Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

A new dc-dc double-boost typology for enhancing the voltage ratio

Abstract: In this paper anew boost topology is proposed. The circuit is similar with two parallel boost dc-to-dc converters, but the two inductors are charged in parallel and release energy in series, thus enhancing the voltage boost ratio. After a short analysis of the circuit, a comparative study with other classic boost converter (single boost and twocascade) is presented. The simulation results show a net improvement of the boost ratio for the new proposed topology

Double-boost DC to DC converter

Abstract In this paper anew boost topology is proposed. The circuit is similar with two parallel boost dc-to-dc converters, but the two inductors are charged in parallel and release energy in series, thus enhancing the voltage boost ratio. After a short analysis of the circuit, a comparative study with other classic boost converter (single boost and two-cascade) is presented. The simulation results show a net improvement of the boost ratio for the new proposed topology

Moontlike nuwe lig op die Paulus-gemeentes

Prof. Fika J. van Rensburg werk die afgelope paar jaar meer aan 'n internasionale projek om 'n nuutontdekte Griekse manuskrip uit die eerste eeu vir navorsing toeganklik te maak. Hy het gedurende November 1995 as deel van die projek die jaarvergadering van die Society of biblical Literature in Philadelphia in die VSA bygewoon. Hy is finansieel ondersteun deur die Raad vir Geesteswetenskaplike Navorsing, die PU vir CHO en die Teologiese Skool Potchefstroom. In die onderstaande mededeling gee hy oorsigtelik inligting oor die projek in die algemeen

Die relevansievlak(ke) van Galasiërs 3:28 vir die hedendaagse Suid-Afrikaanse samelewing

Galations 3:28 has been used by various people, represting different viewpoints, to motivate their positions in terms of a variety of social problems in present-day South African society. The aim of this article is to determine the levels of relevance of this verse for South African problems, especially those relating to intergroup relations. This is done by giving an exegetical and hermeneutical account of the verse. In this way the article aims to construct the meaning which Galatians 3:28 would have had for its first readers/hearers, by transporting its present-day readers to its original context, and assisting them to interpret it from that perspective. The article concludes by proposing a concise formulation of God's revelation for the South African context by means of an interpretation of this verse

Fresh look at randomly branched polymers

We develop a new, dynamical field theory of isotropic randomly branched polymers, and we use this model in conjunction with the renormalization group (RG) to study several prominent problems in the physics of these polymers. Our model provides an alternative vantage point to understand the swollen phase via dimensional reduction. We reveal a hidden Becchi-Rouet-Stora (BRS) symmetry of the model that describes the collapse ($\theta$-)transition to compact polymer-conformations, and calculate the critical exponents to 2-loop order. It turns out that the long-standing 1-loop results for these exponents are not entirely correct. A runaway of the RG flow indicates that the so-called $\theta^\prime$-transition could be a fluctuation induced first order transition.Comment: 4 page

Another case of discrepancies when evaluating power theories using real data

Abstract: Most non-sinusoidal power theories have been developed from theoretical techniques, as well as relying on hypothetical and experimental networks to highlight the advantages of each. The drawback of the power theories is that no single one has been universally accepted as a benchmark for other developments. This paper will however show this weakness by means of evaluating two power theories in the time domain, using real recorded data

Self-tuning curing oven control

Abstract: Certain modern materials used in manufacturing require a specific temperature profile during the curing process to produce the desired characteristics (such as hardness). Classically, to obtain optimum control of an oven, a series of trials should be embarked on to accurately determine the coefficients of the regulator. This paper proposes a method to automatically determine the optimum parameters of the controller during the first heating process. The method has been implemented and validated in a small curing oven (3 kW). The step response and steady state error obtained were acceptable

Experimental and theoretical study of vibrations of a cantilevered beam using a ZnO piezoelectric sensor

Piezoelectric sensors can measure vibrations of solid structures very accurately. A model of a cantilevered beam, with a ZnO film on one side is presented. Both viscous and internal damping are considered. The output of the sensor is modeled and matched with experimental results by adjusting the damping parameters. A theoretical formulation for damage is introduced. Experimental results for a damaged beam confirm the shift in frequencies to lower values. The model is used to identify the extent of the damage