Localisation of discrete change in a transformer winding: a network-function-loci approach

An entirely different approach for localisation of winding deformation based on terminal measurements is presented. Within the context of this study, winding deformation means, a discrete and specific change externally imposed at a particular position on the winding. The proposed method is based on pre-computing and plotting the complex network-function loci e.g. driving-point impedance (DPI)] at a selected frequency, for a meaningful range of values for each element (increasing and decreasing) of the ladder network which represents the winding. This loci diagram is called the nomogram. After introducing a discrete change, amplitude and phase of DPI are measured. By plotting this single measurement on the nomogram, it is possible to estimate the location and identify the extent of change. In contrast to the existing approach, the proposed method is fast, non-iterative and yields reasonably good localisation. Experimental results for actual transformer windings (interleaved and continuous disc) are presented.

Special Issue: Engineering applications of representations of function, Part 1

In engineering design, the end goal is the creation of an artifact, product, system, or process that fulfills some functional requirements at some desired level of performance. As such, knowledge of functionality is essential in a wide variety of tasks in engineering activities, including modeling, generation, modification, visualization, explanation, evaluation, diagnosis, and repair of these artifacts and processes. A formal representation of functionality is essential for supporting any of these activities on computers. The goal of Parts 1 and 2 of this Special Issue is to bring together the state of knowledge of representing functionality in engineering applications from both the engineering and the artificial intelligence (AI) research communities.

Variants of Miyachi�s Theorem for Nilpotent lie Groups

We formulate and prove two versions of Miyachi�s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi�s theorem for the group Fourier transform.

Qualitative theorem proving in linear constraints

We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take place through the elimination of middle terms, and because the computational complexity of the proof is not an issue. Indeed what we need is the existence of the proof and not its mechanization. In this paper, we treat the linear case and illustrate the power of this paradigm by giving extremely simple proofs of two central theorems in the complexity and geometry of linear programming.

Variants Of Miyachi’S Theorem For Nilpotent Lie Groups

We formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.

The carboxy terminal WD domain of the pre-mRNA splicing factor Prp17p is critical for function

In Saccharomyces cerevisiae, Prp17p is required for the efficient completion of the second step of pre-mRNA splicing. The function and interacting factors for this protein have not been elucidated. We have performed a mutational analysis of yPrp17p to identify protein domains critical for function. A series of deletions were made throughout the region spanning the N-terminal 158 amino acids of the protein, which do not contain any identified structural motifs. The C-terminal portion (amino acids 160–455) contains a WD domain containing seven WD repeats. We determined that a minimal functional Prp17p consists of the WD domain and 40 amino acids N-terminal to it. We generated a three-dimensional model of the WD repeats in Prp17p based on the crystal structure of the [beta]-transducin WD domain. This model was used to identify potentially important amino acids for in vivo functional characterization. Through analysis of mutations in four different loops of Prp17p that lie between [beta] strands in the WD repeats, we have identified four amino acids, 235TETG238, that are critical for function. These amino acids are predicted to be surface exposed and may be involved in interactions that are important for splicing. Temperature-sensitive prp17 alleles with mutations of these four amino acids are defective for the second step of splicing and are synthetically lethal with a U5 snRNA loop I mutation, which is also required for the second step of splicing. These data reinforce the functional significance of this region within the WD domain of Prp17p in the second step of splicing.

Filtered density function for large eddy simulation of turbulent reacting flows

A methodology termed the “filtered density function” (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Itô-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). These comparative assessments are conducted by implementations of all three schemes (FDF, DNS and LES-FD) in a temporally developing mixing layer and a spatially developing planar jet under both non-reacting and reacting conditions. In non-reacting flows, the Monte Carlo solution of the FDF yields results similar to those via LES-FD. The advantage of the FDF is demonstrated by its use in reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. The FDF results show a much closer agreement with filtered DNS results. © 1998 American Institute of Physics.

The single ring theorem

We study the empirical measure LA of the eigenvalues of nonnormal square matrices of the form A(n) = U(n)T(n)V(n), with U(n), V(n) independent Haar distributed on the unitary group and T(n) diagonal. We show that when the empirical measure of the eigenyalues of T(n) converges, and T(n) satisfies some technical conditions, L(An) converges towards a rotationally invariant measure mu on the complex plane whose support is a single ring. In particular, we provide a complete proof of the Feinberg-Zee single ring theorem [6]. We also consider the case where U(n), V(n) are independently Haar distributed on the orthogonal group.

Chimeras of Escherichia coli and Mycobacterium tuberculosis Single-Stranded DNA Binding Proteins: Characterization and Function in Escherichia coli

Single stranded DNA binding proteins (SSBs) are vital for the survival of organisms. Studies on SSBs from the prototype, Escherichia coli (EcoSSB) and, an important human pathogen, Mycobacterium tuberculosis (MtuSSB) had shown that despite significant variations in their quaternary structures, the DNA binding and oligomerization properties of the two are similar. Here, we used the X-ray crystal structure data of the two SSBs to design a series of chimeric proteins (m beta 1, m beta 1'beta 2, m beta 1-beta 5, m beta 1-beta 6 and m beta 4-beta 5) by transplanting beta 1, beta 1'beta 2, beta 1-beta 5, beta 1-beta 6 and beta 4-beta 5 regions, respectively of the N-terminal (DNA binding) domain of MtuSSB for the corresponding sequences in EcoSSB. In addition, m beta 1'beta 2(ESWR) SSB was generated by mutating the MtuSSB specific `PRIY' sequence in the beta 2 strand of m beta 1'beta 2 SSB to EcoSSB specific `ESWR' sequence. Biochemical characterization revealed that except for m beta 1 SSB, all chimeras and a control construct lacking the C-terminal domain (Delta C SSB) bound DNA in modes corresponding to limited and unlimited modes of binding. However, the DNA on MtuSSB may follow a different path than the EcoSSB. Structural probing by protease digestion revealed that unlike other SSBs used, m beta 1 SSB was also hypersensitive to chymotrypsin treatment. Further, to check for their biological activities, we developed a sensitive assay, and observed that m beta 1-beta 6, MtuSSB, m beta 1'beta 2 and m beta 1-beta 5 SSBs complemented E. coli Delta ssb in a dose dependent manner. Complementation by the m beta 1-beta 5 SSB was poor. In contrast, m beta 1'beta 2(ESWR) SSB complemented E. coli as well as EcoSSB. The inefficiently functioning SSBs resulted in an elongated cell/filamentation phenotype of E. coli. Taken together, our observations suggest that specific interactions within the DNA binding domain of the homotetrameric SSBs are crucial for their biological function.

An analogue of the Wiener Tauberian Theorem for the Heisenberg Motion group

We show that the Wiener Tauberian property holds for the Heisenberg Motion group TnB

Polynomial Approximation, Local Polynomial convexity, and Degenerate CR Singularities- II

We provide some conditions for the graph of a Holder-continuous function on (D) over bar, where (D) over bar is a closed disk in C, to be polynomially convex. Almost all sufficient conditions known to date - provided the function (say F) is smooth - arise from versions of the Weierstrass Approximation Theorem on (D) over bar. These conditions often fail to yield any conclusion if rank(R)DF is not maximal on a sufficiently large subset of (D) over bar. We bypass this difficulty by introducing a technique that relies on the interplay of certain plurisubharmonic functions. This technique also allows us to make some observations on the polynomial hull of a graph in C(2) at an isolated complex tangency.