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We prove effective Nullstellensatz and elimination theorems for difference equations in sequence rings. More precisely, we compute an explicit function of geometric quantities associated to a system of difference equations (and these geometric quantities may themselves be bounded by a function of the number of variables, the order of the equations, and the degrees of the equations) so that for any system of difference equations in variables x = (x1, ..., xm) and u = (u1, ..., ur), if these equations have any nontrivial consequences in the x variables, then such a consequence may be seen algebraically considering transforms up to the order of our bound. Specializing to the case of m = 0, we obtain an effective method to test whether a given system of difference equations is consistent. [ABSTRACT FROM AUTHOR]

Efficient scheduling is critical for achieving improved performance of distributed applications where an application is to be considered as a group of interrelated tasks and represented by a task graph. In this work, we present a clustering-based scheduling algorithm called effective critical path (ECP) to schedule precedence constrained tasks on multiprocessor computing systems. The main aim of the algorithm is to minimize the schedule length of the given application. It uses the concept of edge zeroing on the critical path of the task graph for clustering the tasks of an application. An experimental analysis is performed using random task graphs and the task graphs derived from the real-world applications such as Gaussian Elimination, fast Fourier transform and systolic array. The results illustrate that the ECP algorithm gives better performance than the previous algorithms, considered herein, in terms of the average normalized schedule length and average speedup. [ABSTRACT FROM AUTHOR]

We develop a finite volume method based on Crank-Nicolson time discretization for the two-dimensional nonsymmetric Riemann-Liouville space-fractional diffusion equation. Stability and convergence are then carefully discussed. We prove that the finite volume scheme is unconditionally stable and convergent with second-order accuracy in time and min ⁡ { 1 + α , 1 + β } order in space with respect to a weighted discrete norm. Here 0 < α , β < 1 are the space-fractional order indexes in x and y directions, respectively. Furthermore, we rewrite the finite volume scheme into a matrix form and develop a matrix-free preconditioned fast Krylov subspace iterative method, which only requires storage of O (N) and computational cost of O (N log ⁡ N) per iteration without losing any accuracy compared to the direct Gaussian elimination method. Here N is the total number of spatial unknowns. Consequently, the fast finite volume method is particularly suitable for large-scale modeling and simulation. Numerical experiments verify the theoretical results and show strong potential of the fast method. • A Crank-Nicolson finite volume method is proposed for two-dimensional Riemann-Liouville space-fractional diffusion equation. • A novel norm-based stability analysis is proposed for non-symmetric anomalously diffusive transport. • A priori error estimate with respect to a weighted discrete norm is strictly proved. • A matrix-free preconditioned fast solution method with almost linear computational complexity is developed. • Numerical experiments are given to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

Advanced production decline analysis methods have become more economic and efficient options due to technical and time limitations of well-testing operations in shale gas reservoirs. By normalizing rate with material balance pseudo-time, Blasingame type decline analysis can be applied to variable rate/variable pressure drop system, making the methodology more widely applicable. Blasingame decline analysis of variable rate/variable pressure drop case for multi-fractured horizontal well (MFHW) in shale has been less investigated, because of multi-scale storage spaces and multi-flow mechanisms. This article presents a semi-analytical Blasingame decline analysis model incorporating multi-flow mechanisms with shale's modified material balance pseudo-time. Laplace transformation, point source function, numerical discrete method, perturbation method, and Gaussian elimination method were employed to solve the mathematical problem caused by multi-flow mechanisms. Besides, the material balance pseudo-time was modified by considering adsorption and desorption. In this study, a workflow to investigate the effects of properties of hydraulic fracture (fracture half-length, number of fractures and fracture spacing) and multi-flow mechanisms (diffusion and desorption) on production decline behaviors through diagnostic Blasingame type curves is proposed. The results indicate that productivity is greater with a larger scale of fracture treatment, and better desorption of adsorbed gas is also beneficial to production. The decline rates affected by the fracture treatment scale and supplement capacity show two opposite trends, which is caused by interference between the fractures and boundary, respectively. Except that the data in the diffusion early flow period do not match very well, because the use of diffusion coefficient as a constant, the good fitting results on the whole verifies the model's validity and reliability. • A new Blasingame decline model of shale accommodating multi-mechanisms is established. • Effects of fracture and flow mechanism on production behaviors are analyzed. • Simulated result matches well with rate data. • Considering diffusivity as a constant may result in poor fitting result. [ABSTRACT FROM AUTHOR]

