MHD mixed convection flow near the stagnation-point on a vertical permeable surface

The steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of a viscous and electrically conducting fluid near the stagnation-point on a vertical permeable surface is investigated in this study. The velocity of the external flow and the temperature of the plate surface are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for both cases, and the range of the mixed convection parameter for which the solution exists increases with suction.     

Convergence rates for forward–backward dynamical systems associated with strongly monotone inclusions

We investigate the convergence rates of the trajectories generated by implicit first and second-order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space. We show that these trajectories strongly converge with exponential rate to a zero of the sum, provided the latter is strongly monotone. We derive from here convergence rates for the trajectories generated by dynamical systems associated to the minimization of the sum of a proper, convex and lower semicontinuous function with a smooth convex one provided the objective function fulfills a strong convexity assumption. In the particular case of minimizing a smooth and strongly convex function, we prove that its values converge along the trajectory to its minimum value with exponential rate, too.     

A Bound of the Finslerian Ricci Scalar

In the Riemannian as well as in the Finslerian geometry, certain conditions on the Ricci scalar or the Ricci tensor provide obstructions on the topology of the base manifold and so on the configuration of cut points by limitations of the injectivity radius, see the Bonnet–Myers theorem and its variants and generalizations. In this paper, we show that conversely, prescribing the injectivity radius of a Finsler manifold, some limitations of the Ricci scalar are obtained. Some consequences of the condition that the Ricci tensor is h-parallel with respect to the Chern–Rund connection are found. In addition, some classes of examples are provided.     

Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data

We consider the problem of minimizing a smooth convex objective function subject to the set of minima of another differentiable convex function. In order to solve this problem, we propose an algorithm which combines the gradient method with a penalization technique. Moreover, we insert in our algorithm an inertial term, which is able to take advantage of the history of the iterates. We show weak convergence of the generated sequence of iterates to an optimal solution of the optimization problem, provided a condition expressed via the Fenchel conjugate of the constraint function is fulfilled. We also prove convergence for the objective function values to the optimal objective value. The convergence analysis carried out in this paper relies on the celebrated Opial Lemma and generalized Fejér monotonicity techniques. We illustrate the functionality of the method via a numerical experiment addressing image classification via support vector machines.     

Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.     

Order-chaos-order transitions in electrosprays: the electrified dripping faucet

Electrosprays have diverse applications including protein analysis, electrospinning, and nanoencapsulation for drug delivery. We show that a variety of electrospray regimes exhibit fundamental analogy with the nonlinear dynamics of a dripping faucet. The applied voltage in electrosprays results in additional period doublings and temporal order-chaos-order transitions. Attractors in the return maps show logarithmic self-similarity in time, suggesting self-similar capillary waves on the meniscus. The bifurcations in ejection time can be explained by phase variations between capillary waves and pinch-off conditions and by ejection mode changes due to contact angle variations.     

Fatty Acid Ethyl Esters (FAEE): A New,Green and Renewable Solvent for the Extraction of Carotenoids from Tomato Waste Products

Currently there is a drive towards the minimisation and reclamation of valuable materials from the waste products of the food and beverage industry. This can be achieved through the extraction of residual nutraceuticals from such materials. