On Some Infinite Convex Invariants

The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions

Analysis and Design of an Adaptive Polynomial Predistorter with the Loop Delay Estimator

Most adaptive linearization circuits for the nonlinear amplifier have a feedback loop that returns the output signal oj'tne eunplifier to the lineurizer. The loop delay of the linearizer most be controlled precisely so that the convergence of the linearizer should be assured lot this Letter a delay control circuit is presented. It is a delay lock loop (ULL) with it modified early-lute gate and can he easily applied to a DSP implementation. The proposed DLL circuit is applied to an adaptive linearizer with the use of a polynomial predistorter, and the simulalion for a 16-QAM signal is performed. The simulation results show that the proposed DLL eliminates the delay between the reference input signal and the delayed feedback signal of the linearizing circuit perfectly, so that the predistorter polynomial coefficients converge into the optimum value and a high degree of linearization is achieved

Bidirectional communication using delay coupled chaotic directly modulated semiconductor lasers

Chaotic synchronization of two directly modulated semiconductor lasers with negative delayed optoelectronic feedback is investigated and this scheme is found to be useful for e±cient bidirectional communication between the lasers. A symmetric bidirec- tional coupling is identified as a suitable method for isochronal synchronization of such lasers. The optimum values of coupling and feedback strength that can provide maxi- mum quality of synchronization are identified. This method is successfully employed for encoding/decoding both analog and digital messages. The importance of a symmetric coupling is demonstrated by studying the variation of decoding efficiency with respect to asymmetric coupling.

Phase effects on synchronization by dynamical relaying in delay-coupled systems

Synchronization in an array of mutually coupled systems with a finite time delay in coupling is studied using the Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by linearizing the equation about the synchronization manifold. The dependence of synchronization on damping parameter, coupling constant, and time delay is studied numerically. The change in the dynamics of the system due to time delay and phase difference between the applied fields is studied. The case where a small frequency detuning between the applied fields is also discussed.

On infinite graphs and related matrices

This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix

Automated synthesis of delay-reduced Reed-Muller universal logic module networks

This paper presents a new approach to implement Reed-Muller Universal Logic Module (RM-ULM) networks with reduced delay and hardware for synthesizing logic functions given in Reed-Muller (RM) form. Replication of single control line RM-ULM is used as the only design unit for defining any logic function. An algorithm is proposed that does exhaustive branching to reduce the number of levels and modules required to implement any logic function in RM form. This approach attains a reduction in delay, and power over other implementations of functions having large number of variables.

RMAC-M: Extending the R-MAC Protocol for an Energy Efficient, Delay Tolerant Underwater Acoustic Sensor Network application with a mobile data mule node

One of the major applications of underwater acoustic sensor networks (UWASN) is ocean environment monitoring. Employing data mules is an energy efficient way of data collection from the underwater sensor nodes in such a network. A data mule node such as an autonomous underwater vehicle (AUV) periodically visits the stationary nodes to download data. By conserving the power required for data transmission over long distances to a remote data sink, this approach extends the network life time. In this paper we propose a new MAC protocol to support a single mobile data mule node to collect the data sensed by the sensor nodes in periodic runs through the network. In this approach, the nodes need to perform only short distance, single hop transmission to the data mule. The protocol design discussed in this paper is motivated to support such an application. The proposed protocol is a hybrid protocol, which employs a combination of schedule based access among the stationary nodes along with handshake based access to support mobile data mules. The new protocol, RMAC-M is developed as an extension to the energy efficient MAC protocol R-MAC by extending the slot time of R-MAC to include a contention part for a hand shake based data transfer. The mobile node makes use of a beacon to signal its presence to all the nearby nodes, which can then hand-shake with the mobile node for data transfer. Simulation results show that the new protocol provides efficient support for a mobile data mule node while preserving the advantages of R-MAC such as energy efficiency and fairness.

Performance of Supply Chain when using selected Coordination Mechanisms

Coordination among supply chain members is essential for better supply chain performance. An effective method to improve supply chain coordination is to implement proper coordination mechanisms. The primary objective of this research is to study the performance of a multi-level supply chain while using selected coordination mechanisms separately, and in combination, under lost sale and back order cases. The coordination mechanisms used in this study are price discount, delay in payment and different types of information sharing. Mathematical modelling and simulation modelling are used in this study to analyse the performance of the supply chain using these mechanisms. Initially, a three level supply chain consisting of a supplier, a manufacturer and a retailer has been used to study the combined effect of price discount and delay in payment on the performance (profit) of supply chain using mathematical modelling. This study showed that implementation of individual mechanisms improves the performance of the supply chain compared to ‘no coordination’. When more than one mechanism is used in combination, performance in most cases further improved. The three level supply chain considered in mathematical modelling was then extended to a three level network supply chain consisting of a four retailers, two wholesalers, and a manufacturer with an infinite part supplier. The performance of this network supply chain was analysed under both lost sale and backorder cases using simulation modelling with the same mechanisms: ‘price discount and delay in payment’ used in mathematical modelling. This study also showed that the performance of the supply chain is significantly improved while using combination of mechanisms as obtained earlier. In this study, it is found that the effect (increase in profit) of ‘delay in payment’ and combination of ‘price discount’ & ‘delay in payment’ on SC profit is relatively high in the case of lost sale. Sensitivity analysis showed that order cost of the retailer plays a major role in the performance of the supply chain as it decides the order quantity of the other players in the supply chain in this study. Sensitivity analysis also showed that there is a proportional change in supply chain profit with change in rate of return of any player. In the case of price discount, elasticity of demand is an important factor to improve the performance of the supply chain. It is also found that the change in permissible delay in payment given by the seller to the buyer affects the SC profit more than the delay in payment availed by the buyer from the seller. In continuation of the above, a study on the performance of a four level supply chain consisting of a manufacturer, a wholesaler, a distributor and a retailer with ‘information sharing’ as coordination mechanism, under lost sale and backorder cases, using a simulation game with live players has been conducted. In this study, best performance is obtained in the case of sharing ‘demand and supply chain performance’ compared to other seven types of information sharing including traditional method. This study also revealed that effect of information sharing on supply chain performance is relatively high in the case of lost sale than backorder. The in depth analysis in this part of the study showed that lack of information sharing need not always be resulting in bullwhip effect. Instead of bullwhip effect, lack of information sharing produced a huge hike in lost sales cost or backorder cost in this study which is also not favorable for the supply chain. Overall analysis provided the extent of improvement in supply chain performance under different cases. Sensitivity analysis revealed useful insights about the decision variables of supply chain and it will be useful for the supply chain management practitioners to take appropriate decisions.