In the present work a set of formal relations connecting different approaches to calculate relativistic effects on magnetic molecular properties are proven. The linear response (LR) within the elimination of the small component (ESC), Breit Pauli, and minimal-coupling approaches are compared. To this end, the leading order ESC reduction of operators within the minimal-coupling four-component approach is carried out. The equivalence of all three approaches within the ESC approximation is proven. It is numerically verified for the NMR nuclear-magnetic shielding tensor taking HX and CH3X (X=Br,I) as model compounds. Formal relations proving the gauge origin invariance of the full relativistic effect on the NMR nuclear-magnetic shielding tensor within the LR-ESC approach are presented. [ABSTRACT FROM AUTHOR]

A Hungarian scaling is a diagonal scaling of a matrix that is typically applied along with a permutation to a sparse linear system before calling a direct or iterative solver. A matrix that has been Hungarian scaled and reordered has all entries of modulus less than or equal to 1 and entries of modulus 1 on the diagonal. An important fact that has been largely overlooked by the previous research into Hungarian scaling of linear systems is that a given matrix typically has a range of possible Hungarian scalings, and direct or iterative solvers may behave quite differently under each of these scalings. Since standard algorithms for computing Hungarian scalings return only one scaling, it is natural to ask whether a superior performing scaling can be obtained by searching within the set of all possible Hungarian scalings. To this end we propose a method for computing a Hungarian scaling that is optimal from the point of view of a measure of diagonal dominance. Our method uses max-balancing, which minimizes the largest off-diagonal entries in the scaled and permuted matrix. Numerical experiments illustrate the increased diagonal dominance produced by max-balanced Hungarian scaling as well as the reduced need for row interchanges in Gaussian elimination with partial pivoting and the improved stability of LU factorizations without pivoting. We additionally find that applying the max-balancing scaling before computing incomplete LU preconditioners improves the convergence rate of certain iterative methods. Our numerical experiments also show that the Hungarian scaling returned by the HSL code MC64 has performance very close to that of the optimal max-balanced Hungarian scaling, which further supports the use of this code in practice. [ABSTRACT FROM AUTHOR]

This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called beurling least angle regression (BLASSO) method, which is an off-the-grid generalization of 1 regularization (also known as the least angle regression). While super-resolution is of paramount importance in overcoming the limitations of many imaging devices, its theoretical analysis is still lacking beyond the one-dimensional case. The reason is that in the two-dimensional (2-D) case and beyond, the relative position of the spikes enters the picture, and different geometrical configurations lead to different stability properties. Our first main contribution is a connection, in the limit where the spikes cluster at a given point, between solutions of the dual of the BLASSO problem and the least interpolant space for Hermite polynomial interpolation. This interpolation space, introduced by De Boor, can be computed by Gaussian elimination and lead to an algorithmic description of limiting solutions to the dual problem. With this construction at hand, our second main contribution is a detailed analysis of the support stability and super-resolution effect in the case of a pair of spikes. This includes in particular a sharp analysis of how the signal-to-noise ratio should scale with respect to the separation distance between the spikes. Lastly, numerical simulations on different classes of kernels show the applicability of this theory and highlight the richness of super-resolution in 2-D. [ABSTRACT FROM AUTHOR]

The Bunch--Parlett algorithm, the Bunch-Kaufman algorithm, the bounded Bunch-- Kaufman algorithm, and Aasen's algorithm are four well-kno wn methods for solving symmetric indefinite linear systems, yet the last three methods are known to suffer from potential numerical instability. In this work, we develop a randomized complete pivoting (RCP) algorithm for solving symmetric indefinite linear systems of equations. RCP is comparable to the Bunch-Kaufman algorithm and Aasen's algorithm in computational efficiency, but still enjoys theoretical element growth and bounded entries in the factorization comparable to that of the Bunch-Parlett algorithm, up to a theoretical failure probability that exponentially decays with an oversampling parameter. In terms of the boundedness of entries in L, the Bunch-Parlett algorithm, the bounded Bunch-Kaufman algorithm, and Aasen's algorithm have maxi

Abstract In this paper we calibrate the strength of the soundness of a set theory KP ω + (Π 1 -Collection) with the assumption that 'there exists an uncountable regular ordinal' in terms of the existence of ordinals. [ABSTRACT FROM AUTHOR]

