Weak Restrictions Research Articles

An adaptive BDF2 implicit time-stepping method for the phase field crystal model

Abstract An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal model. The suggested method is proved to preserve a modified energy dissipation law at the discrete levels when the time-step ratios satisfy $r_k:=\tau _k/\tau _{k-1}<3.561$, which is the zero-stability restriction of the variable-step BDF2 scheme for ordinary differential equations. With the help of discrete orthogonal convolution kernels and corresponding convolution inequalities, an optimal $L^2$ norm error estimate is established under the weak step-ratio restriction $0<r_k<3.561$ to ensure energy stability. As far as we know, this is the first time that such an error estimate is theoretically proved for a nonlinear parabolic equation. Based on tests on random temporal meshes an effective adaptive time-stepping strategy is suggested to efficiently capture the multi-scale behavior and accelerate the numerical simulations.

SVAR (Mis)Identification and the Real Effects of Monetary Policy Shocks

I argue that the seemingly disparate findings of the recent empirical literature on monetary policy transmission are all consistent with the same standard macro models. Weak sign restrictions, which suggest that contractionary monetary policy, if anything, boosts output, present as policy shocks what actually are expansionary demand and supply shocks. Classical zero restrictions are robust to such misidentification, but miss short-horizon effects. Two recent approaches—restrictions on Taylor rules and external instruments—instead work well. My findings suggest that empirical evidence is consistent with models in which the real effects of monetary policy are larger than commonly estimated. (JEL C32, E12, E32, E43, E52)

CDS trading and nonrelationship lending dynamics

We investigate how credit default swaps (CDSs) affect lenders’ incentives to initiate new lending relationships. We predict that CDSs reduce adverse selection that nonrelationship lead arrangers face when competing for loans. Consistently, we find that a loan is more likely to be syndicated by a nonrelationship lead arranger following CDS trading initiation on a borrower’s debt. We also show that borrowers that obtain loans from nonrelationship lead arrangers in the post-CDS trading initiation period are more opaque, in line with the effect of CDSs being more pronounced for borrowers for which adverse selection costs are higher. Further analyses show that, relative to relationship lead arrangers, nonrelationship lead arrangers have lower monitoring incentives in the post-period, as reflected by less restrictive covenants and performance pricing provisions they impose and by the reduced loan shares they retain. Moreover, we find that borrowers of nonrelationship lead arrangers following CDS trading initiation have higher growth opportunities and more volatile operations, consistent with such borrowers benefiting more from weaker restrictions on their activities imposed by lenders. Lastly, lower monitoring incentives of CDS-protected nonrelationship lead arrangers also decrease the propensity of inexperienced participants to join their syndicates. Overall, our findings suggest that CDS trading significantly changes nonrelationship lending dynamics.

Why the financial aid of the EU's regional policy does not impact on the public investment level? The case of the Spanish regions

Given that an expansive impact of the European Regional Development Fund (ERDF) aid on public investment is expected, two models have been estimated to determine, respectively, the size of this impact and the relationship between the own financing of regional public investment and the external financing received from ERDF in Spanish regions. Evidence has been obtained that the impact of transfers from the ERDF on public investment is almost nil. In addition, for each euro that the Spanish regions received from the ERDF, own funds for public investment allocated by regional governments have been reduced 23 cents, showing an important relation of substitution between the two sources of financing. Both models include data between 1994 and 2014 and their estimation has used traditional methods and methods based on the cointegration of variables with a panel structure, such as FMOLS and DOLS. The main results obtained with the two methodologies they are quite close, confirming the initial hypothesis: in the presence of weak donor restrictions, the political process in governments receiving ERDF transfers determine revealed preferences about public investment, neutralizing conditions established by the donor. This study also unequivocally demonstrates the presence of simultaneous causality between investment aid received from the ERDF and regional public investment and between said aid and the own resources that regional governments dedicate to financing public investment. These findings confirm the existence of a bias that seriously affects the effectiveness of the European Union's regional policy.

Parallel coordinates in three dimensions and sharp spectral isoperimetric inequalities

In this paper we show how the method of parallel coordinates can be extended to three dimensions. As an application, we prove the conjecture of Antunes, Freitas and Krej\v{c}i\v{r}\'ik \cite{AFK} that "the ball maximises the first Robin eigenvalue with negative boundary parameter among all convex domains of equal surface area" under the weaker restriction that the boundary of the domain is diffeomorphic to the sphere and convex or axiconvex. We also provide partial results in arbitrary dimensions.

Inflation targeting in low‐income countries: Does IT work?

AbstractPrevious research on inflation targeting (IT) has focused on high‐income countries and emerging market economies (EMEs). Only recently have sufficient data accumulated for the performance of IT in low‐income countries (LICs) to be assessed. We show that IT has not so far been as effective in reducing inflation in LICs as in EMEs. Relatively low central banks’ instrument independence in LICs, associated with weak restrictions limiting a central bank’s lending to the government, helps explain this result.

О существовании граничных и начальных значений для вырождающихся параболических уравнений в областях с ляпуновской границей

В данной работе, являющейся продолжением [1], устанавливаются необходимые и достаточные условия того, чтобы решение параболического уравнения 2-го порядка с боковой границей, принадлежащей классу $C^{1+\lambda}$, $\lambda >0$, вырождающегося на границе области, имело предел в среднем на боковой поверхности цилиндрической области и предел в среднем на ее нижнем основании, и исследуется вопрос об однозначной разрешимости первой смешанной задачи для такого уравнения в случае, когда граничная и начальная функции принадлежат пространствам типа $L_2$. Наиболее близкими к рассматриваемому кругу вопросов являются теоремы Ф. Рисса и Ж. Литтлвуда и Р. Пэли, в которых даются критерии предельных значений в $L_p$, $p > 1$, аналитических в единичном круге функций. Дальнейшее развитие этой тематики для равномерно эллиптических уравнений получило в работах В. П. Михайлова, А. К. Гущина [2–4]. Условие гладкости границы ($\partial Q \in C^2$) можно ослабить (см. [5]). При наиболее слабых ограничениях на гладкость границы (и на коэффициенты уравнения) критерии существования граничного значения установлены в работах [4, 6–8]. При этом, как показано в работе [7], все направления принятия граничных значений для равномерно эллиптических уравнений оказываются равноправными, решение обладает свойством, аналогичным свойству непрерывности по совокупности переменных. В случае вырождения уравнения на границе области, когда направления не являются равноправными, ситуация более сложная. При этом постановка первой краевой задачи определяется типом вырождения. В случае, когда значения соответствующей квадратичной формы вырождающегося эллиптического уравнения на векторе нормали отличны от нуля (вырождение типа Трикоми), корректна задача Дирихле, и свойства такого вырождающегося уравнения весьма близки к свойствам равномерно эллиптического уравнения. В частности, в этой ситуации справедливы аналоги теорем Рисса [9] и Литтлвуда — Пэли [10, 11]. This work, being a continuation of [1], establishes the necessary and sufficient conditions for the solution of the second-order parabolic equations with a lateral boundary from the class $C^{1+\lambda}$, $\lambda >0$, degenerating on the boundary of the domain, to have an average limit on the lateral surface of the cylindrical domain and the limit in the mean on its lower base. Also, we study the question of the unique solvability of the first mixed problem for such equations in the case when the boundary and initial functions belong to spaces of the типа $L_2$ type. The closest to the questions under consideration are the theorems of F. Riesz and J. Littlewood and R. Paley, in which criteria are given for the limit values in $L_p$, $p > 1$, of the functions analytic in the unit disk. Further development of this topic for uniformly elliptic equations was obtained in the papers by V. P. Mikhailov and A. K. Gushchin [2–4]. The boundary smoothness condition ($\partial Q \in C^2$) can be weakened (see [5]). Under the weakest restrictions on the smoothness of the boundary (and on the coefficients of the equation), the criteria for the existence of a boundary value were established in [4, 6–8]. In this case, as shown in [7], all directions of the acceptance of boundary values for uniformly elliptic equations turn out to be equal, while the solution has a property similar to the property of continuity with respect to the set of variables. In the case of degeneracy of the equation on the boundary of the domain when the directions are not equal, the situation is more complicated. In this case, the formulation of the first boundary value problem is determined by the type of degeneracy. In the case when the values of the corresponding quadratic form of the degenerate elliptic equation on the normal vector are different from zero (the Tricomi type degeneracy), the Dirichlet problem is correct, and the properties of such degenerate equations are very close to the properties of uniformly elliptic equations; in particular, in this situation analogues of the Riesz [9] and Littlewood–Paley theorems [10, 11] are valid.

Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments

Abstract Neutral differential equations are one of the most important extensions of classical ordinary differential equations and aim to give a better explanation for modeling phenomena where ordinary differential equations are insufficient. Naturally, all the questions studied in the scope of ordinary differential equations attracted the attention also for neutral differential equations. In this paper we study the oscillatory properties of second order half-linear neutral differential equations. We present oscillation criteria derived using a new approach. This approach allows us to reduce common restrictions on the deviations in arguments which are present in the currently known results of this type.

