Moreau–Yosida Regularization of Maximal Monotone Operators of Type (D)

We propose a Moreau–Yosida regularization for maximal monotone operators of type (D), in non-reflexive Banach spaces. It generalizes the classical Moreau–Yosida regularization as well as Brezis–Crandall–Pazy’s extension of this regularization to strictly convex (reflexive) Banach spaces with strictly convex duals. Our main results are obtained by making use of recent results by the authors on convex representations of maximal monotone operators in non-reflexive Banach spaces.     

The roles of diffusivity and curvature in patterns on surfaces of revolution

We address the question of finding sufficient conditions for existence as well as nonexistence of nonconstant stable stationary solution to the diffusion equation _ut=div(a∇u)+f(u)$u_t=\mathrm{div}(a\mathrm{\nabla }u)+f(u)$ on a surface of revolution with and without boundary. Conditions found relate the diffusivity function a and the geometry of the surface where diffusion takes place. In the case where f is a bistable function, necessary conditions for the development of inner transition layers are given.     

Chemical Physical Characterization and Profile of Fruit Volatile Compounds from Different Accesses of Myrciaria floribunda (H. West Ex Wild.) O. Berg through Polyacrylate Fiber

Among the many species of native fruit of Brazil that have been little explored, there is Myrciaria floribunda (also known as rumberry, cambuizeiro, or guavaberry), a species with significant variability, which has fruits of different colors (orange, red, and purple) when ripe. The physical-chemical characteristics evaluated were fruit weight (FW), seed weight (SW), pulp weight (PW), number of seeds (NS), longitudinal diameter (LD), transverse diameter (TD), format (LD/TD), hydrogen potential (pH), soluble solids (SS), titratable acidity (TA), and ratio (SS/TA); further, the volatile organic compounds (VOCs) of nine accesses of rumberry orchards were identified. The averages of the variables FW, SW, PW, NS, LD, TD, shape, and firmness were 0.76 g, 0.22 g, 0.54 g, 1.45, 10.06 mm, 9.90 mm, 1.02, 2.96 N, respectively. LD/TD data showed that the fruits have a slightly rounded shape (LD/TD = 1). The averages for pH, SS, TA, and SS/TA were 3.74, 17.58 Brix, 4.31% citric acid, and 4.31, respectively. The evaluated parameters indicated that the fruits can be consumed both in natura and industrialized, with the red-colored fruits presenting a good balance of SS/TA, standards demanded by the processing industries. Thirty-six VOCs were identified, with emphasis on the sesquiterpenes. Caryophyllene (21.6% to 49.3%) and γ-selinene (11.3% to 16.3%) were the most predominant compounds in rumberry fruits.     

Pointwise and Ergodic Convergence Rates of a Variable Metric Proximal Alternating Direction Method of Multipliers

In this paper, we obtain global pointwise and ergodic convergence rates for a variable metric proximal alternating direction method of multipliers for solving linearly constrained convex optimization problems. We first propose and study nonasymptotic convergence rates of a variable metric hybrid proximal extragradient framework for solving monotone inclusions. Then, the convergence rates for the former method are obtained essentially by showing that it falls within the latter framework. To the best of our knowledge, this is the first time that global pointwise (resp. pointwise and ergodic) convergence rates are obtained for the variable metric proximal alternating direction method of multipliers (resp. variable metric hybrid proximal extragradient framework).     

Anomalous structural dynamics of minimally frustrated residues in cardiac troponin C triggers hypertrophic cardiomyopathy

Cardiac TnC (cTnC) is highly conserved among mammals, and genetic variants can result in disease by perturbing Ca²⁺-regulation of myocardial contraction. Here, we report the molecular basis of a human mutation in cTnC''s αD-helix (TNNC1-p.C84Y) that impacts conformational dynamics of the D/E central-linker and sampling of discrete states in the N-domain, favoring the “primed” state associated with Ca²⁺ binding. We demonstrate cTnC''s αD-helix normally functions as a central hub that controls minimally frustrated interactions, maintaining evolutionarily conserved rigidity of the N-domain. αD-helix perturbation remotely alters conformational dynamics of the N-domain, compromising its structural rigidity. Transgenic mice carrying this cTnC mutation exhibit altered dynamics of sarcomere function and hypertrophic cardiomyopathy. Together, our data suggest that disruption of evolutionary conserved molecular frustration networks by a myofilament protein mutation may ultimately compromise contractile performance and trigger hypertrophic cardiomyopathy.

Cardiac TnC (cTnC) is highly conserved among mammals, and genetic variants can result in disease by perturbing Ca²⁺-regulation of myocardial contraction.     

Stable equilibria of a singularly perturbed reaction–diffusion equation when the roots of the degenerate equation contact or intersect along a non-smooth hypersurface

We use the variational concept of \({\Gamma}\)-convergence to prove existence, stability and exhibit the geometric structure of four families of stationary solutions to the singularly perturbed parabolic equation \({u_t=\epsilon^2 {\rm div}(k\nabla u)+f(u,x)}\), for \({(t,x)\in \mathbb{R}^+\times\Omega}\), where \({\Omega\subset\mathbb{R}^n}\), \({n\geq 1}\), supplied with no-flux boundary condition. The novelty here lies in the fact that the roots of the bistable function f are not isolated, meaning that the graphs of its roots are allowed to have contact or intersect each other along a Lipschitz-continuous (n ? 1)-dimensional hypersurface \({\gamma \subset \Omega}\); across this hypersurface, the stable equilibria may have corners. The case of intersecting roots stems from the phenomenon known as exchange of stability which is characterized by \({f(\cdot,x)}\) having only two roots.     

An Inexact Spingarn’s Partial Inverse Method with Applications to Operator Splitting and Composite Optimization

In this paper, a pursuit-evasion game involving two non-holonomic agents is examined using the theory of differential games. It is assumed that the two players move on the Euclidean plane with fixed but different speeds and they each have a lower bound on their achievable turn radii. Both players steer at each instant by choosing their turn radii value and directions of turn. By formulating the game as a game of kind, we characterize the regions of initial conditions that lead to capture as well as the regions that lead to evasion, when both the players play optimally. The game is then formulated as a game of degree to obtain time-optimal paths for the pursuer and evader inside a capture region. Besides, all possible scenarios are considered for both players that differ in speed ratios and maneuverability constraints. Solutions are provided for those cases using appropriate simulation parameters, which aid in understanding the characteristics of the game of two cars under a wide range of constraints.