Direct Argument Research Articles

Weak error analysis for the stochastic Allen–Cahn equation

We prove strong rate resp. weak rate O(τ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {O}}}(\ au )$$\\end{document} for a structure preserving temporal discretization (with τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document} the step size) of the stochastic Allen–Cahn equation with additive resp. multiplicative colored noise in d=1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=1,2,3$$\\end{document} dimensions. Direct variational arguments exploit the one-sided Lipschitz property of the cubic nonlinearity in the first setting to settle first order strong rate. It is the same property which allows for uniform bounds for the derivatives of the solution of the related Kolmogorov equation, and then leads to weak rate O(τ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {O}}}(\ au )$$\\end{document} in the presence of multiplicative noise. Hence, we obtain twice the rate of convergence known for the strong error in the presence of multiplicative noise.

GEOMETRICALLY INDUCED BOUND STATES IN SOFT WAVEGUIDES AND QUANTUM DOTS ARRAYS

Abstract. The present talk deals with properties of a quantum particle interacting with a potential having the form of a potential ‘ditch’, or an array of potential wells; we discuss how can be the geometry of the potential support reflected in the spectrum of the corresponding Hamiltonian. In particular, we provide sufficient conditions under which a bend of such a potential guide or array gives rise to a non-empty discrete spectrum; we employ different techniques: the Birman-Schwinger method [1,3] or a direct variational argument based on construction of a suitable trial function [2]. We also address the problem of ground state optimalization in case of loop-shaped configurations [3,4].

Hessenberg-Toeplitz matrix determinants with Schröder and Fine number entries

In this paper, we find determinant formulas of several Hessenberg-Toeplitz matrices whose nonzero entries are derived from the small and large Schröder and Fine number sequences. Algebraic proofs of these results can be given which make use of Trudi's formula and the generating function of the associated sequence of determinants. We also provide direct arguments of our results that utilize various counting techniques, among them sign-changing involutions, on combinatorial structures related to classes of lattice paths enumerated by the Schröder and Fine numbers. As a consequence of our results, we obtain some new formulas for the Schröder and Catalan numbers as well as for some additional sequences from the OEIS in terms of determinants of certain Hessenberg-Toeplitz matrices.

Only CDT values knowledge

Abstract Causal decision theory is often motivated as a ‘revision of [decision theory] intended to solve Newcomb’s problem’ (Bacon 2022). In this paper, I give a direct argument for CDT by deriving it from a venerable decision-theoretic principle: the value of knowledge principle. The general framework that I use to deliver this result also supports a new argument for conditionalization.

Minimizing properties of networks via global and local calibrations

AbstractIn this note, we prove that minimal networks enjoy minimizing properties for the length functional. A minimal network is, roughly speaking, a subset of composed of straight segments joining at triple junctions forming angles equal to ; in particular such objects are just critical points of the length functional a priori. We show that a minimal network : (i) minimizes mass among currents with coefficients in an explicit group (independent of ) having the same boundary of , (ii) identifies the interfaces of a partition of a neighborhood of solving the minimal partition problem among partitions with same boundary traces. Consequences and sharpness of such results are discussed. The proofs reduce to rather simple and direct arguments based on the exhibition of (global or local) calibrations associated to the minimal network.

Determinants of Budget Performance Based on The Value for Money Concept

Purpose: This study aims to determine the effect of accountability, transparency, and supervision on the Value for Money concept budget performance at the Gunung Kidul Regency Government. Methodology/Approach: This study uses respondent data derived from the process of distributing questionnaires. Respondents are the Head of Service, Office Treasurer, Head of Finance, and Head of Planning from 24 Regional Apparatus Organizations of Gunung Kidul Regency. The process of data analysis using multiple linear regression with the analytical tool used is SPSS. Findings: The hypothesis proposed in this study is that accountability, transparency, and supervision positively affect the performance of the Value for Money concept budget. The Local governments that apply the principles of accountability, transparency, and good oversight will improve the budget performance process with the Value for Money concept. Practical and Theoretical contribution/Originality: The Regional Government budget can be realized with the principles of economy, effectiveness, and efficiency. The government of Gunung Kidul Regency is expected to increase accountability, transparency, and control to produce good budget performance. Research Limitation: This study has limitations in the level of generalization of research results. This study only measures the influence of the budget with the concept of Value for Money in Gunung Kidul Regency. Each region has different characteristics and conditions, so this research cannot be generalized. Furthermore, research data collection has closed questions so that researchers do not get direct and detailed arguments from respondents as a whole.