Generic regularity of differentiated product oligopolies

In oligopoly models with differentiated products, producers face a market demand function that reflects the preferences of consumers. However, typical assumptions on preferences place only weak restrictions on the shape of aggregate demand. This may result in profit functions that are not strictly quasiconcave, in best-reply correspondences that are not differentiable, and in equilibria that are not robust to perturbations. This paper establishes differentiability and robustness as a generic property: for an open, dense set of economies, best replies are differentiable in a neighborhood of equilibria, which is a precondition for comparative statics. All these economies have a finite number of equilibria in pure strategies.

Health, migration and human rights

ABSTRACT Doctors, nurses and midwifes from developing countries migrate to affluent countries in large numbers, often leaving behind severely understaffed healthcare systems. One way to limit this ‘brain drain’ is to restrict the freedom of movement of healthcare workers. Yet this seems to give rise to a conflict of human rights: on the one hand rights to freedom of movement, on the other hand rights to health. By motivating its own account of human rights, this paper argues that the conflict is not as acute as it seems, since rights to freedom of movement are in fact more limited than often acknowledged. Weak restrictions of the freedom to leave and strong restrictions of the freedom to enter are in principle compatible with the rights of healthcare workers. Hence, policies that involve restrictions of both kinds can be justified in order to secure the human right to health.

The Causal Impact of Medals on Wine Producers' Prices and the Gains from Participating in Contests

The main objective of this article is to estimate the causal effect of wine medals on producers' prices. Our data set combines information on transactions between wine producers and wholesale traders (these data are registered by a wine broker who acts as a middleman in this market), with records from eleven important wine competitions. Our identification strategy exploits a particularity in our data, namely that medals are not only awarded before transaction dates but sometimes also thereafter. Regressing price on dummies indicating past and future medals (plus controls) allows, under weak restrictions, to consistently estimate causal effects of medals by simply calculating differences in the two types of dummy estimates. In addition, the estimates of future medal coefficients can be interpreted as partial correlations between unobserved quality and medal indicators. Our preferred estimate indicates that producers having earned a medal at a competition can increase their price by 13%. The impact for gold is much larger than for silver and bronze, but we cannot reject that the correlation with quality is the same across the three colors. We then calculate expected profits obtained by producers from participating in competitions and find that the incentives to participate are high. Finally, we investigate the efficiency of contests by measuring to what extent attributed awards are good quality indicators: only a minority of competitions attribute medals that are significantly correlated with quality (primarily the ones founded a long time ago, and whose judges are required to evaluate relatively few wines per day).

Assessment of Pulmonary Functions with Spirometry Method in Hepatic Impairment Patients

Aim: In this study, it has been aimed to investigate whether there is a relationship between pulmonary functions measured by spirometry and hepatic impairment tables. This may contribute to a better understanding of the mechanisms of liver pathophysiology which hasn’t been fully understood.Materials and Methods: This study is a randomized controlled prospective trial. 39-63 years of age, 19 male and 9 female, a total of 28 patients diagnosed with liver failure, with 15 male and 17 female, a total of 32 healthy volunteers with similar social characteristics were studied. All of the participants’ pulmonary parameters (FEV1, FVC, FEV1/FVC, PEF, FEF25-75%, FEF25%, FEF50%, FEF75%, PIF, VC, MVV) were performed by pulmonary function tests (PFT). Groups’ data have been analyzed statistically. The significance level was considered as p0.05.Results: In hepatic impairment patients, there was no significant difference in terms of the expected percentage values of PFT parameters that indicate obstruction. Weak restriction in 8 cases, moderate restriction in 9 cases and severe restriction in 4 cases were diagnosed. PFT parameters of patients with mid-level and refractory ascites were found to be significantly lower compared with those without ascites (FEV1: p=0.009; FVC: p=0.010; VC: p=0.008). There was no remarkable correlation between AST, ALT, ALP, GGT levels and PFT parameters of patients as with ascites status.Conclusion: Ascites that can frequently coexist with chronic liver disease cases, may cause restrictive type pulmonary dysfunctions in PFT by creating mechanical pressure. But also, there is no correlation between the ascites status or PFT diagnoses and liver function tests.

Geometric Mean Type Measure of Marginal Homogeneity for Square Contingency Tables with Ordered Categories

For square contingency tables, some studies have developed the weighted arithmetic mean type measure to represent the degree of departure from the marginal homogeneity. The present paper proposes (1) the cumulative partial marginal homogeneity model which has the weaker restriction than the marginal homogeneity model and (2) the measure to represent the degree of departure from the proposed model. The measure is expressed as a weighted geometric mean of the diversity index. Finally, numerical studies are presented.

