Post-Socialist Culture and Entrepreneurship

In this paper it is argued that locus of control beliefs and preferences concerning state action negatively affect the formation of new firms in former socialist countries. For this purpose Kirzner's theory of costless entrepreneurship is reviewed and criticized. German reunification, in which the formerly Socialist East joined the Federal Republic of Germany, represents an intriguing natural experiment in which the formal institutional structure of one nation was almost fully transplanted into another. Traditional as well as psychological factors are examined. The results suggest that about one third of the east-west gap in new self-employment can be explained by inert informal institutions.Psychology of Entrepreneurship, Self-Employment, Transitional Economies, East Germany

Generalized surface quasi-geostrophic equations with singular velocities

This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals. The first family is a generalized surface quasi-geostrophic (SQG) equation with the velocity field u related to the scalar θ by u = ∇⊥Λ β−2 θ, where 1 1. We obtain the local existence and uniqueness of classical solutions, the global existence of weak solutions and the local existence of patch type solutions. The second family is a dissipative active scalar equation with u = ∇⊥(log(I − ∆))µθ for µ > 0, which is at least logarithmically more singular than the velocity in the first family. We prove that this family with any fractional dissipation possesses a unique local smooth solution for any given smooth data. This result for the second family constitutes a first step towards resolving the global regularity issue recently proposed by K. Ohkitani.National Research Foundation of KoreaNational Science FoundationMinisterio de Ciencia e InnovaciónEuropean Research Counci

Function Spaces on Singular Manifolds

It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in $\mathbb{R}^n$, continue to be valid on a wide class of Riemannian manifolds with singularities and boundary, provided suitable weights, which reflect the nature of the singularities, are introduced. These results are of importance for the study of partial differential equations on piece-wise smooth domains.Comment: 37 pages, 1 figure, final version, augmented by additional references; to appear in Math. Nachrichte

Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations

We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finite time blow-up and as well as global existence of solutions of the problem.Comment: 11 pages. Minor changes and added reference

The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials

This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the problem is reflected by a convolution integral in the space variables. The Fourier transform of the convolution kernel is nonnegative and satisfies a certain growth condition at infinity. For initial data in $L^{2}$ Sobolev spaces, conditions for global existence or finite time blow-up of the solutions of the Cauchy problem are established.Comment: 15 pages. "Section 6 The Anisotropic Case" added and minor changes. Accepted for publication in Nonlinearit

Personality traits and the likelihood of self-employment: a journey into the crafts' way of doing business

Given the renewed scholarly interest in the crafts, this paper explores the nuances of crafts entrepreneurship through a personality-based approach. Our findings validate prior research on the general influence of broad and narrow personality traits on self-employment. However, our analysis also suggests that certain effects differ between crafts and non-crafts, most notably the role of the Big Five trait of conscientiousness – suggesting that there is something ‘unique’ about the crafts’ way of doing business that goes beyond firm size. In this way, we provide evidence that personality may affect self-employment differently depending on the sector or field of entrepreneurship

Numerical Schemes for Rough Parabolic Equations

This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H \textgreater{} 1/3.Comment: Applied Mathematics and Optimization, 201

Fractional div-curl quantities and applications to nonlocal geometric equations

We investigate a fractional notion of gradient and divergence operator. We generalize the div-curl estimate by Coifman-Lions-Meyer-Semmes to fractional div-curl quantities, obtaining, in particular, a nonlocal version of Wente's lemma. We demonstrate how these quantities appear naturally in nonlocal geometric equations, which can be used to obtain a theory for fractional harmonic maps analogous to the local theory. Firstly, regarding fractional harmonic maps into spheres, we obtain a conservation law analogous to Shatah's conservation law and give a new regularity proof analogous to H\'elein's for harmonic maps into spheres. Secondly, we prove regularity for solutions to critical systems with nonlocal antisymmetric potentials on the right-hand side. Since the half-harmonic map equation into general target manifolds has this form, as a corollary, we obtain a new proof of the regularity of half-harmonic maps into general target manifolds following closely Rivi\`{e}re's celebrated argument in the local case. Lastly, the fractional div-curl quantities provide also a new, simpler, proof for H\"older continuity of $W^{s,n/s}$-harmonic maps into spheres and we extend this to an argument for $W^{s,n/s}$-harmonic maps into homogeneous targets. This is an analogue of Strzelecki's and Toro-Wang's proof for $n$-harmonic maps into spheres and homogeneous target manifolds, respectively

Stochastic Reaction-diffusion Equations Driven by Jump Processes

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.Comment: See journal reference for teh final published versio