Existence Of Counterexamples Research Articles

NOMINALIZED CLAUSES AND DISCOURSE‐GIVENNESS: EXPERIMENTAL EVIDENCE FROM RUSSIAN*

AbstractIn a seminal paper, Kiparsky & Kiparsky (1970) proposed a two‐way correspondence between presuppositionality of clauses and nominal structure. The proposal remains highly relevant to current research (a.o. Kastner 2015, Bochnak & Hanink 2022), despite the existence of counterexamples in both directions. In this paper, we examine Russian nominalized clauses to show that presuppositionality is indeed neither necessary nor sufficient for nominalization. However, instead of completely discarding the correspondence between presuppositionality and nominalization, we argue for a weaker “preference” hypothesis, whereby presuppositional, or discourse‐given, contexts are associated with a higher likelihood of nominalization compared to discourse‐new contexts. We provide support for the preference hypothesis based on four experimental studies, a forced‐choice and a givenness‐rating study using matrix negation as a proxy for givenness and a forced‐choice and a sentence completion study directly manipulating the discourse context. We suggest a tentative explanation for the preference hypothesis in terms of definiteness/familiarity marking.

Conjugacy classes of small size in solvable groups

If G is a finite group and , we say that x lies in a small class if is minimal among the sizes of the noncentral conjugacy classes of G. It has been conjectured that if G is a solvable group with trivial center and x belongs to a small class, then x lies in the center of the Fitting subgroup of G. We restrict the structure of a possible counterexample to this conjecture. We discuss the possible existence of a counterexample. As a consequence, we prove the conjecture when the small classes have prime sizes and also when all chief factors of G have rank at most 2. Perhaps surprisingly, the proof in the case when the small classes have prime size and the discussion on the existence of counterexamples use techniques from linear algebra.

Supermodular Batch State Estimation in Optimal Sensor Scheduling

This letter addresses the problem of activating, at each time-step in a finite time horizon problem, a subset of available sensors to generate a “high quality” estimate of the state of a discrete-time linear system operating under limited resources. We propose a sensor schedule that minimizes the mean square estimation error of the batch state vector of the system—the batch state estimation (BSE) problem. Due to the presence of limited resources, we address the cardinality-constrained BSE problem, which is inherently combinatorial and computationally intractable when working with large-scale systems. This NP-hard complexity is overcome by employing a greedy algorithm, which returns a near-optimal sensor schedule with performance guarantees when minimizing a supermodular objective over matroids . To this end, we prove (despite the existence of counter-examples in literature) that our objective function is supermodular when the batch prior information matrix is a strictly diagonally dominant ${M}$ -matrix (with a constraint on its inverse and conditions on the measurement model). Hence, we obtain a near-optimal solution to the BSE problem via a greedy algorithm. Additionally, we provide its time complexity.

Development and necessary norms of reasoning.

The question of whether reasoning can, or should, be described by a single normative model is an important one. In the following, I combine epistemological considerations taken from Piaget’s notion of genetic epistemology, a hypothesis about the role of reasoning in communication and developmental data to argue that some basic logical principles are in fact highly normative. I argue here that explicit, analytic human reasoning, in contrast to intuitive reasoning, uniformly relies on a form of validity that allows distinguishing between valid and invalid arguments based on the existence of counterexamples to conclusions.

Tightness of Semidefinite Programming Relaxation to Robust Transmit Beamforming with SINR Constraints

This paper considers a multiuser transmit beamforming problem under uncertain channel state information (CSI) subject to SINR constraints in a downlink multiuser MISO system. A robust transmit beamforming formulation is proposed. This robust formulation is to minimize the transmission power subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on the receivers. The challenging problem is that the worst-case SINR constraints correspond to an infinite number of nonconvex quadratic constraints. In this paper, a natural semidifinite programming (SDP) relaxation problem is proposed to solve the robust beamforming problem. The main contribution of this paper is to establish the tightness of the SDP relaxation problem under proper assumption, which means that the SDP relaxation problem definitely yields rank-one solutions under the assumption. Then the SDP relaxation problem provides globally optimum solutions of the primal robust transmit beamforming problem under proper assumption and norm-constrained CSI errors. Simulation results show the correctness of the proposed theoretical results and also provide a counterexample whose solutions are not rank one. The existence of counterexample shows that the guess that the solutions of the SDP relaxation problem must be rank one is wrong, except that some assumptions (such as the one proposed in this paper) hold.

A micromechanical model of toughening behavior in the dual-phase composite

The fabrication of a special kind of dual-phase composite consisting of a hard matrix and ductile phase, such as metals with bimodal grain size distribution, is a promising strategy for improving the tensile ductility of nanocrystalline (nc)/ultrafine-grained (ufg) materials ( Wang et al., 2002). This strategy is, however, challenged by the low reproducibility from low controllability of microstructural parameters and the existence of counterexamples ( Prasad et al., 2009). The key to meet these challenges is to control the bimodal microstructural parameters to enable quantificational investigation of the relation between mechanical properties and microstructural parameters, and then set up a correlative quantitative model. In this paper, a new micromechanical model based on the propagation and multiplication of localized deformation bands is developed. To assess the model, a series of hypo-eutectoid Cu–Al alloys with controllable bimodal structures are prepared and their stress–strain curves in tension, together with those of bimodal copper ( Wang et al., 2002) and bimodal Al–Mg alloys ( Han et al., 2005) are predicted. Close agreement between the model-predicted and experimental results is obtained. The strength and uniform ductility of bimodal materials are observed in strong relation to the microstructural and constitutive parameters of volume fraction, strain hardening coefficient, and size of the coarse-grained ductile phase. Additionally, appropriate microstructural and constitutive parameters to achieve effective toughening can also be estimated according to the model.