Convergence and stability of an iterative algorithm for strongly accretive Lipschitzian operator with applications

Using different technique and weaker restrictions on parameters, convergence and stability results of an SP iterative algorithm with errors for a strongly accretive Lipschitzian operator on a Banach space are established. Validity of new convergence results is verified through numerical examples and convergence comparison of various iterative algorithms is depicted. As applications of our convergence result, we solve a nonlinear operator equation and a variational inclusion problem. Our results are refinement and generalization of many classical results.

Convergence in $\ell_2$ and $\ell_\infty$ Norm of One-Stage AMF-W-Methods for Parabolic Problems

For the numerical solution of parabolic problems with a linear diffusion term, linearly implicit time integrators are considered. To reduce the cost on the linear algebra level, an alternating direction implicit approach is applied (so-called AMF-W-methods). The present work proves optimal bounds of the global error for two classes of $1$-stage methods in the Euclidean $\ell_2$ norm as well as in the maximum norm $\ell_\infty$. The bounds are valid under a very weak step size restriction that covers PDE convergence, where the time step size is of the same order as the spatial grid size.

Separation of symmetry for square tables with ordinal categorical data

The present paper considers a model that indicates the structure of asymmetry for cell probabilities for square contingency tables with ordered categories. The model is the closest to the symmetry model in terms of the f-divergence under certain conditions and incorporates existing asymmetry models in special cases. A theorem that the symmetry model can be separated into two models which have weaker restrictions than the symmetry model is given. Also, a property between test statistics for goodness of fit is discussed.

Understanding Events by Eye and Ear: Agent and Verb Drive Non-anticipatory Eye Movements in Dynamic Scenes.

As Macnamara (1978) once asked, how can we talk about what we see? We report on a study manipulating realistic dynamic scenes and sentences aiming to understand the interaction between linguistic and visual representations in real-world situations. Specifically, we monitored participants’ eye movements as they watched video clips of everyday scenes while listening to sentences describing these scenes. We manipulated two main variables. The first was the semantic class of the verb in the sentence and the second was the action/motion of the agent in the unfolding event. The sentences employed two verb classes–causatives (e.g., break) and perception/psychological (e.g., notice)–which impose different constraints on the nouns that serve as their grammatical complements. The scenes depicted events in which agents either moved toward a target object (always the referent of the verb-complement noun), away from it, or remained neutral performing a given activity (such as cooking). Scenes and sentences were synchronized such that the verb onset corresponded to the first video frame of the agent motion toward or away from the object. Results show effects of agent motion but weak verb-semantic restrictions: causatives draw more attention to potential referents of their grammatical complements than perception verbs only when the agent moves toward the target object. Crucially, we found no anticipatory verb-driven eye movements toward the target object, contrary to studies using non-naturalistic and static scenes. We propose a model in which linguistic and visual computations in real-world situations occur largely independent of each other during the early moments of perceptual input, but rapidly interact at a central, conceptual system using a common, propositional code. Implications for language use in real world contexts are discussed.

