Abstract:
Colombeau's generalized functions are used to adapt the distributional approach to singular hypersurfaces in general relativity with signature change. Equations governing the dynamics of singular hypersurface is obtained and it is shown that matching leads to de Sitter space for the Lorentzian region. The matching is possible for different sections of the de Sitter hyperboloid. A relation between the radius of $S^4$, as the Euclidean manifold, and the cosmological constant leading to inflation after signature change is obtained.

Abstract:
We consider the directed first passage percolation model on ${\bf Z}^2$. In this model, we assign independently to each edge $e$ a passage time $t(e)$ with a common distribution $F$. We denote by $\vec{T}({\bf 0}, (r,\theta))$ the passage time from the origin to $(r, \theta)$ by a northeast path for $(r, \theta)\in {\bf R}^+\times [0,\pi/2]$. It is known that $\vec{T}({\bf 0}, (r, \theta))/r$ converges to a time constant $\vec{\mu}_F (\theta)$. Let $\vec{p}_c$ denote the critical probability for oriented percolation. In this paper, we show that the time constant has a phase transition divided by $\vec{p}_c$, as follows: (1) If $F(0) < \vec{p}_c$, then $\vec{\mu}_F(\theta) >0$ for all $0\leq \theta\leq \pi/2$. (2) If $F(0) = \vec{p}_c$, then $\vec{\mu}_F(\theta) >0$ if and only if $\theta\neq \pi/4$. (3) If $F(0)=p > \vec{p}_c$, then there exists a percolation cone between $\theta_p^-$ and $\theta_p^+$ for $0\leq \theta^-_p< \theta^+_p \leq \pi/2$ such that $\vec{\mu} (\theta) >0$ if and only if $\theta\not\in [\theta_p^-, \theta^+_p]$. Furthermore, all the moments of $\vec{T}({\bf 0}, (r, \theta))$ converge whenever $\theta\in [\theta_p^-, \theta^+_p]$. As applications, we describe the shape of the directed growth model on the distribution of $F$. We give a phase transition for the shape divided by $\vec{p}_c$.

Abstract:
Ongoing change is an inevitable part of the current organisational context. Change management practices are oftencited as a reason for resistance to change, and as a cause of stress for individuals during change interventions. A qualitative study was undertaken in a technical division of a large South African organisation to explore the individual experiences of employees in the face of constant organisational change. Grounded theory analysis confirmed that constant organisational change and the related change management practices were indeed a source of unpleasant individual experience for employees at the time. Yet, no serious long-term effects of stress were evident. It is suggested that Strümpfer’s (1983–2000) work on salutogenesis and fortigenesis may be useful in explaining the outcome. Further research incorporating larger sample sizes and multiple triangulation methods in the data gathering process is recommended. Opsomming Kontinue verandering is ’n onvermydelike deel van die huidige organisasiekonteks. Veranderingsbestuurspraktyke word gereeld geopper as ’n rede vir die weerstand teen verandering asook die oorsaak van spanning by individue tydens veranderingsintervensies. ‘n Kwalitatiewe studie in die tegniese divisie van ’n groot Suid-Afrikaanse maatskappy is onderneem om die individuele ervaring van werknemers tydens konstante organisasieverandering te ondersoek. ’n Begronde teorie- ontleding het aangetoon dat konstante organisasieverandering en die gepaardgaande veranderingsbestuurspraktyke inderdaad ’n bron van onaangename ervaring vir werknemers is. Desnieteenstaande was ernstige langtermyn gevolge van spanning nie waarneembaar nie . Dit word aangevoer dat Strümpfer (1983–2000) se werk oor salutogenese en fortigenese nuttig mag wees in die verklaring van die bevindings. Verdere navorsing wat groter steekproefgroottes en intermetodiese kruisvalidering tydens die data-insamelingsproses insluit, word voorgestel.

Abstract:
We proposes an alternative model of duality symmetry, based on the previously obtained divergence theory, including an scalar field, an internal vector and a metric signature. At some small scale an effective scalar field equation has appeared whose potential acts like a Higgs one, where the metric signature plays the role of an order parameter. Non-vanishing Vacuum condensation of this Higgs field occurs once a signature change from Euclidean to Lorentzian is formed. The mass scale of Higgs field excitations around this vacuum may contribute, in the Lorentzian sector, to the cosmological constant, in agreement with observations.

Abstract:
The theme of this year’s LIBER conference emphasises the changing missions libraries envisage for the decade ahead and the different skills that are needed to fulfil these missions. However, change - a word we are hearing often during this week - does not materialise in a void, it does not just happen. There are reasons for the changing world in which libraries need to function and I would like to start by looking at a few of them.