As the only nonlinear operation, masked S-box is the core to resist differential power attack (DPA) for advanced encryption standard (AES) cipher chips. In order to suit for the resource-constrained applications, a compact masked S-box based on composite field is proposed in this paper. Firstly, the architecture of masked S-box is designed with composite field masking method. Secondly, four masked S-boxes based on GF ((24)2), which are based on four basis methods with the optimal coefficient and the corresponding optimal root, are implemented and optimized by the delay-aware common subexpression elimination (DACSE) algorithm. Finally, experimental results show that, while maintaining the DPA-resistance performance, our best masked S-box achieves better area performance with the fastest speed compared with the existing works. Therefore, our masked S-box is suitable for resource-constrained applications with fast speed requirements. [ABSTRACT FROM AUTHOR]

Let K be a field, and a finitely generated K-algebra with the PBW K-basis . It is shown that if L is a nonzero left ideal of A with GK.dim(A∕L) = d<n ( =  the number of generators of A), then L has the elimination property in the sense that V(U)∩L≠{0} for every subset with , where V(U) = K-span. In terms of the structural properties of A, it is also explored when the condition GK.dim(A∕L)<n may hold for a left ideal L of A. Moreover, from the viewpoint of realizing the elimination property by means of Gröbner bases, it is demonstrated that if A is in the class of binomial skew polynomial rings or in the class of solvable polynomial algebras, then every nonzero left ideal L of A satisfies GK.dim(A∕L)< GK.dimA = n ( =  the number of generators of A), thereby L has the elimination property. [ABSTRACT FROM AUTHOR]

Generalizing Cooper’s method of quantifier elimination for Presburger arithmetic, we give a new proof that all parametric Presburger families {St:t∈N} [as defined by Woods (Electron J Comb 21:P21, 2014)] are definable by formulas with polynomially bounded quantifiers in an expanded language with predicates for divisibility by f(t) for every polynomial f∈Z[t]. In fact, this quantifier bounding method works more generally in expansions of Presburger arithmetic by multiplication by scalars {α(t):α∈R,t∈X} where R is any ring of functions from X into Z. [ABSTRACT FROM AUTHOR]

The ϵ-substitution method is a technique for giving consistency proofs for theories of arithmetic. We use this technique to give a proof of the consistency of the impredicative theory ID1 using a variant of the cut-elimination formalism introduced by Mints. [ABSTRACT FROM AUTHOR]

Generation of arynes from aryl triflates has been achieved using lithium diethyl(tetramethylpiperidyl)-zincate base LiZnEt 2 (TMP), via a directed ortho -deprotonative zincation and subsequent elimination of the triflate group. The aryne formation has been demonstrated by the cycloaddition reaction with diene and insertion reactions with ureas. Furthermore, the nucleophilic addition of LiZnEt 2 (TMP) to arynes was observed in the absence of external aryne partners, offering a new cascade strategy for diverse difunctionalization of arynes. [ABSTRACT FROM AUTHOR]

In this paper, a Haar wavelet collocation method (HWCM) is developed for PDEs related to the framework of so-called inverse problem. These include PDEs with unknown time dependent heat source and unknown solution in interior of the domain. To this end, a transformation is used to eliminate the unknown heat source to obtain a PDE without a heat source. After elimination of unknown non-homogeneous term, an implicit finite-difference approximations is used to approximate the time derivative and Haar wavelets are used for approximation of the space derivatives. Several numerical experiments related to one- and two-dimensional heat sources are included to validate small condition number of coefficient matrix, accuracy and simple applicability of the proposed approach. [ABSTRACT FROM AUTHOR]

Quasiconvex functions present some difficulties in global optimization, because their graph contains “flat parts”; thus, a local minimum is not necessarily the global minimum. In this paper, we show that any lower semicontinuous quasiconvex function may be written as a composition of two functions, one of which is nondecreasing, and the other is quasiconvex with the property that every local minimum is global minimum. Thus, finding the global minimum of any lower semicontinuous quasiconvex function is equivalent to finding the minimum of a quasiconvex function, which has no local minima other than its global minimum. The construction of the decomposition is based on the notion of “adjusted sublevel set.” In particular, we study the structure of the class of sublevel sets, and the continuity properties of the sublevel set operator and its corresponding normal operator. [ABSTRACT FROM AUTHOR]

(3 + 1) dimensional nonlinear KdV-type equation is solved by Wazwaz and Zhaqilao’s method which is arisen by employing complex parameters instead of real parameters and considered generalization of simplified Hirota method. Complexiton solutions which include both trigonometric and exponential functions are obtained for referred equation. Also some special conditions to specify the non-singularity and type of solutions are derived. [ABSTRACT FROM AUTHOR]

The QSS codes associated with a MSP code are based on finding an invertible matrix V, solving the system vATMBsa=s. We propose a quantum Gauss-Jordan Elimination Procedure to produce such a pivotal matrix V by using the Grover search code. The complexity of solving is of square-root order of the cardinal number of the unauthorized set 2|B|. [ABSTRACT FROM AUTHOR]