Existence and Concentration Results for the General Kirchhoff-Type Equations

We consider the following singularly perturbed Kirchhoff-type equations $$\begin{aligned} -\varepsilon ^2 M\left( \varepsilon ^{2-N}\int _{{\mathbb {R}}^N}|\nabla u|^2 \textrm{d}x\right) \Delta u +V(x)u=|u|^{p-2}u~\hbox {in}~{\mathbb {R}}^N, u\in H^1({\mathbb {R}}^N),N\ge 1, \end{aligned}$$ where $$M\in C([0,\infty ))$$ and $$V\in C({\mathbb {R}}^N)$$ are given functions. Under very mild assumptions on M, we prove the existence of single-peak or multi-peak solution $$u_\varepsilon $$ for above problem, concentrating around topologically stable critical points of V, by a direct corresponding argument. This gives an affirmative answer to an open problem raised by Figueiredo et al. (Arch Ration Mech Anal 213(3):931–979, 2014)

New existence for the higher order prescribed curvature problem

We consider the following prescribed curvature problem involving polyharmonic operator on $ \mathbb{S}^{N}: $ \begin{document}$ \begin{align*} D^{m}u = K(|y|)u^{m^{*}-1}, \quad u > 0 \quad \hbox{in} \quad \mathbb{S}^{N}, \quad u \in H^{m}(\mathbb{S}^{N}), \end{align*} $\end{document} where $ K(|y|) $ is a positive function, $ m^{*} = \frac{2N}{N-2m} $ is the critical exponent of Sobolev embedding, $ N>6m. $ $ D^m $ is the $ 2m $ order differential operator given by$ D^m = \prod\limits_{l = 1}^m (-\Delta_g+\frac{1}{4}(N-2l)(N+2l-2)), $where $ \Delta_g $ is the Laplace-Beltrami operator on $ \mathbb{S}^N, $ and $ \mathbb{S}^N $ is the unit sphere with Riemann metric $ g. $ By applying the non-degenerate result of positive multi-bubbling solutions constructed in [15], we construct new type solutions by using Lyaponov Schmidt reduction arguments combining with the gluing method. One will see that this type of new solution is difficult to be obtained through direct critical theory and reduction argument. We consider the problem from a different point of view and glue $ n $ bubble solution to $ k $ bubble solution and obtain new type multi bubble solution.

An aspectual account of constructions headed by unergatives and unaccusatives

AbstractThis article presents an aspectual account of the interface between lexicon and syntax. Following Tenny’s AIH (Aspectual Interface Hypothesis), we assume that only the aspectual property of lexical information is sensitive and predictive to argument structure. Based on this assumption, the article claims that aspectual roles associated with measuring-out and delimitedness offer a single and unified account of argument structure. To begin with, a peculiar focus is given to the direct internal argument which serves as the only measuring-out role and participates the measurement constraint in three verb types including the incremental-theme verbs, the change-of-state verbs and route verbs with path objects, Another aspectual property is delimitedenss that functions as the terminus role of event progression in the form of delimiting markers such as verb particles or resultative predicates.To better testify the claim, the article focuses on constructional variations derived from some typical unergatives and unaccusatives, because the semantic distinction between the two verb types is mainly reflected on the syntactic property that urergatives normally require an agent while unaccusatives ask for a compulsory theme or patient. Yet Constructional variations derived from unergatives and unaccusatives consistently instantiate the measuring-out constraint on direct internal argument. For unergatives, an undelimited event is converted into a delimited one by addition of measuring direct argument, while for unaccusatives, semantic differences arise from alternating arguments that go through changes. Hence constructional variations further prove that syntactic structure fundamentally operates over the aspectual roles rather than thematic roles.

A short proof of Host’s equidistribution theorem

This note contains a new proof of Host’s equidistribution theorem for multiplicatively independent endomorphisms of ℝ/ℤ. The method is a simplified version of our recent work on equidistribution under toral automorphisms [2] and is related to the argument in [3], but avoids the use of the scenery flow and of Marstrand’s projection theorem, using instead a direct Fourier argument to establish smoothness of the limit measure.

