Suslin’s algorithms for reduction of unimodular rows

A well-known lemma of Suslin says that for a commutative ring $A$ if $(v_1\left(X\right),\dots ,v_n\left(X\right))\in {\left(A\left[X\right]\right)}^n$ is unimodular where $v_1$ is monic and $n\ge 3$, then there exist ${\gamma }_1,\dots ,{\gamma }_{\ell }\in E_{n-1}\left(A\left[X\right]\right)$ such that the ideal generated by $\mathrm{Res}(v_1,e_1.{\gamma }_1{}^t(v_2,\dots ,v_n)),\dots ,\mathrm{Res}(v_1,e_1.{\gamma }_{\ell }{}^t(v_2,\dots ,v_n))$ equals $A$. This lemma played a central role in the resolution of Serre’s Conjecture. In the case where $A$ contains a set $E$ of cardinality greater than $deg{v}_1+1$ such that $y-y^{\prime }$ is invertible for each $y\ne y^{\prime }$ in $E$, we prove that the ${\gamma }_i$ can simply correspond to the elementary operations $L_1\to L_1+y_i{\sum }_{j=2}^{n-1}{u}_{j+1}{L}_j$, $1\le i\le \ell =deg{v}_1+1$, where $u_1{v}_1+\cdots +u_n{v}_n=1$. These efficient elementary operations enable us to give new and simple algorithms for reducing unimodular rows with entries in $K[X_1,\dots ,X_k]$ to ${}^t(1,0,\dots ,0)$ using elementary operations in the case where $K$ is an infinite field. Another feature of this paper is that it shows that the concrete local–global principles can produce competitive complexity bounds.     

Reliability analysis of fault tolerant pipeline ring networks

In this paper the application of software implemented voting (ring structures) to pipeline networks is presented. The TMR characterization of the ring is extended to various topologies such as trees, cascade and locally voted pipelines. Both the aspects of reliability and data flow are analyzed in detail.     

Healing DNA Self-Assemblies Using Punctures

In self-assembly, individual components (commonly referred to as tiles) have sufficient infor mation to build templates for structures such as lat tices for two-dimensional scaffolds. Tile sets that can heal (fully or partially) an erroneous DNA assembly have been proposed. Healing requires growth to be restarted such that erroneous tiles can be removed and the correct tiles can bind to the aggregate. Punctures have been proposed for this purpose; in this paper, a puncture is intentionally induced in the self-assembly to restart the growth process. The goal of this paper is to characterize an intentionally induced puncture (and its relevant properties) on an erroneous tile site in the grown crystal as part of a healing process. This allows to propagate any newly generated error away from the source of growth (i.e. the seed tile), such that self-assembly can continue along specific directions. Different types of puncture are considered with respect to healing and related features, such as growth direction, error and aggregate types. Punctures are analyzed using a new characterization and metric; different tile sets are investigated in detail for healing of a DNA self-assembly.

Gelcasting of dense and porous ceramics by using a natural gelatine

An improved gel-casting procedure was successfully exploited to produce porous ceramic bodies having controlled porosity features in terms of mean pore size, total pore volume as well as pore geometry. The gel-casting process in which a natural gelatine for food industry is used as gelling agent was firstly set-up to prepare dense alumina and zirconia components. Then, commercial PE spheres, sieved to select proper dimensional ranges, were added to the starting slurries as pore-forming agent. Both alumina and zirconia porous bodies were then produced, having a porosity ranging between 40 and 50 vol%. The fired components were characterised by spherical pores surrounded by highly dense ceramic walls and struts, having a homogeneous and fine microstructure. Their mean pore size was directly dependent on the sieved fraction of the starting PE spheres selected as pore-forming phase.     

Machine Precision Evaluation of Singular and Nearly Singular Potential Integrals by Use of Gauss Quadrature Formulas for Rational Functions

A new technique for machine precision evaluation of singular and nearly singular potential integrals with 1/R singularities is presented. The numerical quadrature scheme is based on a new rational expression for the integrands, obtained by a cancellation procedure. In particular, by using library routines for Gauss quadrature of rational functions readily available in the literature, this new expression permits the exact numerical integration of singular static potentials associated with polynomial source distributions. The rules to achieve the desired numerical accuracy for singular and nearly singular static and dynamic potential integrals are presented and discussed, and several numerical examples are provided.     

Precision Measurements of Time Characteristics of ETL9351 Photomultipliers

The measured characteristics of 2200 photomultiplier tubes (PMTs) for the future Borexino experiment are considered to provide the most complete information for evaluating the time characteristics of ETL9351 PMTs with a high precision. The unique time characteristics of the apparatus used and the large statistics obtained during the tests of the PMTs allow the fine structure of the PMT time response to be resolved. A method for obtaining the probability density function of the single-photoelectron counting from the experimental data is proposed and used to derive the PMT average characteristics. For the first time, an analytical model is proposed to describe all the features of the single-photoelectron PMT time response. The origin of small-amplitude pulses, as well as the shape of the time spectra of PMT, is explained.     

Optimization of properties in a rubber compound containing a ternary polymer blend using response surface methodology

In order to find the best combination of three synthetic rubbers, that is, styrene‐butadiene rubber (SBR) grade 1712, SBR grade 1721 and high‐1,4‐cis polybutadiene, that produce a compound with specific end‐use properties, a statistical experimental design is proposed in this work. The design consists of ten mixtures containing specific amounts of total styrene and BR content. A number of properties are tested in each mixture, selecting those related to requirements for the tread of a high performance tire: glass transition temperature (T_g), the ratio between the viscous modulus and the elastic modulus (tanδ@60 °C), Mooney viscosity, and the tensile properties. The values obtained for each property are fit to statistically significant models, obtaining the respective response surfaces. These are next used to define a desirable formulation with the optimal ratio of each rubber, and finally the optimized formulation is validated by comparing the experimental and predicted values for each modeled property. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46548.     

Analysis of punctures in DNA self-assembly under forward growth

This paper deals with the characterization and analysis of intentionally induced punctures on a DNA self-assembly. Based on forward growth, punctures are utilized to remove errors in DNA tiles from the self-assembly. Initially, a Markov model is proposed by considering different types of punctures under various bonding conditions in the tiles. For different values of on and off rates (as corresponding to the parameters G(se) and G(mc)), it is shown that the proposed models can assess the types of puncture for removing mismatched tiles as errors. Subsequently, a novel model of puncturing is introduced to establish the condition by which a generic aggregate can utilize punctures for error resilience. It is proven that by using the correct puncture(s), errors as frozen mismatched tiles are moved toward the boundaries, thus ensuring the generation of the target assembly and ease in removal of the errors. As an example, the Sierpinski tile set is analyzed based on the proposed models to fully assess the appropriate type of puncture for this pattern. Simulation results are provided as evidence that the proposed models are effective.     

Design verification of FPGA implementations

This approach uses the criterion of equivalent classes to establish the equivalence between two circuits and designs. Combining simulation and automatic test pattern generation, it exploits similarities among designs to assess logical equivalence quickly and reliably