Approximately seventy isolated and overlapping methane absorption lines in the 5647 − 6164 cm −1 spectral region were processed with seven line profiles accounting for all main line shape forming physical mechanisms in different combinations. It was shown that at low methane pressures the conventional Nelkin–Ghatak line profile gives satisfactory results in retrieving line parameters as opposed to the Voigt profile. It was found that most of the considered lines do not interfere. The FTS instrumental function elimination technique based on Doppler-broadened line's records was applied, and its applicability was proved. [ABSTRACT FROM AUTHOR]

In this paper, an extension Elimination and Choice Translating Reality (ELECTRE) method is introduced to handle multi-valued neutrosophic multi-criteria decision-making (MCDM) problems. First of all, some outranking relations for multi-valued neutrosophic numbers (MVNNs), which are based on traditional ELECTRE methods, are defined, and several properties are analyzed. In the next place, an outranking method to deal with MCDM problems similar to ELECTRE III, where weights and data are in the form of MVNNs, is developed. At last, an example is provided to demonstrate the proposed approach and testify its validity and feasibility. This study is supported by the comparison analysis with other existing methods. [ABSTRACT FROM AUTHOR]

We derive a unified representation for all types of generalized inverses related to the {1}-inverse. Based on this representation, we propose a unified Gauss–Jordan elimination procedure for the computation of all types of generalized inverses related to the {1}-inverse. Complexity analysis indicates that when applied to compute the Moore–Penrose inverse, our method is more efficient than the existing Gauss–Jordan elimination methods in the literature for a large class of problems. Finally, numerical experiments show our method for Moore–Penrose inverse has good efficiency and accuracy, and especially for computing the Moore–Penrose inverse of m × n matrices with m < n our method gives the best performance in practice. [ABSTRACT FROM AUTHOR]

A single-elimination (SE) tournament is a popular way to select a winner both in sports competitions and in elections. A natural and well-studied question is the tournament fixingproblem (TFP): given the set of all pairwise match outcomes, can a tournament organizer rig an SE tournament by adjusting the initial seeding so that the organizer's favorite player wins? We prove new sufficient conditions on the pairwise match outcome information and the favorite player, under which there is guaranteed to be a seeding where the player wins the tournament. Our results greatly generalize previous results. We also investigate the relationship between the set of players that can win an SE tournament under some seeding (so-called SE winners) and other traditional tournament solutions. In addition, we generalize and strengthen prior work on probabilistic models for generating tournaments. For instance, we show that every player in an n player tournament generated by the Condorcet random model will be an SE winner even when the noise is as small as possible, p = ϴ(ln n / n); prior work only had such results for p ≥ Ω(√ln n / n). We also establish new results for significantly more general generative models. [ABSTRACT FROM AUTHOR]

We describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In particular, the notion of connected components of semialgebraic sets is not used. [ABSTRACT FROM AUTHOR]

We introduce a new family of sequential selection procedures wherein the subsets selected have random sizes. In comparison to subset selection procedures that select subsets of fixed size, the new procedures alleviate the need to specify the subset size prior to the experiment. We discuss the application of such procedures in the context of early phase clinical trials. The new procedures retain the adaptive features of the Levin-Robbins-Leu family of sequential subset selection procedures for selecting subsets of fixed size, namely, sequential elimination of inferior treatments and sequential recruitment of superior treatments. These two adaptive features respectively address ethical concerns that diminish interest in nonadaptive procedures and also allow promising treatments to be brought forward for further testing without having to wait until the end of the trial. The new procedures differ from the classical subset selection procedures of Shanti S. Gupta in terms of their respective goals and operating characteristics and we compare the two approaches in a simulation study. The findings suggest that whereas Gupta’s procedure achieves its goal of including the single best treatment in the final selected subset with high probability, it does so by virtue of a nonadaptive, fixed sample size procedure that lacks necessary flexibility in the context of clinical research. By contrast, the new procedures aim to select treatment subsets that satisfy a different criterion, that ofacceptable subset selectionwith high probability, while allowing adaptive elimination and recruitment and other flexibilities which we discuss to fit the practical needs of selection methods in clinical research. [ABSTRACT FROM PUBLISHER]

We reconsider whether a grand multi-winner contest elicits more equilibrium effort than a collection of sub-contests. Fu and Lu (2009) employ a sequential winner-selection mechanism and find support for running a grand contest. We show that this result is completely reversed if a simultaneous winner-selection mechanism or a sequential loser-elimination mechanism is implemented. We then discuss the optimal allocation of players and prizes among sub-contests. [ABSTRACT FROM AUTHOR]