Assumptions, Hypotheses, and Antecedents

This paper is about the distinction between arguments and conditionals, and the corresponding distinction between premises and antecedents. I will also propose a further distinction between two different kinds of argument, and, correspondingly, two kinds of premise that I will call "assumption" and "hypothesis." The distinction between assumptions, hypotheses, and antecedents is easily made in artificial languages, and we are already familiar with it from our first logic courses (although not necessarily under those names, since there is no standard terminology for the distinction). After explaining their differences in artificial languages, I will argue that there are ordinary-language counterparts of these three notions, meaning that some formal properties of the artificial notions nicely capture some features of the ordinary-language counterparts and their behavior in contexts of reasoning. My next crucial claim is that these three notions often get confused in ordinary language, which leads to problems for translation into symbols. I will suggest a solution to the translation problem by pointing to some distinctive characteristics of the three notions that link them to their artificial-language counterparts. Next, I will argue that this confusion is behind some well-known philosophical problems and puzzles. I will apply the distinctions in order to explain away some famous paradoxes: the direct argument (also known as or-to-if inference), a standard argument for fatalism, and McGee's counterexample to modus ponens. As Stalnaker also solved the first two of these paradoxes by using his theory of reasonable inference, I will elucidate the similarities between our solutions, and also explain why my distinctions apply more broadly, to some cases involving indicative and counterfactuals conditionals, where reasonable inference does not apply.

The Effects of Fiscal Policy on the Performance of Commercial Banks in Kenya

Fiscal policy refers to the use of government spending and tax policies to influence economic conditions. Fiscal policies have existed for a long time, with major debates between proponents of the Keynesian model and the monetary approach. Fiscal policy can either be contractionary, expansionary, or neutral. This study analyses the literature on the effect of the national budget on banks performance; effect of Taxation on bank performance; and the effect of public expenditure on performance of Banks in Kenya. The literature shows that government expenditure is a good fiscal policy measure in terms of the positive performance of commercial banks however, there is a need to consider the issue of corruption that negatively affects the expenditure controls that are crucial in an effective government approach in terms of the way the authorities ensure effective expenditure programs. Budget surplus and the positive impact on banks’ lending, no direct or clear argument shows the role of budgeting on commercial banks' performance. Taxes also play an important role in developing infrastructures that are crucial for the improved performance of firms. However, gaps exist in literature that needs to explored by further studies.

Symplectic embeddings into disk cotangent bundles

In this paper, we compute the embedded contact homology (ECH) capacities of the disk cotangent bundles $D^*S^2$ and $D^*\mathbb{R} P^2$. We also find sharp symplectic embeddings into these domains. In particular, we compute their Gromov widths. In order to do that, we explicitly calculate the ECH chain complexes of $S^*S^2$ and $S^* \mathbb{R} P^2$ using a direct limit argument on the action inspired by Bourgeois's Morse-Bott approach and ideas from Nelson-Weiler's work on the ECH of prequantization bundles. Moreover, we use integrable systems techniques to find explicit symplectic embeddings. In particular, we prove that the disk cotangent bundles of a hemisphere and of a punctured sphere are symplectomorphic to an open ball and a symplectic bidisk, respectively.

Németh T., Enikő: Implicit Subject and Direct Object Arguments in Hungarian Language use: Grammar and Pragmatics Interacting

Article Németh T., Enikő: Implicit Subject and Direct Object Arguments in Hungarian Language use: Grammar and Pragmatics Interacting was published on September 1, 2022 in the journal Intercultural Pragmatics (volume 19, issue 4).

The Sidney Sperry/Heber Snell Debates: Critical Biblical Scholarship and Mormon Tradition

The Sidney Sperry/Heber Snell Debates: Critical Biblical Scholarship and Mormon Tradition

Diagnoses and special educational support. A study of institutional decision-making of provision of special educational support for children at school

ABSTRACT This study investigates what role diagnoses play in institutional decision-making in regards to provision of special educational support and in the referral of pupils from mainstream schooling to special needs schools or classes. During the past decades, many countries have witnessed a radical increase in the number of children receiving psychiatric diagnoses, and increasing demands for special educational support. This development raises the question of how these two observations relate, and if psychiatric diagnoses serve as a prerequisite for allocating support. This study uses an institutional ethnographic approach to analyse qualitative data from four Danish municipal referral committees, processing 13 children’s cases. In these settings, representatives of school authorities and educational psychologists decide if a child should be offered special educational support. The results show that the committees do not use diagnoses as direct arguments for their decisions. However, the institutional setup of the referral system creates an expectation that children referred to the committees already are diagnosed, as the types of special educational support are organised according to diagnostic categories. When a child is identified as experiencing problems at school, this expectation might prompt schools, parents or educational psychologists to request that a psychiatric assessment is carried out.