Legislative Versus Judicial Checks and Balances: Comparing Rights Policies Across Regimes

There is a longstanding debate in liberal constitutionalism over which method of rights protection – legislative or judicial – best achieves the moderate policy outcomes envisioned by democratic theorists. This article examines this question by comparing two Commonwealth countries, Canada and Australia, which explicitly placed themselves on opposite sides of the debate. After outlining the historical debate, a case study design compares the policy process and outcome in the two countries on the issues of prisoner voting and same-sex marriage. The data suggest that bicameral legislatures best serve their moderating functions when the government is not in control of the upper chamber, whereas rights-based judicial involvement in policy making tends to promote extreme policy outcomes. The evidence is mixed, however, and the existence of counter-examples points the way to further research.

Failure of privalov's theorem on flatC2−∊Curves in the Unit Ball ofC2

In this paper we prove an extension of an estimate first proved by Ahern and Bruna of the modulus of absolute continuity holomorphic functions have on real analytic curves in the unit ball to a certain class of smooth curves satisfying a finite type condition. We then show that this yields insights into the sharpness of recent formulations of Privalov's theorem in the unit ball and in particular to the existence of counterexamples on flat C 2−∊ curves.

The Tyranny of Tests

Disclaimer This article is full of generalizations, many about student attitudes. Such generalizations, unlike generalizations in mathematics, are not invalidated by the existence of counterexamples. All of us know the joy of teaching those exceptional undergraduates who really want to learn and are stimulated by the beauty and power of the mathematics they are learning. It is these students who give us the conviction that we are, as teachers, doing something thoroughly worthwhile, despite our many failures. 1. INTRODUCTION. I have been distressed for many years by the defects in our methods of evaluating students-at all levels from 3rd grade upwards to graduate students-and have railed especially against the unfortunate effects of over-frequent testing and inappropriate tests, especially multiple-choice and standardized tests. I have not changed my point of view on these issues; but I have come to realize that the ubiquity of intrusive testing, contaminating the learning environment, distorting the curriculum, and undermining the fabric of the teacher-student relationship, springs from a deep malaise in our whole approach to education, and is not to be remedied simply by attempting to improve the quality and relevance of the tests administered and reducing their frequency. Such a superficial approach may be thought of as treating a symptom and leaving the cause of the disease untouched. In this article I would like to develop this thought, and then raise the question of whether any change-any beneficial change, that is-is possible. I will largely confine myself to undergraduate education-principally, of course, in mathematics. 2. THE ROOT CAUSE OF THE PROBLEM. I have often remarked that, in this country, there is a fundamental confusion of education with training. Thus, whereas drivers of lethal automobiles stand in evident need of first-class training, we provide 'driver education'; and whereas teachers stand in evident need of first-class education, we provide 'teacher training.' Indeed, I would now go further and say that, in general, our students-and their parents-only feel comfortable with the presence of a curricular item if it has an evident value for the students'

The Tyranny of Tests

Disclaimer This article is full of generalizations, many about student attitudes. Such generalizations, unlike generalizations in mathematics, are not invalidated by the existence of counterexamples. All of us know the joy of teaching those exceptional undergraduates who really want to learn and are stimulated by the beauty and power of the mathematics they are learning. It is these students who give us the conviction that we are, as teachers, doing something thoroughly worthwhile, despite our many failures. 1. INTRODUCTION. I have been distressed for many years by the defects in our methods of evaluating students-at all levels from 3rd grade upwards to graduate students-and have railed especially against the unfortunate effects of over-frequent testing and inappropriate tests, especially multiple-choice and standardized tests. I have not changed my point of view on these issues; but I have come to realize that the ubiquity of intrusive testing, contaminating the learning environment, distorting the curriculum, and undermining the fabric of the teacher-student relationship, springs from a deep malaise in our whole approach to education, and is not to be remedied simply by attempting to improve the quality and relevance of the tests administered and reducing their frequency. Such a superficial approach may be thought of as treating a symptom and leaving the cause of the disease untouched. In this article I would like to develop this thought, and then raise the question of whether any change-any beneficial change, that is-is possible. I will largely confine myself to undergraduate education-principally, of course, in mathematics. 2. THE ROOT CAUSE OF THE PROBLEM. I have often remarked that, in this country, there is a fundamental confusion of education with training. Thus, whereas drivers of lethal automobiles stand in evident need of first-class training, we provide 'driver education'; and whereas teachers stand in evident need of first-class education, we provide 'teacher training.' Indeed, I would now go further and say that, in general, our students-and their parents-only feel comfortable with the presence of a curricular item if it has an evident value for the students'