require cheap and optimal transmitters for widespread implementation. The authors report on a gain switched Discrete Mode (DM) laser that can be employed as a cost efficient transmitter in a 10.7 Gb/s RZ DPSK system and compare its performance to that of a gain switched Distributed Feed-Back (DFB) laser. Experimental results show that the gain switched DM laser readily provides error free performance and a receiver sensitivity of -33.1 dBm in the 10.7 Gbit/s RZ DPSK system. The standard DFB laser on the other hand displays an error floor at 10(-1) in the same RZ DPSK system. The difference in performance, between the two types of gain switched transmitters, is analysed by investigating their linewidths. We also demonstrate, for the first time, the generation of a highly coherent gain switched pulse train which displays a spectral comb of approximately 13 sidebands spaced by the 10.7 GHz modulation frequency. The filtered side-bands are then employed as narrow linewidth Continuous Wave (CW) sources in a 10.7 Gb/s NRZ DPSK system.

Differential ability and attainment in language and arithmetic of Dutch primary school pupils.

Background. In pre-school and primary education pupils differ in many abilities and competences (‘giftedness’). Yet mainstream educational practice seems rather homogeneous in providing age-based or grade-class subject matter approaches. Aims. To clarify whether pupils scoring initially at high ability level do develop and attain differently at school with respect to language and arithmetic compared with pupils displaying other initial ability levels. To investigate whether specific individual, family or educational variables co-vary with the attainment of these different types of pupils in school. Samples. Data from the large-scale PRIMA cohort study including a total of 8258 grade 2 and 4 pupils from 438 primary schools in The Netherlands. Methods. Secondary analyses were carried out to construct gain scores for both language and arithmetic proficiency and a number of behavioural, attitudinal, family and educational characteristics. The pupils were grouped into different ability categories (highly able; able; above average; average and below). Further analyses used Pearson correlations and analyses of variance both between and within ability categories. Cross-validation was done by introducing a cohort of younger pupils in pre-school and grouping both cohorts into decile groups based on initial ability in language and arithmetic. Results. Highly able pupils generally decreased in attainment in both language and arithmetic, whereas pupils in average and below average groups improved their language and arithmetic scores. Only with highly able pupils were some educational characteristics correlated with the pupils’ development in achievement, behaviour and attitudes. Conclusions. Pre-school and primary education should better match pupils’ differences in abilities and competences from their start in pre-school to improve their functioning, learning processes and outcomes. Recommendations for educational improvement strategies are presented in closing.

Innate immune humoral factors, C1q and factor H, with differential pattern recognition properties, alter macrophage response to carbon nanotubes

Interaction between the complement system and carbon nanotubes (CNTs) can modify their intended biomedical applications. Pristine and derivatised CNTs can activate complement primarily via the classical pathway which enhances uptake of CNTs and suppresses pro-inflammatory response by immune cells. Here, we report that the interaction of C1q, the classical pathway recognition molecule, with CNTs involves charge pattern and classical pathway activation that is partly inhibited by factor H, a complement regulator. C1q and its globular modules, but not factor H, enhanced uptake of CNTs by macrophages and modulated the pro-inflammatory immune response. Thus, soluble complement factors can interact differentially with CNTs and alter the immune response even without complement activation. Coating CNTs with recombinant C1q globular heads offers a novel way of controlling classical pathway activation in nanotherapeutics. Surprisingly, the globular heads also enhance clearance by phagocytes and down-regulate inflammation, suggesting unexpected complexity in receptor interaction. From the Clinical Editor: Carbon nanotubes (CNTs) maybe useful in the clinical setting as targeting drug carriers. However, it is also well known that they can interact and activate the complement system, which may have a negative impact on the applicability of CNTs. In this study, the authors functionalized multi-walled CNT (MWNT), and investigated the interaction with the complement pathway. These studies are important so as to gain further understanding of the underlying mechanism in preparation for future use of CNTs in the clinical setting.

Systemic Granulomatous Diseases Associated With Multiple Palpable Masses That May Involve The Breast: Case Presentation And An Approach To The Differential Diagnosis.

Palpable mass is a common complaint presented to the breast surgeon. It is very uncommon for patients to report breast mass associated with palpable masses in other superficial structures. When these masses are related to systemic granulomatous diseases, the diagnosis and initiation of specific therapy can be challenging. The purpose of this paper is to report a case initially assessed by the breast surgeon and ultimately diagnosed as granulomatous variant of T-cell lymphoma, and discuss the main systemic granulomatous diseases associated with palpable masses involving the breast.

Water Stress Reveals Differential Antioxidant Responses Of Tolerant And Non-tolerant Sugarcane Genotypes.

