On the reduction of the degree of linear differential operators

Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type

The X-Factor: On the Relevance of Implicit Leadership and Followership Theories for Leader-Member Exchange (LMX) Agreement

While Leader-Member Exchange (LMX) research shows that leaders engage in different kinds of relationships with different followers, it remains somewhat of an enigma why one and the same relationship is often rated differently by a leader and the respective follower. We seek to fill that conceptual void by explaining when and why such LMX disagreement is likely to occur. To do so, we reconsider antecedents of LMX quality perceptions and outline how each party’s LMX quality perception is primarily dependent on the perceived contributions of the other party, moderated by perceived own contributions. We then integrate the notion of Implicit Leadership and Followership Theories (ILTs and IFTs) to argue that the currencies of contributions differ between leaders and followers. This dyadic model sets the stage to explain that LMX disagreement can stem from (1) differences in both parties’ ILTs as well as both parties’ IFTs, but also from (2) differences in perceptions of own and other’s behavior. We conclude by discussing communication as a means of overcoming LMX disagreement and propose an array of potential studies along the lines of our conceptualization

Tango in the Dark: The Interplay of Leader’s and Follower’s Level of Self-Construal and its Impact on Ethical Leadership

In line with romantic views on leadership, leaders are traditionally held responsible for any kind of ethical misconduct in organizations. Through explicating the influence of followers on their leaders' (unethical) decision-making, we aim to add some nuances to this view with the present chapter. To begin with, we suggest that people generally regard leadership as ethical when the leader takes the collective into account, while only focusing on own gains is largely regarded as unethical. We then posit that the degree to which leaders' decisions are directed towards the one versus the other outcome depends on the leaders’ level of self-construal, that is, the way how they see themselves in relation to others. Looking at leader's ethical decision making through this lens suggests that it is open to external influence, in that leaders’ self-construal is susceptible to external cues. In particular, followers form an important part of such external cues for a leader's level of self-construal. We thus suggest various mechanisms via which followers indirectly influence their leaders' ethical decision making. In sum, we put forward a model in which we show how leaders and followers reciprocally affect their level of self-construal and thus ultimately the degree to which ethical leadership is enacted

Morality in Interactions: On the Display of Moral Behavior by Leaders and Employees

Recent research has tried to understand moral behavior in the workplace mainly from an intra-personal perspective, blaming ethical failures on the person’s moral character, moral development or moral identity, or on isolated aspects of the situation. In doing so, little attention has been paid to the interplay between the person and the interpersonal context in which this behavior takes place. Thus, an important angle for investigating the question why good people do bad things has yet remained unexplored. In this thesis I present four chapters that illustrate this interpersonal influence in the context of ethical behavior within organizations – I discuss how leaders and followers influence each other’s moral behavior, how the organization’s moral norms influence employees moral decisions especially when they identify strongly with the organization, how follower moral awareness influences the effects of ethical leadership on the employee’s deviant behavior, and how demographic differences between leaders and followers influences the effect moral leadership has on employee performance. Together these chapters aim to increase understanding of the importance of factors in the interpersonal for moral decision making by individuals

Measurement of angular momentum transport in turbulent flow between independently rotating cylinders

We present measurements of the angular momentum flux (torque) in Taylor-Couette flow of water between independently rotating cylinders for all regions of the \(\Omega_1, \Omega_2\) parameter space at high Reynolds numbers, where $\Omega_1$ \(\Omega_2\) is the inner (outer) cylinder angular velocity. We find that the Rossby number Ro = \(\Omega_1 - \Omega_2\)/\Omega_2 fully determines the state and torque $G$ as compared to G(Ro = \infty) \equiv \Gi. The ratio G/\Gi is a linear function of $Ro^{-1}$ in four sections of the parameter space. For flows with radially-increasing angular momentum, our measured torques greatly exceed those of previous experiments [Ji \textit{et al.}, Nature, \textbf{444}, 343 (2006)], but agree with the analysis of Richard and Zahn [Astron. Astrophys., \textbf{347}, 734 (1999)].Comment: 4 pages, 4 figures, to appear in Physical Review Letter

In the moral eye of the beholder:the interactive effects of leader and follower moral identity on perceptions of ethical leadership and LMX quality

Previous research indicated that leader moral identity (MI; i.e., leaders’ self-definition in terms of moral attributes) predicts to what extent followers perceive their leader as ethical (i.e., demonstrating and promoting ethical conduct in the organization). Leadership, however, is a relational process that involves leaders and followers. Building on this understanding, we hypothesized that follower and leader MI (a) interact in predicting whether followers will perceive their leaders as ethical and, as a result, (b) influence followers’ perceptions of leader–follower relationship quality. A dyadic field study (N = 101) shows that leader MI is a stronger predictor of followers’ perceptions of ethical leadership for followers who are high (vs. low) in MI. Perceptions of ethical leadership in turn predict how the quality of the relationship will be perceived. Hence, whether leader MI translates to perceptions of ethical leadership and of better relationship quality depends on the MI of followers

On Kink-Dynamics of Stacked-Josephson Junctions

Dynamics of a fluxon in a stack of coupled long Josephson junctions is studied numericallv. Based on the numerical simulations, we show that the dependence of the propagation velocity c on the external bias current γ is determined by the ratio of the critical currents of thc two junctions J