Efficient Solution of A, x ( k )?= b ( k ) Using A ?1

In this work, we consider the problem of solving , , where b ^(k+1) = f(x ^(k)). We show that when A is a full matrix and , where depends on the specific software and hardware setup, it is faster to solve for by explicitly evaluating the inverse matrix A ⁻¹ rather than through the LU decomposition of A. We also show that the forward error is comparable in both methods, regardless of the condition number of A.     

Bounded Error Schemes for the Wave Equation on Complex Domains

This paper considers the application of the method of boundary penalty terms (SAT) to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell’s equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g., the staggered Yee scheme)—we achieve a decrease of two orders of magnitude in the level of the L₂-error.     

Guaranteeing the Diversity of Number Generators

A major problem in using iterative number generators of the form x_i=f(x_i−1) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is used, and can have devastating cryptanalytic implications. In this paper we define a measure of security, called sequence diversity, which generalizes the notion of cycle-length for noniterative generators. We then introduce the class of counter-assisted generators and show how to turn any iterative generator (even a bad one designed or seeded by an adversary) into a counter-assisted generator with a provably high diversity, without reducing the quality of generators which are already cryptographically strong.     

On Delivery Times in Packet Networks under Adversarial Traffic

We consider packet networks and make use of the "adversarial queuing theory" model [10]. We are interested in the question of guaranteeing that all packets are actually delivered to destination, and of having an upper bound on the delivery times of all packets. Whether this is possible against all adversarial queuing theory rate-1 adversaries was previously posed as an open question [13],[10]. Among other things, we give a queuing policy that guarantees bounded delivery time whenever the rate-1 adversary injects a sequence of packets for which there exists a schedule with a finite upper bound on the delivery times of all packets, and adheres to certain additional conditions. On the negative side we show that there exist rate-1 sequences of packets for which there is no schedule with a finite upper bound on the delivery times of all packets. We thus answer an open question posed by Gamarnik [13]. We further show that delivering all packets while maintaining stability (we coin the term "reliability" for this property) can be done by an offline scheduler whenever the injection of packets is done at rate of at most 1. However, on the other hand, we also show that there is no online protocol (even centralized) that can achieve that property against all rate-1 adversaries. We thus answer an open question of Borodin et al. [10].     

Randomness versus Fault-Tolerance

We investigate the relations between two major properties of multiparty protocols: fault tolerance (or resilience ) and randomness . Fault-tolerance is measured in terms of the maximum number of colluding faulty parties, t , that a protocol can withstand and still maintain the privacy of the inputs and the correctness of the outputs (of the honest parties). Randomness is measured in terms of the total number of random bits needed by the parties in order to execute the protocol. Previously, the upper bound on the amount of randomness required by general constructions for securely computing any nontrivial function f was polynomial both in n , the total number of parties, and the circuit-size C(f) . This was the state of knowledge even for the special case t=1 (i.e., when there is at most one faulty party). In this paper we show that for any linear-size circuit, and for any number t < n/3 of faulty Received 30 April 1998 and revised 3 January 1999 and 1 July 1999     

Dynamic mechanical properties of polystyrene-polydimethylsiloxane blends

It was found that commercial silicone grease incorporated accidentally into polystyrene bars yields a major dynamic mechanical loss peak at ca. ?128°C. This finding was followed up with a study of various polydimethylsiloxanes and silicone rubber, in which up to three peaks were found. In order of increasing temperature (at 1 Hz) these are the glass transition (T_g; ca. ?128°C), crystallization (T_c; ca. ?110°C) and melting peaks (T_m; ca. ?50°C). Hydrocarbon-based greases were also investigated. The results indicate that the methods employed may be of use for the investigation of the dynamic mechanical properties of small amounts of material of varying particle sizes, such as powders of cross-linked polymers, that need not be compatible with, or soluble in, the host matrix. The sensitivity of the method is such at a 1 percent by weight contamination of silicone grease in polystyrene gives a loss tangent peak of at least 0.002 above background, and emphasizes the necessary care to be taken during sample preparation to exclude unwanted substances.     

Organocatalytic Application of Direct Organo-Functionalized Mesoporous Catalysts Prepared by Microwave

The organic functional groups such as primary and quaternary amine, sulfonic acid, and amino acid, especially l-proline, have been tried to immobilize onto mesoporous materials by the direct synthesis method using microwave. Microwave induced direct functionalization enabled to get well ordered mesoporous structures and stable organic tethered groups with enhanced hydrothermal stability due to more hydrophobic surfaces as well as enhanced activity. The method is also useful for overcoming several shortcomings in the post-synthesis grafting method which suffers from pore blocking at the aperture, and difficulties in controlling the as obtained from the direct co-condensation method had their functional groups spatially loadings, as well as the dispersion of active sites. The organo-functionalized mesoporous silica dispersed on the surface which could play roles as single site catalysts. Direct tethering of organic functional groups was preferably synthesized by microwave, gave morphological control and illustrated superiority in some organocatalytic application such as Knoevenagel and Henry reactions base catalytic reaction, Claisen–Schmidt condensation, and diethyl malonate addition reactions.     

Solid-state photoelectrochemical device based on poly(3-hexylthiophene) and an ion conducting polymer electrolyte, amorphous poly(ethylene oxide) complexed with I3/I redox couple

The photoelectrochemical properties of a solid-state photoelectrochemical cell (PEC) based on poly(3-hexylthiophene), P3HT, and an ion-conducting polymer electrolyte, amorphous poly(ethylene oxide), POMOE, complexed with I₃⁻/I⁻ redox couple has been constructed and studied. The current–voltage characteristics in the dark and under white light illumination, transient photocurrent and photovoltage studies, photocurrent action spectra for front and back side illuminations and an open-circuit voltage and short-circuit current dependence on light intensity have been studied. An open-circuit voltage of 130 mV and a short-circuit current of 0.47 μA cm⁻² were obtained at light intensity of 100 mW/cm². IPCE% of 0.024% for front side illumination (ITO/PEDOT) and IPCE% of 0.003% for backside illumination (ITO/P3HT) were obtained.