The biochemical responses of the enzymatic antioxidant system of a drought-tolerant cultivar (IACSP 94-2094) and a commercial cultivar in Brazil (IACSP 95-5000) grown under two levels of soil water restriction (70% and 30% Soil Available Water Content) were investigated. IACSP 94-2094 exhibited one additional active superoxide dismutase (Cu/Zn-SOD VI) isoenzyme in comparison to IACSP 95-5000, possibly contributing to the heightened response of IACSP 94-2094 to the induced stress. The total glutathione reductase (GR) activity increased substantially in IACSP 94-2094 under conditions of severe water stress; however, the appearance of a new GR isoenzyme and the disappearance of another isoenzyme were found not to be related to the stress response because the cultivars from both treatment groups (control and water restrictions) exhibited identical changes. Catalase (CAT) activity seems to have a more direct role in H2O2 detoxification under water stress condition and the shift in isoenzymes in the tolerant cultivar might have contributed to this response, which may be dependent upon the location where the excessive H2O2 is being produced under stress. The improved performance of IACSP 94-2094 under drought stress was associated with a more efficient antioxidant system response, particularly under conditions of mild stress.

Association Between Parity, Pre-pregnancy Body Mass Index And Gestational Weight Gain.

To analyze the relationship between parity, pre-pregnancy body mass index (BMI), and gestational weight gain (GWG). This observational controlled study was conducted from November 2013 to April 2014, with postpartum women who started antenatal care up to 14 weeks and had full-term births. Data were collected from medical records and antenatal cards. Descriptive and bivariate analyses were performed. The significance level was 5%. Data were collected from 130 primiparous and 160 multiparous women. At the beginning of prenatal care, 54.62% of the primiparous were eutrophic, while the majority of multiparous were overweight or obese (62.51%). Multiparas are two times more likely to be obese at the beginning of their pregnancies, when compared to primiparas. The average pre-pregnancy weight and final pregnancy weight was significantly higher in multiparous, however, the mean GWG was higher among primiparous. We found an inverse correlation between parity and the total GWG, but initial BMI was significantly higher in multiparas. Nevertheless, monitoring of the GWG through actions that promote a healthier lifestyle is needed, regardless of parity and nutritional status, in order to prevent excessive GWG and postpartum weight retention and consequently inadequate pre-pregnancy nutritional status in future pregnancies.

Enhanced D1 And D2 Inhibitions Induced By Low-frequency Trains Of Conditioning Stimuli: Differential Effects On H- And T-reflexes And Possible Mechanisms.

Mechanically evoked reflexes have been postulated to be less sensitive to presynaptic inhibition (PSI) than the H-reflex. This has implications on investigations of spinal cord neurophysiology that are based on the T-reflex. Preceding studies have shown an enhanced effect of PSI on the H-reflex when a train of ~10 conditioning stimuli at 1 Hz was applied to the nerve of the antagonist muscle. The main questions to be addressed in the present study are if indeed T-reflexes are less sensitive to PSI and whether (and to what extent and by what possible mechanisms) the effect of low frequency conditioning, found previously for the H-reflex, can be reproduced on T-reflexes from the soleus muscle. We explored two different conditioning-to-test (C-T) intervals: 15 and 100 ms (corresponding to D1 and D2 inhibitions, respectively). Test stimuli consisted of either electrical pulses applied to the posterior tibial nerve to elicit H-reflexes or mechanical percussion to the Achilles tendon to elicit T-reflexes. The 1 Hz train of conditioning electrical stimuli delivered to the common peroneal nerve induced a stronger effect of PSI as compared to a single conditioning pulse, for both reflexes (T and H), regardless of C-T-intervals. Moreover, the conditioning train of pulses (with respect to a single conditioning pulse) was proportionally more effective for T-reflexes as compared to H-reflexes (irrespective of the C-T interval), which might be associated with the differential contingent of Ia afferents activated by mechanical and electrical test stimuli. A conceivable explanation for the enhanced PSI effect in response to a train of stimuli is the occurrence of homosynaptic depression at synapses on inhibitory interneurons interposed within the PSI pathway. The present results add to the discussion of the sensitivity of the stretch reflex pathway to PSI and its functional role.

Ratio of weight to height gain: a useful tool for identifying children at risk of becoming overweight or obese at preschool age

PURPOSE: To analyze the usefulness of the weight gain/height gain ratio from birth to two and three years of age as a predictive risk indicator of excess weight at preschool age. METHODS: The weight and height/length of 409 preschool children at daycare centers were measured according to internationally recommended rules. The weight values and body mass indices of the children were transformed into a z-score per the standard method described by the World Health Organization. The Pearson correlation coefficients (rP) and the linear regressions between the anthropometric parameters and the body mass index z-scores of preschool children were statistically analyzed (alpha = 0.05). RESULTS: The mean age of the study population was 3.2 years (± 0.3 years). The prevalence of excess weight was 28.8%, and the prevalence of overweight and obesity was 8.8%. The correlation coefficients between the body mass index z-scores of the preschool children and the birth weights or body mass indices at birth were low (0.09 and 0.10, respectively). There was a high correlation coefficient (rP = 0.79) between the mean monthly gain of weight and the body mass index z-score of preschool children. A higher coefficient (rP = 0.93) was observed between the ratio of the mean weight gain per height gain (g/cm) and the preschool children body mass index z-score. The coefficients and their differences were statistically significant. CONCLUSION: Regardless of weight or length at birth, the mean ratio between the weight gain per g/cm of height growth from birth presented a strong correlation with the body mass index of preschool children. These results suggest that this ratio may be a good indicator of the risk of excess weight and obesity in preschool-aged children.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.