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The EUREF permanent network (EPN) is a network of continuously operating global navigation satellite system (GNSS) stations, primarily installed for reference frame maintenance. In order to ensure the long term reliability of the EPN products, a thorough station performance monitoring has been initiated and carried out in addition to the routine GNSS data management, processing and analysis. This paper addresses the main factors influencing the quality of the coordinate time series in a permanent GNSS network. Relevant examples, based on the EPN experience are given, the analysis strategy is introduced, the estimated coordinate offsets are published and the importance of this analysis for site velocity estimation is demonstrated. The results are derived from the analysis of the EPN weekly combined solutions covering the period from 1996 to 2003. Our target is the identification, interpretation and elimination of offsets and outliers present in the EPN coordinate time series in order to estimate reliable coordinates and velocities and consequently maintain a high quality kinematic reference network. [ABSTRACT FROM AUTHOR]

Quantum error prevention strategies will be required to produce a scalable quantum computing device and are of central importance in this regard. Progress in this urea has been quite rapid in the past few years. In order to provide an overview of the achievements in this area, we discuss the three major classes of error prevention strategies, the abilities of these methods and the shortcomings. We then discuss the combinations of these strategies which have recently been proposed in the literature. Finally, we present recent results in reducing errors on encoded subspaces using decoupling controls. We show how to generally remove mixing of an encoded subspace with external states (termed leakage errors) using decoupling controls. Such controls are known as 'leakage elimination operations' or 'LEOs'. [ABSTRACT FROM AUTHOR]

Abstract: β-Trifluoromethylated enaminones 1 were prepared stereospecifically or high stercoselectively in 31–92% yields from the reaction of Weinreb amides with trifluoropropynyl lithium, followed by quenching with H2O in the presence of amine derivatives. β-Trifluoromethylated enaminone 1a was reacted with aryl or alkynyl Grignard reagents to give Michael addition products 5 at 0°C, whereas addition–elimination adducts, β-aryl (or alkynyl)-β-trifluoromethylated enones 6, were obtained stereospecifically in 50–92% yields after stirring at room temperature for several hours. [Copyright &y& Elsevier]

Abstract: An easy and general sequenced elimination/reduction or elimination/cyclopropanation process promoted by samarium diiodide or/and CH2I2/Sm provide an efficient method for synthesising 2,3-dideuterioamides 3 or cyclopropanamides 8, respectively. The transformations take place in high yields and with total or high selectivity from the easily available 2,3-epoxyamides. [Copyright &y& Elsevier]

Using the classical Lazard's elimination theorem, we obtain a decomposition theorem for Lie algebras defined by generators and relations of a certain type. [ABSTRACT FROM AUTHOR]

Addition of BF3·OEt2 to ethereal solutions of the Ni(ll) β-diketiminates (Me2NN]Ni(F1)(2,4-lutidine) (R = Et (1), Pr (2)) allows the isolation of the neutral β-H agostic monoalkyls (Me2NN]Ni(R) (R = Et (3), Pr (4)). X-ray studies of primary alkyls 3 and 4a reveal acute Ni-Cα-Cβ angles with short Ni-Cβ distances, indicating structures along the β-H elimination pathway. Positional disorder of the alkyl group in the X-ray structure of 4 corresponds to partial (22%) occupancy by the secondary alkyl [Me2NN)Ni(CHMe2) (4b). Variable-temperature NMR spectra of 3 and 4 reveal fluxional behavior that result from β-H elimination, in-plane rotation of the β-CH3 group, and a tetrahedral triplet structure for 3 that were investigated by density functional theory calculations at the Becke3LYP/6-31 G* level of theory without simplifications on the β-diketiminate ancillary ligand. Calculations support low temperature NMR studies that identify the linear β-H agostic propyl isomer 4a as the ground state with the branched β-H agostic isomer 4b slightly higher in energy. NMR studies and calculations show that the β-agostic 3 reluctantly coordinates ethene and that 3 is the ground state for this ethylene oligomerization catalyst. The thermodynamic isotope effect KH/KD = 1.3(2) measured for the loss of 2,4-lutidine from 1 to form β-agostic 3 was also examined by DFT calculations. [ABSTRACT FROM AUTHOR]

