Infinite number of stable periodic solutions for an equation with negative feedback

For all $\mu>0$, a locally Lipschitz continuous map $f$ with $xf\left(x\right)>0$, $x\in\mathbb{R}\setminus\left\{ 0\right\}$, is constructed, such that the scalar equation $\dot{x}\left(t\right)=-\mu x\left(t\right)-f\left(x\left(t-1\right)\right)$ with delayed negative feedback has an infinite number of periodic orbits. All periodic solutions defining these orbits oscillate slowly around $0$ in the sense that they admit at most one sign change in each interval of length of $1$. Moreover, if $f$ is continuously differentiable, then the periodic orbits are hyperbolic and stable. In this example $f$ is not bounded, but the Lipschitz constants for the restrictions of $f$ to certain intervals are small. Based on this property, an infinite sequence of contracting return maps is given. Their fixed points are the initial segments of the periodic solutions

On the fundamental solution of linear delay differential equations with multiple delays

For a class of linear autonomous delay differential equations with parameter $\alpha$ we give upper bounds for the integral \int_{0}^{\infty}\left|X\left(t,\alpha\right)\right|\mbox{d}t of the fundamental solution $X\left(\cdot,\alpha\right)$. The asymptotic estimations are sharp at a critical value $\alpha_{0}$ where $x=0$ loses stability. We use these results to study the stability properties of perturbed equations

UNIAXIAL COMPRESSIVE STRENGTH, DRY UNIT WEIGHT AND FRACTURE PATTERNS OF ULTRABASIC ROCKS IN OTHRYS MOUNTAIN (CENTRAL GREECE): CORRELATIONS AND EVALUATION

Στη παρούσα δημοσίευση μελετούνται τα υπερβασικά πετρώματα από την περιοχή της Όθρυος (Στερεά Ελλάδα). Η γεωλογική δομή και η τεκτονική της εξεταζόμενης περιοχής περιγράφοντα συνοπτικά. Οι αντοχές σε ανεμπόδιστη μονοαξονική θλίψη και τα φαινόμενα βάρη υπολογίζονται και οι γωνίες θραύσης μετρούνται. Τα αποτελέσματα αξιολογούνται στατιστικά και παρουσιάζονται εμπειρικές σχέσεις μεταξύ της αντοχής σε μονοαξονική θλίψη και του φαινόμενου βάρους. Εξαιτίας του χαμηλού συντελεστή συσχέτισης στους Σερπεντινιωμένους Περιδοτίτες, αποφασίσαμε οι Σερπεντινιωμένοι Περιδοτίτες και οι Σερπεντινίτες να εξεταστούν μαζί. Ο νέος συντελεστής συσχέτισης είναι πολύ μεγαλύτερος από τον προηγούμενο Επιπλέον, στην παρούσα δημοσίευση φαίνεται πως η πλειοψηφία των υπερβασικών πετρωμάτων θραύεται σε μια μόνο γωνία (φ°), η οποία κυμαίνεται κυρίως μεταξύ 75° και 90°, ενώ γίνεται και συσχετισμός των γωνιών θραύσης με την τεκτονική. Οι όποιες αποκλίσεις παρατηρήθηκαν αποδίδονται στην πετρογραφική ποικιλία, στη δομική πολυπλοκότητα, στον προτιμητέο προσανατολισμό του ολιβίνη και του ορθοπυρόξενου και στην εσωτερικά αποτυπωμένη τεκτονική παραμόρφωση.Ultrabasic rocks, taken from the Othrys mt. (Central Greece), are studied in this paper. The structural geology and tectonics of the study area are described. Uniaxial Compressive Strength (UCS) and dry unit weight (γ) values are calculated and fracture angles are measured. The results are statistically assessed and empirical relationships (exponential equations) between UCS and γ are presented for the ultrabasic roch, divided in Peridotites, Serpentinised Peridotites and Serpentinites. Due to the low correlation coefficient of the Serpentinised Peridotites, it was decided that the Serpentinised Peridotites and Serpentinites should be examined together. The correlation coefficient of the combined category is much better than the separate ones. Furthermore, this paper demonstrates that the majority of the ultrabasic rocks tested were breaking at one angle (φ°), which mainly fluctuated between 75° and 90°. The fracture angles correlate with previously recognised geological (mainly tectonic) structures. The observed deviations are due to pétrographie variety, structural complexity, preferred orientation of olivine and orthopyroxene and internal imprinted tectonic deformation

Investigation of fiber/matrix adhesion: test speed and specimen shape effects in the cylinder test

The cylinder test, developed from the microdroplet test, was adapted to assess the interfacial adhesion strength between fiber and matrix. The sensitivity of cylinder test to pull-out speed and specimen geometry was measured. It was established that the effect of test speed can be described as a superposition of two opposite, simultaneous effects which have been modeled mathematically by fitting two parameter Weibull curves on the measured datas. Effects of the cylinder size and its geometrical relation on the measured strength values have been analyzed by finite element method. It was concluded that the geometry has a direct influence on the stress formation. Based on the results achieved, recommendations were given on how to perform the novel single fiber cylinder test