On computation of limiting coderivatives of the normal-cone mapping to inequality systems and their applications

The paper concerns the computation of the limiting coderivative of the normal-cone mapping related to $C^{2}$ inequality constraints under weak qualification conditions. The obtained results are applied to verify the Aubin property of solution maps to a class of parameterized generalized equations

On the Aubin property of a class of parameterized variational systems

The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets and also parameterized generalized equations with conic constraints. The new criterion requires computation of directional limiting coderivatives of the normal-cone mapping for the so-called critical directions. The respective formulas have the form of a second-order chain rule and extend the available calculus of directional limiting objects. The suggested procedure is illustrated by means of examples.Comment: 20 pages, 1 figur

Stability analysis for parameterized variational systems with implicit constraints

In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems include, e.g., quasi-variational inequalities and implicit complementarity problems. Concerning the Aubin property, possible restrictions imposed on the parameter are also admitted. Throughout the paper, tools from the directional limiting generalized differential calculus are employed enabling us to impose only rather weak (non-restrictive) qualification conditions. Despite the very general problem setting, the resulting conditions are workable as documented by some academic examplesComment: 26 page

Empowerment and Engagement through Informal Learning: Exploring the Relationship Between Learning Opportunities and the Work Environment of Nurses

The purpose of this exploratory case study was to understand how informal learning phenomena influence nurses’ perceived levels of empowerment and engagement in the work environment. Four registered nurses employed at a pediatric specialty hospital, located in a large metropolitan city in the Midwest, participated in the study. Face to face semi-structured interviews of the participants were the primary source of data. In addition to the interview, the participants were asked to answer a question in writing regarding a conflict situation in the work environment. Data analysis was completed within each case and across cases. The findings resulted in narrative that described numerous examples of the relationship of empowerment and engagement to informal learning. Another finding was the study participants gave numerous examples of conditions that enabled informal learning. There were no examples of barriers to informal learning in the work environment identified by the study participants. The study is significant in that the importance of informal learning was explained in detail by the study participants in their responses to the interview questions. Such detailed explanations may be utilized by hospital leaders, nurse leaders, nurse educators, and nurses themselves to improve the work environment to support elements of informal learning that provide a palpable sense of empowerment and engagement. In addition, the detailed explanations by the study participants explaining informal learning may serve as resource material for Organization Development professionals in working with healthcare organizations to help develop and further test the significance of informal learning in the workplace