We consider a four-dimensional model in which the field strength associated with a vector gauge field is coupled directly to an antisymmetric tensor field and a pseudoscalar mass term for the tensor field appears. Analysis of the constraint structure of the model shows that the only dynamical degrees of freedom are the two transverse polarizations of the vector field. Tertiary constraints arise in this discussion. Explicit elimination of non-physical degrees of freedom is performed in a particular reference frame. Propagators are computed in a Feynman-like gauge. Both an Abelian model and its non-Abelian extension are considered. [Copyright &y& Elsevier]

C–Si reductive elimination from Pt(R)(SiPh3)(PMe3)2 (R=Me, Pr) was theoretically studied with the density functional theory. For comparisons with the experiment, substitution of PMe3 with diphenylacetylene was taken into account. The calculated activation barriers in the C–Si elimination step after the ligand exchange were 22.0 and 28.9 kcal mol-1 for R=Me and Pr, respectively, which explains the reactivity difference reported experimentally. In order to analyze the energy difference, we optimized transition states of several model complexes, and examined the influence of the steric repulsion between R and the other ligands. Comparisons of the geometries and the barrier heights reveal that the steric repulsion and the Si–alkyl bond energy are important factors controlling the reaction rate. [Copyright &y& Elsevier]

The unimolecular fragmentation of metastable anisole dications is studied by tandem-mass spectrometry. Permutations of OH, OCH3, and NH2 substituents as well as extensive labeling experiments are used as probes to unravel the mechanisms of the various fragmentation pathways observed. The main channel corresponds to methyl ion elimination, which leads to an energetically favorable charge separation (“Coulomb explosion”). Loss of a neutral CO molecule forms another important branch, and the expelled CO has incorporated a carbon atom from the phenyl ring of anisole. Substitution of the anisole dication with OH, OCH3, and NH2 groups results in more specific fragmentations. Ortho- and para-substitutions lead to preferential methyl ion elimination, whereas meta-substitution favors CO loss. The substituent effects are also reflected in pronounced changes in the apparent kinetic isotope effects upon substitution of OCH3 by OCD3. On the basis of the various experimental findings and some explorative DFT calculations, possible mechanisms for the skeletal rearrangements prior to CO elimination are proposed. [ABSTRACT FROM AUTHOR]

A direct ab initio dynamics study is carried out for three channels of the unimolecular reaction of fluoromethoxy, CH2FO. The minimum energy paths (MEPs) of the three channels are computed with the MPW1K/6-31+G(d,p) method. The geometries, harmonic vibrational frequencies, energies, and enthalpies of all stationary points are calculated at the MPW1K and QCISD levels of theory in conjunction with the 6-31+G(d,p) basis set. The energies of stationary points and the points along MEP for each channel are further refined by using single-point multilevel energy calculations. The rate constants are evaluated by means of the conventional transition state theory (TST), the canonical varitional transition state theory (CVT), and the canonical varitional transition state theory with small-curvature tunneling correction (CVT/SCT) in the temperature range of 200-2500 K. The fitted Arrhenius expressions of the calculated CVT/SCT rate constants are k1CVT/SCT(T) = (1.26 × 106)T2.19e-7150.6/T s-1, k2CVT/SCT(T) = (3.68 × 102)T3.23e-12327.7/T s-1, k3CVT/SCT(T) = (9.97 × 10-26)T10.90e-3873.3/T s-1 for the H elimination, HF elimination, and isomerization channels, respectively. [ABSTRACT FROM AUTHOR]

Irradiation of ascomycin 1a and its derivatives in MeOH, EtOH and propanol resulted in alkoxylation of the pipecolic acid moiety in the ϵ-position with concomitant reduction in the tricarbonyl region leading to 6-alkoxy-9-hydroxy derivatives in high stereoselectivities and good yields. The products, after reoxidation of the C(9)-OH, afforded the 6-alkoxy analogues of the parent compounds. Elimination of MeOH from the photoproducts, followed by oxidation gave the corresponding 5,6-dehydro amino acid analogues. Similarly, starting from the proline analogue 7 modifications in the pyrrolidine moiety could be achieved. [Copyright &y& Elsevier]