Abstract:
Using the concept of real tunneling configurations (classical signature change) and nucleation energy, we explore the consequences of an alternative minimization procedure for the Euclidean action in multiple-dimensional quantum cosmology. In both standard Hartle-Hawking type as well as Coleman type wormhole-based approaches, it is suggested that the action should be minimized among configurations of equal energy. In a simplified model, allowing for arbitrary products of spheres as Euclidean solutions, the favoured space-time dimension is 4, the global topology of spacelike slices being ${\bf S}^1 \times {\bf S}^2$ (hence predicting a universe of Kantowski-Sachs type). There is, however, some freedom for a Kaluza-Klein scenario, in which case the observed spacelike slices are ${\bf S}^3$. In this case, the internal space is a product of two-spheres, and the total space-time dimension is 6, 8, 10 or 12.

Abstract:
The modified quark-meson coupling model, which features a density dependent bag constant and bag radius in nuclear matter, is checked against the EMC effect within the framework of dynamical rescaling. Our emphasis is on the change in the average bag radius in nuclei, as evaluated in a local density approximation, and its implication for the rescaling parameter. We find that when the bag constant in nuclear matter is significantly reduced from its free-space value, the resulting rescaling parameter is in good agreement with that required to explain the observed depletion of the structure functions in the medium Bjorken $x$ region. Such a large reduction of the bag constant also implies large and canceling Lorentz scalar and vector potentials for the nucleon in nuclear matter which are comparable to those suggested by the relativistic nuclear phenomenology and finite-density QCD sum rules.

Abstract:
Facility location problems are captivating both from theoretical and practical point of view. In this paper, we study some fundamental facility location problems from the space-efficient perspective. Here the input is considered to be given in a read-only memory and only constant amount of work-space is available during the computation. This {\em constant-work-space model} is well-motivated for handling big-data as well as for computing in smart portable devices with small amount of extra-space. First, we propose a strategy to implement prune-and-search in this model. As a warm up, we illustrate this technique for finding the Euclidean 1-center constrained on a line for a set of points in $\IR^2$. This method works even if the input is given in a sequential access read-only memory. Using this we show how to compute (i) the Euclidean 1-center of a set of points in $\IR^2$, and (ii) the weighted 1-center and weighted 2-center of a tree network. The running time of all these algorithms are $O(n~poly(\log n))$. While the result of (i) gives a positive answer to an open question asked by Asano, Mulzer, Rote and Wang in 2011, the technique used can be applied to other problems which admit solutions by prune-and-search paradigm. For example, we can apply the technique to solve two and three dimensional linear programming in $O(n~poly(\log n))$ time in this model. To the best of our knowledge, these are the first sub-quadratic time algorithms for all the above mentioned problems in the constant-work-space model. We also present optimal linear time algorithms for finding the centroid and weighted median of a tree in this model.

Abstract:
In this paper we derive a bound on the rate of change of the gravitational constant G coming from the pulsating white dwarf G117-B15A. This star is a ZZ Ceti pulsator extensively studied with astroseismological techniques for last three decades. The most recent determination of {\dot P} = (2.3 \pm 1.4) * 10^{-15} s/s^{-1} for the 215.2s fundamental mode agrees very well with predictions of the best fit theoretical model. The rate of change of the oscillation period can be explained by two effects: the cooling (dominant factor) and change of gravitational binding energy (residual gravitational contraction). Since the white dwarfs are pulsating in g-modes whose frequencies are related to the Brunt-Vaisala frequency (explicitly dependent on G) observational determination of the change of the period (more precisely the difference between observed and calculated \dot P) can be used to set the upper bound on the rate of change of G. In the light of the current data concerning G117-B15A we derive the following bound: |{\frac {\dot G}{G}}| \leq 4.10 \times 10^{-10} yr^{-1}. Our result is model independent in the sense that it does not need to invoke a concrete physical theory (such like Brans-Dicke theory)underlying the temporal variability of G. We also demonstrate that varying gravitational constant G does not modify cooling of white dwarfs in a significant way. This result implies that some earlier claims present in the literature that varying G can be reflected in the WD luminosity function are not correct.

Abstract:
We propose a noninvasive method to estimate the time constant. The calculation of this factor permits us to understand the pressure variations of the inner ear and also predict the behavior of the flow resistance of the cochlear aqueduct. A set of mathematical relationships incorporating the intralabyrinthine pressure, the intracranial pressure, and the time constant was applied. The modeling process describes the hydrodynamic effects of the cerebrospinal fluid in the intralabyrinthine fluid space, where the input and output of the created model are, respectively, the sinusoidal variation of the respiration signal and the distortion product of otoacoustic emissions. The obtained results were compared with those obtained by different invasive techniques. A long time constant was detected each time when the intracranial pressure increased; this phenomenon is related to the role of the cochlear aqueduct described elsewhere. The interpretation of this model has revealed the ability of these predictions to provide a greater precision for hydrodynamic variation of the inner ear, consequently the variation of the dynamic process of the cerebrospinal fluid.