ON THE POTENTIALITY OF A CLASS OF OPERATORS RELATIVE TO LOCAL BILINEAR FORMS

The inverse problem of the calculus of variations (IPCV) is solved for a second-order ordinary differential equation with the use of a local bilinear form. We apply methods of analytical dynamics, nonlinear functional analysis, and modern methods for solving the IPCV. In the paper, we obtain necessary and sufficient conditions for a given operator to be potential relative to a local bilinear form, construct the corresponding functional, i.e., found a solution to the IPCV, and define the structure of the considered equation with the potential operator. As a consequence, similar results are obtained when using a nonlocal bilinear form. Theoretical results are illustrated with some examples.

Concurrent Engineering Model for the Implementation of New Products in the Textile Industry: A Case Study

Concurrent engineering (CE) aims to provide a collaborative environment in which all involved parties work simultaneously to optimize resources. However, some aspects can make it hard to implement in organizations. This study presents the development of a CE model and its implementation in a Mexican textile maquiladora. The information about the process was obtained using administrative and quality tools (brainstorming, Pareto and Ishikawa charts, flowcharts, spreadsheets). A CE model based on the management of new products was designed, in consideration of the enterprise culture. The workgroup evaluated the proposed model in two projects to verify the functionality. The time for the development and approval of prototypes was reduced from three months to one. Now the process has a robust design, having identified design problems, potential operator errors, and bottlenecks. Losses from raw material replacements and reworks decreased by 39.4%, and there was an additional cost saving of 22.86%. CE implementation is not easy; the firsts steps are to change the organizational culture and the training of employees to work collaboratively.

Characterizations for the potential operators on Carleson curves in local generalized Morrey spaces

In this paper, we give a boundedness criterion for the potential operator { {\mathcal I} }^{\alpha } in the local generalized Morrey space L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the generalized Morrey space {M}_{p,\varphi }(\text{Γ}) defined on Carleson curves \text{Γ} , respectively. For the operator { {\mathcal I} }^{\alpha } , we establish necessary and sufficient conditions for the strong and weak Spanne-type boundedness on L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the strong and weak Adams-type boundedness on {M}_{p,\varphi }(\text{Γ}) .

Isoperimetric inequalities for the heat potential operator

In this paper we prove that the circular cylinder is a maximizer of the Schatten p-norm of heat potential operator among all Euclidean cylindric domains of a given measure. We also give analogues of a Rayleigh-Faber-Krahn and a Hong-Krahn-Szeg? type inequalities.