The explicit expressions for the recently formulated general-model-space (GMS) version of the multireference state-universal (SU) coupled-cluster (CC) method [X. Li and J. Paldus, J. Chem. Phys. 119 (2003) 5320], truncated at the level of single (S) and double (D) excitations, are re-derived using the spin-orbital form of the diagrammatic technique. The focus is on the so-called coupling coefficients, which represent a new type of quantity that does not appear in the single-reference CC approaches. The role of the connectivity conditions, referred to as the C-conditions, in the elimination of disconnected terms in the GMS SU CC method is analyzed in terms of the connectivity of the resulting diagrams and is illustrated on typical examples. [ABSTRACT FROM AUTHOR]

The explicit expressions for the recently formulated general-model-space (GMS) version of the multireference state-universal (SU) coupled-cluster (CC) method [X. Li and J. Paldus, J. Chem. Phys. 119 (2003) 5320], truncated at the level of single (S) and double (D) excitations, are re-derived using the spin-orbital form of the diagrammatic technique. The focus is on the so-called coupling coefficients, which represent a new type of quantity that does not appear in the single-reference CC approaches. The role of the connectivity conditions, referred to as the C-conditions, in the elimination of disconnected terms in the GMS SU CC method is analyzed in terms of the connectivity of the resulting diagrams and is illustrated on typical examples. [ABSTRACT FROM AUTHOR]

Sequential forward selection (SFS) and sequential backward elimination (SBE) are two commonly used search methods in feature subset selection. In the present study, we derive an orthogonal forward selection (OFS) and an orthogonal backward elimination (OBE) algorithms for feature subset selection by incorporating Gram-Schmidt and Givens orthogonal transforms into forward selection and backward elimination procedures, respectively. The basic idea of the orthogonal feature subset selection algorithms is to find an orthogonal space in which to express features and to perform feature subset selection. After selection, the physically meaningless features in the orthogonal space are linked back to the same number of input variables in the original measurement space. The strength of employing orthogonal transforms is that features are decorrelated in the orthogonal space, hence individual features can be evaluated and selected independently. The effectiveness of our algorithms to deal with real world problems is finally demonstrated. [ABSTRACT FROM AUTHOR]

An n × m real matrix A is a totally positive matrix if all its minors are nonnegative. The Neville elimination process is studied in relation to the existence of a totally positive factorization LS of a rectangular matrix. An LS factorization is obtained for a totally positive matrix, where L is a lower echelon form matrix, of size n × k, and S is an upper echelon form matrix, of size k × m, and both L and S are totally positive matrices. [ABSTRACT FROM AUTHOR]

We provide elementary and uniform proofs of order independence for various strategy elimination procedures for finite strategic games, both for dominance by pure and by mixed strategies. The proofs follow the same pattern and focus on the structural properties of the dominance relations. They rely on Newman?s Lemma established in 1942 and related results on the abstract reduction systems. [ABSTRACT FROM AUTHOR]

In J.K. Kruschke's (2001) study, it is argued that attentional theory is the sole satisfactory explanation of the inverse base rate effect and that eliminative inference (P. Juslin, P. Wennerholm, & A. Winman, 2001) plays no role in the phenomenon. In this comment, the authors demonstrate that, in contrast to the central tenets of attentional theory, (a) rapid attention shifts as implemented in ADIT decelerate learning in the inverse base-rate task and (b) the claim that the inverse base-rate effect is directly caused by an attentional asymmetry is refuted by data. It is proposed that a complete account of the inverse base-rate effect needs to integrate attention effects with inference rules that are flexibly used for both induction and elimination. [ABSTRACT FROM AUTHOR]

Elimination theory was at the origin of algebraic geometry in the nineteenth century and now deals with the algorithmic solving of multivariate polynomial equation systems over the complex numbers or, more generally, over an arbitrary algebraically closed field. In this paper we investigate the intrinsic sequential time complexity of universal elimination procedures for arbitrary continuous data structures encoding input and output objects of elimination theory (i.e., polynomial equation systems) and admitting the representation of certain limit objects. Our main result is the following: let there be given such a data structure and together with this data structure a universal elimination algorithm, say P, solving arbitrary parametric polynomial equation systems. Suppose that the algorithm P avoids “unnecessary” branchings and that P admits the efficient computation of certain natural limit objects (as, e.g., the Zariski closure of a given constructible algebraic set or the parametric greatest common divisor of two given algebraic families of univariate polynomials). Then P$ cannot be a polynomial time algorithm. The paper contains different variants of this result and discusses their practical implications. [ABSTRACT FROM AUTHOR]