[Display omitted] • A system for noninvasive quantitative analysis of human blood components. • This paper proposes a spectral elimination method. • The models of seven blood components were established in this paper. • The Rp-all predicted by the seven models respectively reach 0.95 and above. • Noninvasive detection based on dynamic spectrum theory and "M + N" theory. Noninvasive detection of human blood components is the dream of human beings and the goal of clinical detection. From the perspective of mathematical analysis, based on the grey analysis system, the principle of spectral chemical quantitative analysis and the solution method of multivariate linear equation, this paper pioneers the spectrum elimination method, and obtains a complete, high-precision, synchronous and noninvasive detection system for a variety of human blood components. The spectral elimination method applies the principle of elimination method in mathematics to the noninvasive quantitative analysis of human blood components by spectral method, reduces the influence of non-target components on the detection of target components, and improves the accuracy of noninvasive quantitative analysis of human blood components. To demonstrate the effectiveness of the method, taking the analysis of the contents of seven blood components (hemoglobin, red blood cell count, neutrophils, lymphocytes, monocytes, eosinophils and basophils) in blood as an example, fourteen models were established by two different methods. From the comparison of modeling results, it can be concluded that when the seven models established by spectral elimination method predict the corresponding seven components of all samples, the predicted correlation coefficients are more than 0.9500. The experimental results show that the spectral elimination method and non-invasive detection system proposed can predict the content of human blood components with high accuracy. This paper studies a high-precision, simultaneous and noninvasive quantitative analysis system of multiple human blood components for the first time, which not only makes great progress in the non-invasive chemical quantitative analysis of human blood components by spectroscopy, but also has great application value for clinical medical treatment and disease diagnosis. [ABSTRACT FROM AUTHOR]

[Display omitted] • A system for noninvasive quantitative analysis of human blood components. • This paper proposes a spectral elimination method. • The models of seven blood components were established in this paper. • The Rp-all predicted by the seven models respectively reach 0.95 and above. • Noninvasive detection based on dynamic spectrum theory and "M + N" theory. Noninvasive detection of human blood components is the dream of human beings and the goal of clinical detection. From the perspective of mathematical analysis, based on the grey analysis system, the principle of spectral chemical quantitative analysis and the solution method of multivariate linear equation, this paper pioneers the spectrum elimination method, and obtains a complete, high-precision, synchronous and noninvasive detection system for a variety of human blood components. The spectral elimination method applies the principle of elimination method in mathematics to the noninvasive quantitative analysis of human blood components by spectral method, reduces the influence of non-target components on the detection of target components, and improves the accuracy of noninvasive quantitative analysis of human blood components. To demonstrate the effectiveness of the method, taking the analysis of the contents of seven blood components (hemoglobin, red blood cell count, neutrophils, lymphocytes, monocytes, eosinophils and basophils) in blood as an example, fourteen models were established by two different methods. From the comparison of modeling results, it can be concluded that when the seven models established by spectral elimination method predict the corresponding seven components of all samples, the predicted correlation coefficients are more than 0.9500. The experimental results show that the spectral elimination method and non-invasive detection system proposed can predict the content of human blood components with high accuracy. This paper studies a high-precision, simultaneous and noninvasive quantitative analysis system of multiple human blood components for the first time, which not only makes great progress in the non-invasive chemical quantitative analysis of human blood components by spectroscopy, but also has great application value for clinical medical treatment and disease diagnosis. [ABSTRACT FROM AUTHOR]

For a system of three first-order partial differential equations with three independent variables, we obtain sufficient conditions for one component of the solution to satisfy a third-order Bianchi equation. We also obtain conditions for the solvability of this system by quadratures. [ABSTRACT FROM AUTHOR]

We present a binary analysis framework based on symbolic execution with the distinguishing capability to execute stepwise forward and also backward through the execution tree. It was developed internally at Bitdefender and code-named RIVER. The framework provides components such as a taint engine, a dynamic symbolic execution engine, and integration with Z3 for constraint solving. In this paper we will provide details on the framework and give an example of analysis on binary code. [ABSTRACT FROM AUTHOR]

Based on Wu’s elimination method, an algorithm about the consistent Riccati expansion (CRE) method is presented to find different types of interaction wave solutions for nonlinear partial differential equations. Furthermore, a Maple package is developed to entirely implement the algorithm, and several examples are given to illustrate the effectiveness of the package. [ABSTRACT FROM AUTHOR]

