On Well-Posedness of Some Constrained Variational Problems

By considering the new forms of the notions of lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity of the considered scalar multiple integral functional, in this paper we study the well-posedness of a new class of variational problems with variational inequality constraints. More specifically, by defining the set of approximating solutions for the class of variational problems under study, we establish several results on well-posedness.

Biderivations and Commuting Linear Maps on Topologically Simple ℒ ∗ -Algebras

Let ℒ be a topologically simple ℒ ∗ -algebra of arbitrary dimension. In this paper, we introduce the notion of semi-inner biderivation in order to prove that every continuous commuting linear mapping on ℒ is a scalar multiple of the identity mapping.

On a Class of Second-Order PDE&PDI Constrained Robust Modified Optimization Problems

In this paper, by using scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian, we develop a new mathematical framework on multi-dimensional scalar variational control problems with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Concretely, we introduce and investigate an auxiliary (modified) variational control problem, which is much easier to study, and provide some equivalence results by using the notion of a normal weak robust optimal solution.

A Two-Step Spectral Gradient Projection Method for System of Nonlinear Monotone Equations and Image Deblurring Problems

In this paper, we propose a two-step iterative algorithm based on projection technique for solving system of monotone nonlinear equations with convex constraints. The proposed two-step algorithm uses two search directions which are defined using the well-known Barzilai and Borwein (BB) spectral parameters.The BB spectral parameters can be viewed as the approximations of Jacobians with scalar multiple of identity matrices. If the Jacobians are close to symmetric matrices with clustered eigenvalues then the BB parameters are expected to behave nicely. We present a new line search technique for generating the separating hyperplane projection step of Solodov and Svaiter (1998) that generalizes the one used in most of the existing literature. We establish the convergence result of the algorithm under some suitable assumptions. Preliminary numerical experiments demonstrate the efficiency and computational advantage of the algorithm over some existing algorithms designed for solving similar problems. Finally, we apply the proposed algorithm to solve image deblurring problem.

On approximately dual frames for Hilbert C*-modules

In this paper we discuss approximately dual frames for a frame or an outer frame of a Hilbert C*-module. We show that every frame or an outer frame, up to a scalar multiple, is approximately dual to itself. This enables us to get a canonical dual frame of a given frame (xn)n as a limit of approximately dual frames defined by (xn)n.

An extension of orthogonality relations based on norm derivatives

We introduce the relation ρλ-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives and present some of its essential properties. Among other things, we give a characterization of inner product spaces via the functional ρλ. Moreover, we consider a class of linear mappings preserving this new kind of orthogonality. In particular, we show that a linear mapping preserving ρλ-orthogonality has to be a similarity, that is, a scalar multiple of an isometry.

2243 Perceptions of translational science among faculty researchers: A survey to inform the efforts of a multidisciplinary education and research program

OBJECTIVES/SPECIFIC AIMS: Opinions regarding translational science vary incredibly. We aimed to gather a baseline of perceptions, barriers, and needs for translational science among faculty investigators. We will use these data to define areas in which the Duke Multidisciplinary Education and Research in Translational Science program (MERITS) can work to address, educate and improve. METHODS/STUDY POPULATION: Data was collected via a scalar, multiple-choice, open-ended survey including questions regarding, definition, impact, barriers, resources, and training preferences specific to translational science. Digital survey links were emailed to Duke University faculty. RESULTS/ANTICIPATED RESULTS: In total, 350 responses were collected. While perceptions of translational science varied, common defining elements were noted, including multidisciplinary collaboration (69%) and transitions between research stages (63%). Translational science was said to have an overall positive impact, despite 37% of participants stating issues of insufficient institution-wide support and 62% citing minimal training in translational science skills. DISCUSSION/SIGNIFICANCE OF IMPACT: Effective support for translational science requires a multi-faceted approach, as perceptions differ among investigators and between career stages. Duke MERITS will seek to standardize education and support ranging from teambuilding to entrepreneurship, and to promote support from institutional leadership to reduce barriers and facilitate acceleration of translational science.

Lagrangian Constant Cycle Subvarieties in Lagrangian Fibrations

We show that the image of a dominant meromorphic map from an irreducible compact Calabi–Yau manifold X whose general fiber is of dimension strictly between 0 and $\dim X$ is rationally connected. Using this result, we construct for any hyper-Kähler manifold X admitting a Lagrangian fibration a Lagrangian constant cycle subvariety ΣH in X which depends on a divisor class H whose restriction to some smooth Lagrangian fiber is ample. If $\dim X = 4$, we also show that up to a scalar multiple, the class of a zero-cycle supported on ΣH in CH0(X) depend neither on H nor on the Lagrangian fibration (provided b2(X) ≥ 8).

Large Dataset Assessment of the Upper Shelf Master Curve Model

In 2006, EricksonKirk and EricksonKirk proposed a model describing a temperature dependence for upper shelf fracture toughness (JIc), based on the Zerilli-Armstrong (ZA) temperature dependence of the flow stress, that was common to the large number of ferritic steel datasets studied. The equation describing the temperature dependence of JIc was found to be a simple scalar multiple of the temperature dependence predicted by ZA for flow stress. Since that time a large dataset has been developed containing many experimental measurements of JIc for the purpose assessing and refining the previously proposed model. The new data, reported herein, validates the previously proposed model of JIc temperature dependence but suggests that revisions of the previously proposed model of JIc uncertainty are needed to ensure the applicability of the model to both low and high fracture toughness steels.