Properties of zero polyhedral cones are studied by making use of Fourier-Motzkin eliminations. Algorithms are presented for the characterization of zero polyhedral cones. [Copyright &y& Elsevier]

It is well known that some pivoting strategies are backward stable for Gauss elimination but are not backward stable for Gauss–Jordan elimination (GJE) when these procedures are used to solve a linear system Ax=b. We analyse the simultaneous backward stability for Gauss and GJE of several pivoting strategies, including a pivoting strategy which we call double partial pivoting. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We introduce the new notion of additive “multibox” for linear logic proof-nets. Thanks to this notion, we define a cut-elimination procedure which associates with every proof-net of multiplicative and additive linear logic a unique cut-free one. [Copyright &y& Elsevier]

Small angle X-ray scattering measurements, bulk and skeleton density data and an in-situ study by dilatometric thermal analysis about the nanoporosity elimination above 800 °C in TEOS sonogels are presented. Apparently, two processes act during the nanoporosity elimination, which precedes the foaming phenomenon often observed in such systems. The first, with an activation energy of (3.9 ± 0.4) × 102 kJ/mol and high frequency factor, is the controlling process of the most nanoporosity elimination at higher temperature. The value of this activation energy is compatible to that for viscous flux throughout densification process in typical silica-based materials. The second, with an activation energy of (49 ± 5) kJ/mol and low frequency factor, seems to be the controlling process of the first and extremely slow nanoporosity elimination at low temperature. [ABSTRACT FROM AUTHOR]

The anti-Markownikoff products of bromination and bromomethoxylation of 3-methylenecyclobutane-1-carbonitrile and methyl 3-methylenecyclobutane-1-carboxylate were subjected to dehydrobromination by the action of potassium tert-butoxide in THF. The reaction takes two elimination pathways: 1,3-dehydrobromination to give bicyclobutane derivatives and 1,2-dehydrobromination leading to substituted methylenecyclobutane. Structural factors in the substrate were revealed, which are responsible for the ratio of the two concurrent elimination processes. [ABSTRACT FROM AUTHOR]

Recently, Evans [1] has given a variant of the classical Choleski factorization, called Choleski Q.I.F., for the solution of symmetric linear systems. In the present paper we address the questions of existence and stability of the factorization. We show that Evans' Choleski Q.I.F. exists if the coefficient matrix is symmetric positive definite. Our proof of existence of the factorization is via obtaining the diagonal elements of the factor matrices in a closed-form in terms of certain principal minors of the coefficient matrix. By interpreting the Choleski Q.I.F. as an elimination procedure in which eliminations are carried out, alternately, in columns from the left and the right, we show that the Choleski Q.I.F. is also (numerically) strongly stable if the coefficient matrix is symmetric positive definite. We include arithmetical operations counts for the Choleski Q.I.F.; these agree with the counts for the classical Choleski factorization. [ABSTRACT FROM AUTHOR]

Based on the mechanized mathematics and WU Wen-tsun elimination method, using oil film forces of short-bearing model and Muszynska’s dynamic model, the dynamical behavior of rotor-bearing system and its stability of motion are investigated. As example, the concept of Wu characteristic set and Maple software, whirl parameters of short-bearing model, which is usually solved by the numerical method, are analyzed. At the same time, stability of zero solution of Jeffcott rotor whirl equation and stability of self-excited vibration are studied. The conditions of stable motion are obtained by using theory of nonlinear vibration. [ABSTRACT FROM AUTHOR]