We study a class of homotopies between maps from 4-manifolds to surfaces which we call cusp merges. These homotopies naturally appear in the uniqueness problems for certain pictorial descriptions of 4-manifolds derived from maps to the 2-sphere (for example, broken Lefschetz fibrations, wrinkled fibrations, or Morse 2-functions). Our main results provide a classification of cusp merge homotopies in terms of suitably framed curves in the source manifold, as well as a fairly explicit description of a parallel transport diffeomorphism associated to a cusp merge homotopy. The latter is the key ingredient in understanding how the aforementioned pictorial descriptions change under homotopies involving cusp merges. We apply our methods to the uniqueness problem of surface diagrams of 4-manifolds and describe algorithms to obtain surface diagrams for total spaces of (achiral) Lefschetz fibrations and 4-manifolds of the form M × S1, where M is a 3-manifold. Along the way we provide extensive background material about maps to surfaces and homotopies thereof and develop a theory of parallel transport that generalizes the use of gradient flows in Morse theory [ABSTRACT FROM AUTHOR]

In 2007 Cortés and Peña introduced a pivoting strategy for the Neville elimination of nonsingular sign regular matrices and called it two-determinant pivoting. Neville elimination has been very useful for obtaining theoretical and practical properties for totally positive (negative) matrices and other related types of matrices. A real matrix is said to be almost strictly sign regular if all its nontrivial minors of the same order have the same strict sign. In this paper, some nice properties related with the application of Neville elimination with two-determinant pivoting strategy to almost strictly sign regular matrices are presented. [ABSTRACT FROM AUTHOR]

A quantifier elimination algorithm by cylindrical algebraic decomposition based on regular chains is presented. The main idea is to refine a complex cylindrical tree until the signs of polynomials appearing in the tree are sufficient to distinguish the true and false cells. We report an implementation of our algorithm in the RegularChains library in Maple and illustrate its effectiveness by examples. [ABSTRACT FROM AUTHOR]

We report on our on-going efforts to apply real quantifier elimination to the synthesis of optimal numerical algorithms. In particular, we describe a case study on the square root problem: given a real number x and an error bound ε , find a real interval such that it contains x and its width is less than or equal to ε . A typical numerical algorithm starts with an initial interval and repeatedly updates it by applying a “refinement map” on it until it becomes narrow enough. Thus the synthesis amounts to finding a refinement map that ensures the correctness and optimality of the resulting algorithm. This problem can be formulated as a real quantifier elimination. Hence, in principle, the synthesis can be carried out automatically. However, the computational requirement is huge, making the automatic synthesis practically impossible with the current general real quantifier elimination software. We overcame the difficulty by (1) carefully reducing a complicated quantified formula into several simpler ones and (2) automatically eliminating the quantifiers from the resulting ones using the state-of-the-art quantifier elimination software. As the result, we were able to synthesize semi-automatically an optimal quadratically 1 convergent map, which is better than the well known hand-crafted Secant-Newton map. Interestingly, the optimal synthesized map is not contracting as one would naturally expect. [ABSTRACT FROM AUTHOR]

Inferentialism claims that the rules for the use of an expression express its meaning without any need to invoke meanings or denotations for them. Logical inferentialism endorses inferentialism specifically for the logical constants. Harmonic inferentialism, as the term is introduced here, usually but not necessarily a subbranch of logical inferentialism, follows Gentzen in proposing that it is the introduction-rules which give expressions their meaning and the elimination-rules should accord harmoniously with the meaning so given. It is proposed here that the logical expressions are those which can be given schematic rules that lie in a specific sort of harmony, general-elimination (ge) harmony, resulting from applying a certain operation, the ge-procedure, to produce ge-rules in accord with the meaning defined by the I-rules. Griffiths (2014) claims that identity cannot be given such rules, concluding that logical inferentialists are committed to ruling identity a nonlogical expression. It is shown that the schematic rules for identity given in Read (2004), slightly amended, are indeed ge-harmonious, so confirming that identity is a logical notion. [ABSTRACT FROM AUTHOR]

We prove that if T is a complete theory with weak elimination of imaginaries, then there is an explicit bijection between strict independence relations for T and strict independence relations for Teq. We use this observation to show that if T is the theory of the Fraïssé limit of finite metric spaces with integer distances, then Teq has more than one strict independence relation. This answers a question of Adler (J Math Log 9(1):1-20, , Question 1.7). [ABSTRACT FROM AUTHOR]

