Introduction to Area Functional

Our result is a generalization of a classical theorem: among all convex n-gons contained in a given disc, the regular n-gon inscribed in the circle (up to rotation) uniquely maximizes the area functional.

The central object of this article is (a special version of) the Helfrich functional which is the sum of the Willmore functional and the area functional times a weight factor $$\varepsilon \ge 0$$ ε ≥ 0.

The Bay Area Functional Performance Evaluation-Task-Oriented Assessment (BaFPE-TOA) is a tool that evaluates functional performance.

Tourism, fishing, aquaculture, and activities that eliminate the area functionality are prohibited in the no-take zone area.

Using cross-correlation analysis, we reveal that the organization of inter-area functional connectivity during visual stimulation mirrors the anatomical hierarchy from the Allen Mouse Brain Connectivity Atlas3.

Research on blend films prepared through solution casting are typically done to investigate their properties, however, electrospun fibers are of particular interest especially on technologies requiring mechanically robust and high surface area functional materials.

Last, we study the second variation of the area functional for collections of helical motifs with asymptotic helicoidal structure and show that in this subclass of minimal surfaces stability requires that the collection of motifs is pitch balanced.

Instead of variational minimization of usual area functional, the quasi-minimal Bézier surface with shifted knots is obtained as the solution of variational minimization of Dirichlet functional that turns up as the sum of two integrals and the vanishing condition gives us the system of linear algebraic constraints on the control points.

This confirms part of the program ( [31] , [34] , [36] , [43] ) proposed by the authors with the goal of developing a Morse theory for the area functional.

Thus, the work solves the extreme problem for the area functional of the image of disks under a certain class of regular homeomorphic solutions of nonlinear systems of the Cauchy--Riemann--Beltrami type with generalized derivatives integrated with a square.

We consider in this paper an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric.

Part of the newly added seating furniture in this area functionally works, but one of them does not functionally integrate into the surroundings of Taman Fatahillah as a historical revitalized public area.

A suitable notion of the increment of the (sub-Riemannian) area functional is introduced, the differentiability of this functional is proved, and necessary minimality conditions for graph surfaces are deduced.

A suitable notion of the (sub-Riemannian) area functional increment is introduced, differentiability of this functional is proved, and necessary minimality conditions are deduced.

Roll-to-roll ultraviolet (R2R-UV) imprinting is a low-cost and high-throughput method that includes the manufacturing of large-area functional films.

This is accomplished based on the first order variation of the area functional in arbitrary dimensions.

Two novel PDI derivatives with bay area functionalization and thionation of the carbonyls, respectively, were designed and their absorption was evaluated by DFT calculation, which predicted to be in the NIR region that is desired for potential application.

The present work addresses this issue by developing large-area functional polymeric coatings on linear low-density polyethylene films by a rapid and effective layer-by-layer assembly involving orthoboric acid (H3BO3) and poly(vinyl alcohol) (PVA).

Using spike cross-correlation analysis, we find that inter-area functional connectivity mirrors the anatomical hierarchy from the Allen Mouse Brain Connectivity Atlas.

High-resolution remote sensing images are widely used in urban area functional classification, and urban area functions are closely related to human activities.

In the most impacted area functional responses included an increase in mobile carnivores/omnivores and species utilizing symbionts.

While the direct minimization of the Area functional may lead to limits that are disconnected, we prove that, if the infimum of the problem is $<4\pi$, there exists a connected compact minimizer of $\mathcal{W}$ in the class of integer rectifiable curvature varifolds with the assigned boundary conditions.

This work was motivated by the famous Plateau's Problem which concerns the existence of a minimizing set of the area functional with prescribed boundary.

One example of such an equation is the Hamiltonian Stationary Lagrangian equation, which governs Lagrangian surfaces that minimize the area functional.

By combining these molecular and optical approaches we made wide-area functional maps in acute brain slices from mice of both sexes.

These hypersurfaces are critical points for the area functional, and hence their study can be seen as a high-dimensional generalization of the classical theory of closed geodesics (Birkhoff, Morse, Lusternik, Schnirel’mann,…).

Our approach combines the geographic characteristics of the city with mobility patterns of human activity by considering human activity, area functionality, road network, and the toileting demand of taxi drivers.