Iterated elimination of strictly dominated strategies is an order dependent procedure. It can also generate spurious Nash equilibria, fail to converge in countable steps, or converge to empty strategy sets. If best replies as well-defined, then spurious Nash equilibria cannot appear; if strategy spaces are compact and payoff functions are uppersemicontinuous in own strategies, then order does not matter; if strategy sets are compact and payoff functions are continuous in all strategies, then a unique and nonempty maximal reduction exists. These positive results extend neither to the better-reply secure games for which Reny has established the existence of a Nash equilibrium, nor to games in which (under iterated eliminations) any dominated strategy has an undominated dominator. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to demonstrate how Lafont''s interaction combinators, a system of three symbols and six interaction rules, can be used to encode linear logic. Specifically, we give a translation of the multiplicative, exponential, and additive fragments of linear logic together with a strategy for cut-elimination which can be faithfully simulated. Finally, we show briefly how this encoding can be used for evaluating λ-terms. In addition to offering a very simple, perhaps the simplest, system of rewriting for linear logic and the λ-calculus, the interaction net implementation that we present has been shown by experimental testing to offer a good level of sharing in terms of the number of cut-elimination steps (resp. β-reduction steps). In particular it performs better than all extant finite systems of interaction nets. [Copyright &y& Elsevier]

New formulae are given for Chow forms, discriminants and resultants arising from (not necessarily normal) toric varieties of codimension 2. The Newton polygon of the discriminant is determined exactly. [Copyright &y& Elsevier]

Elimination of potential hypotheses is a fundamental component of many learning processes. In order to understand the nature of elimination, herein we study the following model of learning recursive functions from examples. On any target function, the learning machine has to eliminate all, save one, possible hypotheses such that the missing one correctly describes the target function. It turns out that this type of learning by the process of elimination (elm-learning, for short) can be stronger, weaker or of the same power as usual Gold style learning.While for usual learning any r.e. class of recursive functions can be learned in all of its numberings, this is no longer true for elm-learning. For elm-learnability of an r.e. class in a given of its numberings, we derive sufficient conditions of this numbering (decidability of index equivalence and paddability) as well as a condition being both necessary and sufficient. Then we deal with the problem of which r.e. classes are elm-learnable in all of their numberings and which are not.Elm-learning of arbitrary classes of recursive function is shown to be of the same power as usual learning. For elm-learnability of an arbitrary class in an arbitrary numbering, paddability of this numbering remains to be useful, whereas decidability of index equivalence can be “maximally weak” or “extremely useful”. We also give a characterization for elm-learnability of an arbitrary class of recursive functions.Finally, we consider some generalizations of elm-learning. One of them is of the same power as usual learning by teams. A further generalization even allows to learn the class of all recursive functions. [Copyright &y& Elsevier]

The transition state energy for Cl2 molecular elimination from 1,2-dichloroethane is computed at compostite CBS-Q (based on B3LYP/6-31++G(d) optimized structure) and G3MP2 (based on MP2/6-31++G(d) optimized structure) levels of theory. Forward rate constants are calculated as 4.25E11 T0.826·exp(−93.4 kcal mol−1/RT) and 7.62E10 T0.892·exp(−98.5 kcal mol−1/RT) s−1, respectively for these two methods. Intrinsic reaction coordinate (IRC) analysis is performed to verify the transition state structures. While the overall, elimination of Cl2 plus olefin formation has a relative low ΔHrxn; the reaction with these barriers is evaluated to be not important in thermal reactions of chlorocarbons. [Copyright &y& Elsevier]

In this paper, the well known singular value decomposition (SDV) method is extended to explicit (2 × 2) block form, by using the Quadrant Interlocking Factorisation (QIF) method. Numerical results are presented to portray the validity of the proposed method. [ABSTRACT FROM AUTHOR]

We extend the elimination method of Chawla and Khazal [1] to uncouple partitioned blocks of "periodic" tridiagonal linear systems. At each step of the elimination stage, we now need three simultaneous eliminations: within each block, one usual forward elimination and one backward elimination from across the succeeding block, and one elimination in the last row of the last block. An interesting feature of the present elimination procedure is that at the end of it, the property of periodicity of the original system is now passed on to the core system . Once the core system is solved, the blocks uncouple and the solution is obtained in parallel from each block by back substitution. For a system of size N , the classical elimination has an arithmetical operations count of 17N . A best serial algorithm, based on the Sherman-Morrison formula, has an operations count of 0 14N . The present parallel elimination algorithm, employing p partition blocks, has an operations count of O 17N p and, in comparison with the Sherman-Morrison algorithm, it can achieve an efficiency of nearly 82% on a p -processor machine. [ABSTRACT FROM AUTHOR]