The $$\Omega $$ -rule was introduced by W. Buchholz to give an ordinal-free proof of cut-elimination for a subsystem of analysis with $$\Pi ^{1}_{1}$$ -comprehension. W. Buchholz's proof provides cut-free derivations by familiar rules only for arithmetical sequents. When second-order quantifiers are present, they are introduced by the $$\Omega $$ -rule and some residual cuts are not eliminated. In the present paper, we introduce an extension of the $$\Omega $$ -rule and prove the complete cut-elimination by the same method as W. Buchholz: any derivation of arbitrary sequent is transformed into its cut-free derivation by the standard rules (with induction replaced by the $$\omega $$ -rule). In fact we treat the subsystem of $$\Pi ^{1}_{1}$$ -CA (of the same strength as $$ID_{1}$$ ) that W. Buchholz used for his explanation of G. Takeuti's finite reductions. Extension to full $$\Pi ^{1}_{1}$$ -CA is planned for another paper. [ABSTRACT FROM AUTHOR]

Motivated by a recent Basu–Martin–Ryan paper, we obtain a reduced primal-dual pair of a linear semi-infinite programming problem by applying an amended Fourier–Motzkin elimination method to the linear semi-infinite inequality system. The reduced primal-dual pair is equivalent to the original one in terms of consistency, optimal values and asymptotic consistency. Working with this reduced pair and reformulating a linear semi-infinite programme as a linear programme over a convex cone, we reproduce all the theorems that lead to the full eleven possible duality state classification theory. Establishing classification results with the Fourier–Motzkin method means that the two classification theorems for linear semi-infinite programming, 1969 and 1974, have been proved by new and exciting methods. We also show in this paper that the approach to study linear semi-infinite programming using Fourier–Motzkin elimination is not purely algebraic, it is mixed algebraic-analysis. [ABSTRACT FROM AUTHOR]

A number of philosophers think that grounding is, in some sense, well-founded. This thesis, however, is not always articulated precisely, nor is there a consensus in the literature as to how it should be characterized. In what follows, I consider several principles that one might have in mind when asserting that grounding is well-founded, and I argue that one of these principles, which I call 'full foundations', best captures the relevant claim. My argument is by the process of elimination. For each of the inadequate principles, I illustrate its inadequacy by showing either that it excludes cases that should not be ruled out by a well-foundedness axiom for grounding, or that it admits cases that should be ruled out. [ABSTRACT FROM AUTHOR]

A method for eliminating residual vibrations in multimode systems is presented using a command shaping technique. The proposed command shaping technique captures two main advantages. Namely, the independence of the time length of the shaped command from the resonant frequencies of the system, and the ability to generate the command profile without a full system model. Experiments on systems with partial models represented by their resonant frequencies show that shaped command profiles generated using actual measured resonant frequencies of a system outperform those based on mathematical models. This feature of the proposed command shaping technique makes it very attractive for complicated multimode systems where mathematical models are difficult to build. Profiles of the proposed shaped command are simple and do not require intensive calculations. Performance of the proposed shaped command is validated using numerical simulations and experiments. Numerical simulations prove that the shaped commands are capable of completely eliminating residual vibrations of multimode systems. Experiments show that residual vibration elimination depends on the level of accuracy of the measured resonant frequencies of the system. [ABSTRACT FROM AUTHOR]

The sports elimination problem asks whether a team participating in a competition still has a chance to win, given the current standings and the remaining matches to be played among the teams. This problem can be viewed as a graph labelling problem, where arcs receive labels that contribute to the score of both endpoints of the arc, and the aim is to label the arcs in a way that each vertex obtains a score not exceeding its capacity. We investigate the complexity of this problem in detail, using a multivariate approach to examine how various parameters of the input graph (such as the maximum degree, the feedback vertex/edge number, and different width parameters) influence the computational tractability. We obtain several efficient algorithms, as well as certain hardness results. [ABSTRACT FROM AUTHOR]

While tools from structural graph theory such as tree- or path-width have proved to be highly successful in coping with computational intractability on undirected graphs, corresponding width measures for directed graphs have not yet fulfilled their promise for broad algorithmic applications on directed graphs. One reason for this is that in most existing digraph width measures the class of acyclic digraphs has small width which immediately implies hardness of problems such as computing directed dominating sets. Fernau and Meister (2014) introduce the concept of elimination width and a corresponding graph searching game which overcomes this problem with acyclic digraphs. In their paper, the focus was on structural characterizations of classes of digraphs of bounded elimination width. In this paper we study elimination width from an algorithmic and graph searching perspective. We analyse variations of the elimination width game and show that this leads to width measures on which the directed dominating set problem and some variants of it become tractable. [ABSTRACT FROM AUTHOR]

