Algebraic curves over finite fields

Algebraïsche krommen over een eindig lichaam is een fascinerend onderwerp binnen de getaltheorie en de algebraïsche meetkunde. Het heeft toepassingen in diverse gebieden, bijvoorbeeld in cryptografie en in coderingstheorie. Dergelijke krommen worden namelijk gebruikt voor het construeren van foutenverbeterende codes en voor het ontwerpen van veilige protocollen voor datacommunicatie. Gemotiveerd door deze toepassingen hebben wiskundigen als Ihara, Serre, Vladut en Drin'feld het maximale aantal punten op krommen bestudeerd bij een vast eindig lichaam. Hier wordt het maximum genomen over alle krommen in een zekere klasse die bepaald wordt door een meetkundige invariant, namelijk het zogeheten geslacht van de kromme. Bovengrenzen voor dit maximum in termen van het geslacht en het eindige lichaam zijn gevonden door Weil en Serre. In zijn proefschrift geeft Afzal Soomro constructies van krommen met veel punten. Als het geslacht 1 of 2 is, levert dit expliciete gevallen waarvoor het maximum wordt bereikt. Voor hoger geslacht noemen we een kromme ‘goed’ als het aantal punten erop minder dan 10% afwijkt van de door Weil en Serre gevonden bovengrens. We blijken in staat, veel ’goede’ krommen te construeren. Dit heeft heel veel data opgeleverd voor de website www.manypoints.org. Tenslotte wordt in het proefschrift voor het geval van geslacht 1 een uitbreiding gegeven van een elementair bewijs afkomstig van Yuri I. Manin (1956) voor een klassiek resultaat van Helmut Hasse (1933) dat een goede bovengrens voor het aantal punten in dit speciale geval levert

Twists of Elliptic Curves

In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence between the twists and the Galois cohomology set $H^1\big(\operatorname{G}_{\overline{K}/K}, \operatorname{Aut}_{\overline{K}}(E)\big)$. The results are illustrated by examples

On coefficient estimates for certain subclasses of bi-univalent functions

We introduce certain subclasses of bi-univalent functions related to the generalized Janowski functions and estimate the general coefficient bound for the newly defined classes. Also, we deduce certain new results and the improvement of known results as special cases of our investigation.Publisher's Versio

Condition Survey for Evaluation of Pavement Condition Index of a Highway

Pavements are major means of highway infrastructure. Maintenance and rehabilitation of these pavements for the required serviceability is a routine problem faced by highway engineers and organizations. Improvement in road management system results in reduction of time and cost, the pavement condition survey plays a big role in the pavement management. The initial phase in setting up a pavement management system (PMS) is road network identification. A vital element of a PMS is the capacity to assess the present condition of a pavement network and anticipation of future condition. The pavement condition index (PCI) is a numerical index generally utilized for the assessment of the operational condition & structural reliability of pavements. Estimation of the PCI is dependent on the results of a visual inspection in which the type, severity, and quantity of distresses are distinguished. In this research, a pavement distress condition rating strategy was utilized to accomplish the goals of this study. The main targets of this research were to categorize the common types of distress that exist on “Lakhi Larkana National Highway (N-105)”, and to estimate the pavement condition index. Using these data, Average PCI for the highway section was calculated. PCI to assess the pavement performance, 10 out of 19 defects were recognized in the pavement, as stated by the PCI method. Results indicated that the common pavement distress types were depressions, polished aggregate, rutting, potholes, block cracking, and alligator cracking

The Impact of Supply Chain Capabilities on Logistic Efficiency for the Construction Projects

Rapid technological advancements force organizations to be more proactive and efficient it operations while previous studies revealed that most of the public sector projects go over in term of time and cost. Although extensive literature is available but only for the private sector, the investigations on the public sector are scarce. After plentiful literature, it has found that timely and sage supply chain is a major hurdle. Various strategies and approaches have been proposed to tackle the situation but after a thorough investigation, it was found that flexibility and collaboration are the topmost influencing factors in improving logistic efficiency. Thus the aim of this study is to empirically verify the positive impact of flexibility and collaboration on logistic efficiency. A questionnaire was adopted and distributed by random sampling to the strategic level of the construction projects in the city of Lahore, Pakistan. Multiple regressions were applied through SPSS. The finding of the study revealed that flexibility contributes 33%, collaboration contributes 35.5% in the logistic efficiency. It can be concluded that construction projects must be flexible and force stakeholders for collaboration. This study added in the frame of knowledge as new findings for public sector projects. This study will help the managers in completing their projects timely and accurately

Electrochemical investigations of unexplored anthraquinones and their DNA binding

The redox behaviour of two potential anticancer anthraquinones, 9,10-anthraquinone and 2-chloromethyl-9,10-anthraquinone was investigated in a wide pH range. Cyclic voltammetry based assay was developed for the assessment of the effect of medium, substituents, potential scan rate and number of scans on the voltammetric response of anthraquinones. The electrode reaction mechanism was suggested on the basis of cyclic and differential pulse voltammetric results. The effect of DNA on anthraquinones was also probed at physiological pH which could lead to further investigation of possible citotoxic activity in vitro. The results revealed that anthraquinones interact with DNA more strongly than the clinically used anticancer drug, epirubicin