Analytic properties of heat equation solutions and reachable sets

There recently has been some interest in the space of functions on an interval satisfying the heat equation for positive time in the interior of this interval. Such functions were characterised as being analytic on a square with the original interval as its diagonal. In this short note we provide a direct argument that the analogue of this result holds in any dimension. For the heat equation on a bounded Lipschitz domain (Omega subset mathbb {R}^{d}) at positive time all solutions are analytically extendable to a geometrically determined subdomain {mathcal {E}}(Omega ) of {mathbb {C}}^d containing (Omega ). This domain is sharp in the sense that there is no larger domain for which this is true. If (Omega ) is a ball we prove an almost converse of this theorem. Any function that is analytic in an open neighbourhood of {mathcal {E}}(Omega ) is reachable in the sense that it can be obtained from a solution of the heat equation at positive time. This is based on an analysis of the convergence of heat equation solutions in the complex domain using the boundary layer potential method for the heat equation. The converse theorem is obtained using a Wick rotation into the complex domain that is justified by our results. This gives a simple explanation for the shapes appearing in the one-dimensional analysis of the problem in the literature. It also provides a new short and conceptual proof in that case.

Competing with God?

Summary Christians often presume that immediate and universally extensive divine governance of human behavior is incompatible with human agency and responsibility. Against this presumption, Kathryn Tanner argues for a distinctive metalinguistic paradigm whereby Christians can coherently speak of God’s transcendence in such a way that divine action could never in principle ‘compete’ with human action. Thus, it is said, God can comprehensively will each human action without thereby compromising significant human freedom and corresponding moral responsibility. In this article, it is argued that Tanner’s non-competitivist paradigm fails to circumvent a theological version of the ‘direct argument’ for the incompatibility between human moral responsibility and causal determinism.

Assessment of Foreign Direct Investment-Led Growth Argument in South Africa Amidst Urbanization and Industrialization: Evidence from Innovation Accounting Tests

The objective of this study is to investigate the FDI-led growth hypothesis for the case of South Africa for the period between 1970 and 2017. The preliminary analysis of unit root test using traditional methods shows a different order of integration, which necessitates the use of autoregressive distributive lag (ARDL) methodology. Additionally, the current study also leverages on the innovative accounting techniques which comprised of impulse response function and forecast error variance decomposition (FEVD), which are employed to explore the responsiveness of the variables on each other. Our study results show that FDI inflow exerts a very strong positive impact on economic growth, thus validating the FDI-induced growth nexus in the South African economy. Furthermore, causality results show a one-way link running only from FDI inflow to economic growth and a unidirectional connection from urbanization to FDI inflow. The implication is that only urbanization matters in attracting FDI inflow to South Africa. These outcomes suggest that there is a need for the government administrators to develop urban centers through improving infrastructure facilities and the provision of industrial zones as a way of expanding both the ready market and the absorptive capacity of the country.

Assignment of Macroroles to the Double Objects of Verbs of Transferring: A Role and Reference Grammar Perspective

Ditransitive verbs that have two objects can be challenging when analyzed from the perspective of universal theories like Role and Reference Grammar (RRG) because each language deals with them in a different way. That is, each language has its own way to classify these verbs. This leads to some differences in the semantic role that each element performs in the sentence. RRG assumes two main macroroles for arguments in the clause: actor and undergoer. Therefore, the second object of a ditransitive verb is given the role of “non-macrorole direct core argument.” Haspelmath (2008) argues that two macroroles may not be enough to cover the cross-linguistic variations. Therefore, he suggests two additional macroroles. This paper, then, tackles the issue of role assignment in English and Arabic double-object constructions (DOCs) in the light of RRG taking into consideration Haspelmath’s suggestion. A limitation is made in this concern; it will be with ditransitive verbs that encode the action of receiving. It was concluded that the third argument of ditransitive verbs may not receive a non-macrorole direct core argument as the theory assumes, but can receive new roles that express the nature of the relationship between these arguments and their verbs.