Solvers for linear systems with tridiagonal coefficient matrices sometimes employ direct methods such as the Gauss elimination method or the cyclic reduction method. In each step of the cyclic reduction method, nonzero offdiagonal entries in the coefficient matrix move incrementally away from diagonal entries and eventually vanish. The steps of the cyclic reduction method are generalized as forms of the stride reduction method. For example, the 2-stride reduction method coincides with the 1st step of the cyclic reduction method which transforms tridiagonal linear systems into pentadiagonal systems. In this paper, we explain arbitrary-stride reduction for linear systems with coefficient matrices with three nonzero bands. We then show that arbitrary-stride reduction is equivalent to a combination of 2-stride reduction and row and column permutations. We thus clarify eigenvalue clustering of coefficient matrices in the step-by-step process of the stride reduction method. We also provide two examples verifying this property. [ABSTRACT FROM AUTHOR]

Classifying large and real-world datasets is a challenging problem in machine learning algorithms. Among the machine learning methods, the support vector machine (SVM) is a well-known approach with high generalization ability. Unfortunately, while the number of training data increases and the data contain noise, the performance of SVM signifcantly decreases. In this paper, a fast and de-noise two-stage method for training SVMs to deal with large, real- world datasets is proposed. In the frst stage, data that contain noises or are suspected to be noisy are identifed and eliminated from the genuine training dataset. The process of elimination and identifcation is based on the movement of the center of the convex hull data in the training dataset. The convex hull data are computed via the QHull algorithm. On the other hand, the well-known fuzzy clustering method (FCM) is applied to compress and reduce the size of the training dataset. Finally, the reduced and purifed cluster centers are used for training the SVM. A set of experiments is conducted on the four benchmarking datasets of the UCI database. Moreover, the amount of training time and the generalization of the proposed approach are compared with FCM-SVM and normal SVM. The results indicate that the proposed method reduces the amount of training time and has a considerable success in removing noisy data from the training dataset. Therefore, the proposed method can achieve a higher generalization performance in comparison with the other methods in large, real-world datasets. [ABSTRACT FROM AUTHOR]

This paper proposes an unambiguous correlation function applicable to generic sine-phased binary offset carrier (BOC) signal tracking. In the proposed scheme, first, we view the BOC sub-carrier pulse as a sum of multiple rectangular pulses. Then, we obtain partial correlation functions by correlating the multiple rectangular pulses with the received signal, and subsequently, construct two symmetric correlation functions by combining the partial correlation functions in a specialized way. Finally, we generate an unambiguous correlation function by combining the two symmetric correlation functions. The proposed correlation function has a sharper main-peak, and consequently, provides a better tracking performance than those of the conventional correlation functions in terms of the tracking error standard deviation (TESD). [ABSTRACT FROM AUTHOR]

Nuisance parameter elimination is a central problem in capture–recapture modelling. In this paper, we consider a closed population capture–recapture model which assumes the capture probabilities varies only with the sampling occasions. In this model, the capture probabilities are regarded as nuisance parameters and the unknown number of individuals is the parameter of interest. In order to eliminate the nuisance parameters, the likelihood function is integrated with respect to a weight function (uniform and Jeffrey's) of the nuisance parameters resulting in an integrated likelihood function depending only on the population size. For these integrated likelihood functions, analytical expressions for the maximum likelihood estimates are obtained and it is proved that they are always finite and unique. Variance estimates of the proposed estimators are obtained via a parametric bootstrap resampling procedure. The proposed methods are illustrated on a real data set and their frequentist properties are assessed by means of a simulation study. [ABSTRACT FROM AUTHOR]

The inaccuracy and delay of speed feedback cause a vibration problem when the permanent magnet synchronous motor runs at low speed. As the low-speed smoothness is a key point of many applications of the permanent magnet synchronous motor, this article solves this problem by adding a real-time adjusted extended Kalman filter to low-precision-sensor vector control. In the mathematical model, the estimated speed of the extended kalman filter is significantly impacted by the deviations of the resistance and magnetic flux rather than other parameters. Thus, underid= 0 vector control, aRs-ψf-identifier is designed to calculate the values of the resistance and flux simultaneously with a small compensatingid. This algorithm runs on the platform in real time. Finally, the experiment results validate that when the velocity reaches as low as 1 r/min, the proposed method eliminates the vibration problem in the low-precision-sensor permanent magnet synchronous motor. [ABSTRACT FROM PUBLISHER]