SVD and QR Decomposition have attracted much attention recently for solving linear algebra and digital signal processing problems. The House-holder QR Decomposition requires a smaller number of operations then the Givens QR Decomposition and therefore is strongly recommended for sequential computer implementations (as found in nearly all known libraries like NAG, LINPACK, EISPACK etc.) However for parallel implementation it has not been widely used, because the Givens Rotations possess inherent parallelism and the Householder Reflections do not. This is true if one analyzes the original algorithm. Four independent loops and three bottlenecks between the loops are constraint for pipelining the computations. This leads to an inefficient solution, i.e. 4n time moments for each iteration and since there are n iterations then the total time to execute the algorithm is O(4n 2 ). Compared to 3n-2 time steps for the Givens QR Decomposition it is uneconomic. In this paper we have used some recent results for the elimination of the computational and data broadcast, and data synchronization to derive a fully localized form of the Householder QR Decomposition algorithm. We have succeeded in reorganizing and transforming the algorithm from three bottlenecks to one and four loops to one. A linear and a double pipeline array of n+1 processors are presented to solve the problem in O ( n 2 /2) time steps. It is also shown that the bottlenecks for the bidiagonalization and SVD computation cannot be eliminated. [ABSTRACT FROM AUTHOR]

I show that there exists no scoring rule which ensures that an alternative considered as best by a strict majority is chosen while an alternative considered as worst by a strict majority remains outside of the choice set. The negative result is valid for standard scoring rules where scores depend on the number of alternatives only, as well as for generalized ones defined via vectors of scores which are functions of both the number of alternatives and agents. [Copyright &y& Elsevier]

This paper introduces a method for finding the non-dominated set in criterion space of an MOLP problem based on Fourier–Motzkin Elimination. The method incorporates a procedure that eliminates decision variables from constraints and transforms a feasible region from decision space to criterion space. While avoiding characterization of the efficient set in decision space, it finds the non-dominated set in criterion space. After the decision maker's most preferred criterion vector has been identified, the corresponding efficient solutions can be found by backward substitution. The method was implemented in MATLAB using a tabular form and computational experiments were conducted. The results indicate that although the method performs well for relatively small problems, it can be computationally intensive for larger problems. Nonetheless, the method is intuitively appealing and it provides useful insights into the geometry and theory of MOLP. As such it makes it a valuable educational tool for students of multi-criteria decision analysis. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We consider the problem of partitioning a set of normal populations, with respect to a control population, into two subsets according to their unknown means, under the indifference zone formulation. For this problem Tong (1969) constructed a two-stage and purely sequential procedures and recently Datta and Mukhopadhyay (1998) have considered various multistage methodologies emphasizing the second-order asymptotics. However, all these methodologies adopt a vector-at-a-time sampling approach and lack the desirable feature of eliminating treatments from further sampling at an earlier stage. We propose an elimination type sequential procedure using the Paulson's (1964) elimination idea and design a sampling methodology which eliminates “superior” and “inferior” treatments during the sampling, thereby reducing the average sample size considerably. Theoretical results are obtained to show that the proposed elimination-type procedure maintains the probability of correct partition above a pre specified level. The proposed procedure is studied and compared via the Monte Carlo simulation studies with other competitive procedures known in the literature, under both the LFC and a few non-LFC configurations. The elimination-type procedure is found to be vastly more efficient than its competitors in terms of average sample size. [ABSTRACT FROM AUTHOR]

Genera connections between quantifier elimination and decidability for first order theories are studied and exemplified. [ABSTRACT FROM AUTHOR]

Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as a means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by μn < 3 n-1, as compared to 2n-1 for the standard partial pivoting. This bound μn, close to 3n-2, is attainable for a class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting. [ABSTRACT FROM AUTHOR]

Abstract. Context-dependent rules are an obstacle to cut elimination. Turning to a generalised sequent style formulation using deep inferences is helpful, and for the calculus presented here it is essential. Cut elimination is shown for a substructural, multiplicative, pure propositional calculus. Moreover we consider the extra problems induced by non-logical axioms and extend the results to additive connectives and quantifiers. [ABSTRACT FROM AUTHOR]