О СМЕШАННОЙ ЗАДАЧЕ E ДЛЯ ВЫРОЖДАЮЩИХСЯ НА ГРАНИЦЕ ОБЛАСТИ ПАРАБОЛИЧЕСКИХ УРАВНЕНИЙ 2ГО ПОРЯДКА

Исследуется вопрос об однозначной разрешимости первой смешанной задачи для вырождающегося параболического уравнения 2го порядка в случае, когда граничная и начальная функции принадлежат пространствам типа L2. Данная тематика берет начало с классических работ Ф. Рисса 1 и Литтлвуда и Пэли 2, посвященных граничным значениям аналитических функций. Дальнейшее развитие этой тематики для равномерно эллиптических уравнений получило в работах В. П. Михайлова, А. К. Гущина 3 9. Условие гладкости границы (Q C2) можно ослабить (см. 7). При наиболее слабых ограничениях на гладкость границы (и на коэффициенты уравнения) критерий существования граничного значения установлен в 7 9. При этом, как показано в работе 9, все направления принятия граничных значений для равномерно эллиптических уравнений оказываются равноправными, решение обладает свойством, аналогичным свойству непрерывности по совокупности переменных. В случае вырождения уравнения на границе области, когда направления не являются равноправными, ситуация более сложная. При этом постановка первой краевой задачи определяется типом вырождения. В случае, когда значения соответствующей квадратичной формы вырождающегося эллиптического уравнения на векторе нормали отличны от нуля (вырождение типа Трикоми), корректна задача Дирихле, и свойства такого вырождающегося уравнения весьма близки к свойствам равномерно эллиптического уравнения. В частности, в этой ситуации справедливы аналоги теорем Рисса 1 и Литтлвуда Пэли 2, 3. В случае вырождения типа Келдыша ситуация более сложная. Постановка первой краевой задачи и поведение решения вблизи границы определяются порядком вырождения уравнения, а в случае сильного вырождения коэффициентами при младших членах. Вопросам разрешимости первой краевой задачи для вырождающихся эллиптических и параболических уравнений посвящено большое число работ. Достаточно отметить работы Ф. Трикоми 10, М. В. Келдыша11, А. В. Бицадзе 12, С. А. Терсенова 13, И. М. Петрушко 14, 15, О. А. Олейник, Е. В. Радкевича 16, Г. Фикеры 17 и др. Из недавних работ можно отметить 18. В настоящей работе рассматривается случай сильного вырождения параболического уравнения 2го порядка, когда соответствующая квадратичная форма убывает как r(x) и постановка первой смешанной задачи определяется коэффициентом при первой производной по нормали. The paper investigates the question of the unique solvability of the first mixed problem for a degenerate secondorder parabolic equation in the case when the boundary and initial functions belong to spaces of type L2. This topic originates from the classical works of F. Riesz 1 and Littlewood and Paley 2 devoted to the boundary values of analytic functions. Under the weakest restrictions on the smoothness of the boundary (and on the coefficients of the equation), the criterion for the existence of a boundary value was established in 7 9. The boundary smoothness condition (Q C2) can be weakened (see 10). Moreover, as shown in 9, all directions of the adoption of boundary values for uniformly elliptic equations turn out to be equal the solution has the property similar to the property of continuity in the set of variables. In the case of degeneration of the equation at the boundary of the region, when the directions are not equal, the situation is more complicated. Moreover, the formulation of the first boundary value problem is determined by the type of degeneracy. In the case when the values of the corresponding quadratic form of the degenerate elliptic equation on the normal vector are nonzero (Tricomi type degeneracy), the Dirichlet problem is correct, and the properties of such degenerate equation are very close to the properties of a uniformly elliptic equation. In particular, in this situation, analogs of the Riesz theorems 1 and Littlewood Paley 2, 3 are valid. In the case of degeneracy of the Keldysh type, the situation is more complicated. The statement of the first boundaryvalue problem and the behavior of the solution near the boundary are determined by the order of degeneracy of the equation, and in the case of strong degeneracy, by the coefficients of the lower terms. A large number of papers have been devoted to the solvability of the first boundaryvalue problem for degenerate elliptic and parabolic equations. Note the works of F. Tricomi 11, M. V. Keldysh 12, A. V. Bitsadze 13, S. A. Tersenov 14, I. M. Petrushko 15, O. A. Oleinik and E. V. Radkevich 16, G. Fichera 17, etc. From recent works it is worth noting 18. In this paper, we consider the case of strong degeneracy of a secondorder parabolic equation when the corresponding quadratic form decreases as r(x) and the formulation of the first mixed problem is determined by the coefficient of the first normal derivative.

Mechanism Design for Multi-Type Housing Markets with Acceptable Bundles

We extend the Top-Trading-Cycles (TTC) mechanism to select strict core allocations for housing markets with multiple types of items, where each agent may be endowed and allocated with multiple items of each type. In doing so, we advance the state of the art in mechanism design for housing markets along two dimensions: First, our setting is more general than multi-type housing markets (Moulin 1995; Sikdar, Adali, and Xia 2017) and the setting of Fujita et al. (2015). Further, we introduce housing markets with acceptable bundles (HMABs) as a more general setting where each agent may have arbitrary sets of acceptable bundles. Second, our extension of TTC is strict core selecting under the weaker restriction on preferences of CMI-trees, which we introduce as a new domain restriction on preferences that generalizes commonly-studied languages in previous works.

On Coercive Solvability of Parabolic Equations with Variable Operators

In a Banach space E, the Cauchy problem $$ \upsilon^{\prime }(t)+A(t)\upsilon (t)=f(t)\kern1em \left(0\le t\le 1\right),\kern1em \upsilon (0)={\upsilon}_0, $$ is considered for a differential equation with linear strongly positive operator A(t) such that its domain D = D(A(t)) does not depend on t and is everywhere dense in E and A(t) generates an analytic semigroup exp{−sA(t)}(s ≥ 0). Under natural assumptions on A(t), we prove the coercive solvability of the Cauchy problem in the Banach space $$ {C}_0^{\beta, \upgamma} $$ (E). We prove a stronger estimate for the solution compared with estimates known earlier, using weaker restrictions on f(t) and v0.