Why study translation universals?

Abstract: Research on translation universals has its roots in the need to make generalizations about the features that distinguish translations from non-translations. They go back to the old tradition of negative comments about the failings of typical translations. These comments concern the relations between translations and the target language, and between translations and their source texts. With the rise of descriptive studies, and the use of corpus research methods borrowed from linguistics, the search for the typical features of translations became more systematic. A number of hypotheses about potential universals have been proposed, and tested on different languages and language pairs. Some of them are evidently false; on others, the jury is still out. If some hypotheses continue to be supported by empirical evidence, the question then arises of how they might best be explained. There has been fierce criticism of some of the assumptions underlying the search for universals, including the use of the term 'universal'itself, but the approach has also brought clear methodological benefits.

Polypyrimidine tract-binding protein interacts with coxsackievirus B3 RNA and influences its translation

We have investigated the possible role of trans-acting factors interacting with the untranslated regions (UTRs) of coxsackievirus B3 (CVB3) RNA. We show here that polypyrimidine tract-binding protein (PTB) binds specifically to both 5' and 3' UTRs, but with different affinity. We have demonstrated that PTB is a bona fide internal ribosome entry site (IRES) trans-acting factor (ITAF) for CVB3 RNA by characterizing the effect of partial silencing of FIB ex vivo in He La cells. Furthermore, IRES activity in BSC-1 cells, which are reported to have a very low level of endogenous FIB, was found to be significantly lower than that in He La cells. Additionally, we have mapped the putative contact points of PTB on the 5' and 3' UTRs by an RNA toe-printing assay. We have shown that the 3' UTR is able to stimulate CVB3 IRES-mediated translation. Interestingly, a deletion of 15 nt at the 5' end or 14 rut at the 3' end of the CVB3 3' UTR reduced the 3' UTR-mediated enhancement of IRES activity ex vivo significantly, and a reduced interaction was shown with PTB. It appears that the FIB protein might help in circularization of the CVB3 RNA by bridging the ends necessary for efficient translation of the viral RNA.

Spectral Invariance of SG Pseudo-Differential Operators on L-P(R-n)

We prove the spectral invariance of SG pseudo-differential operators on L-P(R-n), 1 < p < infinity, by using the equivalence of ellipticity and Fredholmness of SG pseudo-differential operators on L-p(R-n), 1 < p < infinity. A key ingredient in the proof is the spectral invariance of SC pseudo-differential operators on L-2(R-n).

Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.

Descriptions of operators in quantum mechanics

The problem of expressing a general dynamical variable in quantum mechanics as a function of a primitive set of operators is studied from several points of view. In the context of the Heisenberg commutation relation, the Weyl representation for operators and a new Fourier-Mellin representation are related to the Heisenberg group and the groupSL(2,R) respectively. The description of unitary transformations via generating functions is analysed in detail. The relation between functions and ordered functions of noncommuting operators is discussed, and results closely paralleling classical results are obtained.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

Inhibition of in Vitro Aminoacylation and Translation by RNA Reactive Antibodies

Antibodies were raised against guanosine-BSA, GMP-BSA and tRNA-mBSA conjugates separately in rabbits. Binding characteristics of these antibodies to various RNAs were studied using a sensitive avidin-biotin micro ELISA. These antibodies inhibited in vitro aminoacylation of tRNA in a dose dependent manner. This inhibition was reversed by the addition of the respective homologous haptens thereby showing the specificity of these antibodies. In vitro translation of endogenous mRNAs in rabbit reticulocyte lysate was also inhibited by these antibodies in a dose dependent manner.

A classification of homogeneous operators in the Cowen-Douglas class

An explicit construction of all the homogeneous holomorphic Hermitian vector bundles over the unit disc D is given. It is shown that every such vector bundle is a direct sum of irreducible ones. Among these irreducible homogeneous holomorphic Hermitian vector bundles over D, the ones corresponding to operators in the Cowen-Douglas class B-n(D) are identified. The classification of homogeneous operators in B-n(D) is completed using an explicit realization of these operators. We also show how the homogeneous operators in B-n(D) split into similarity classes. (C) 2011 Elsevier Inc. All rights reserved.

Optimal polygon placement by translation

Let M be an m-sided simple polygon and N be an n-sided polygon with holes. In this paper we consider the problem of computing the feasible region, i.e., the set of all placements by translation of M so that M lies inside N without intersecting any hole. First we propose an O (mn(2)) time algorithm for computing the feasible region for the case when M is a monotone polygon. Then we consider the general case when M is a simple polygon and propose an O(m(2)n(2)) time algorithm for computing the feasible region. Both algorithms are optimal upto a constant factor.