Abstract. Gentzen's original proof of the Hauptsatz used a rule of multicut in the case that the right premiss of cut was derived by contraction. Cut elimination is here proved without multicut, by transforming suitably the derivation of the premiss of the contraction. [ABSTRACT FROM AUTHOR]

Let D be a diagonal matrix and Eij denote the n-by-n matrix with a 1 in entry (i,j) and 0 in every other entry. An n-by-n matrix A has a successively ordered elementary bidiagonal (SEB) factorization if it can be factored as [This symbol cannot be presented in ASCII format] in which Lj(sjk) = I + sjkEj,j -1 and Uj(tkj) = I + tkjEj -1,j for some scalars sjk,tkj. Note that some of the parameters sjk,tkj may be zero, and the order of the bidiagonal factors is fixed. If this factorization corresponds to reduction of A to D via successive row/column operations in the specified order, it is called an elimination SEB factorization. New rank conditions are formulated that are proved to be necessary and sufficient for matrix A to have such a factorization. These conditions are related to known but more restrictive properties that ensure a bidiagonal factorization as above, but with all parameters sjk,tkj nonzero. [ABSTRACT FROM AUTHOR]

Based on the computation mode introduced in [13], we deal with the time complexity of computations over arbitrary first-order structures.The main emphasis is on parameter-free computations. Some transfer results for solutions of P versus NP problems as well as relationships to quantifier elimination are discussed. By computation tree analysis using first-order formulas, it follows that P versus NP solutions and other results of structural complexity theory are invariant under elementary equivalence of structures. [ABSTRACT FROM AUTHOR]

In his paper 'Generalised Ortho Negation' [2] J.Michael Dunn mentions a claim of mine to the effect that there is no condition on 'perp frames' equivalent to the holding of double negation elimination ∼∼A ⊩ A. That claim is wrong. In this paper I correct my error and analyse the behaviour of conditions on frames for negations which verify a number of different theses. [ABSTRACT FROM PUBLISHER]

Smullyan maintains that the importance of cut-free proofs does not stem from cut elimination per se but rather from the fact that they satisfy the subformula property. In accordance with such a viewpoint in this paper we introduce analytic cut trees, a system from which cuts cannot be eliminated but satisfying the subformula property. Like tableaux analytic cut trees are a refutation system but unlike tableaux they have a single inference rule (a form of the analytic cut rule) and several branch closure rules. The main advantage of analytic cut trees over tableaux is efficiency: while analytic cut trees can simulate tableaux with an increase in complexity by at most a constant factor, tableaux cannot polynomially simulate analytic cut trees. Indeed analytic cut trees are intrinsically more efficient than any cut-free system. [ABSTRACT FROM PUBLISHER]

The goal of this paper is to introduce a new Gentzen formulation of the modal logic S5. The history of this problem goes back to the fifties where a counter-example to cut-elimination was given for an otherwise natural and straightforward formulation of S5. Since then, several cut-free Gentzen style formulations of S5 have been given. However, all these systems are technically involved, and furthermore, they differ considerably from Gentzen's original formulation of classical logic. In this paper we give a new sequent system for S5 which is a straightforward and technically simple extension of Gentzen's original sequent system for classical logic. A characteristic feature is the notion of a connection in a proof. The new system satisfies cut-elimination as well as the subformula property. Cut-elimination is proved by giving an algorithm for eliminating cuts. The fact that we give an algorithm for eliminating cuts makes it clear that our system is susceptible to a formulae-as-types computational interpretation. [ABSTRACT FROM AUTHOR]

According to the improved sine-cosine method and Wu-elimination method, a new algorithm to construct solitary wave solutions for systems of nonlinear evolution equations is put forward. The algorithm has some conclusions which are better than what the hyperbolic function method known does and simpler in use. With the aid of MATHEMATICA, the algorithm can be carried out in computer. [ABSTRACT FROM AUTHOR]

Recently Ekman gave a derivation in natural deduction such that it either contains a substantial redundant part or else is not normal. It is shown that this problem is caused by a non-normality inherent in the usual modus ponens rule. [ABSTRACT FROM AUTHOR]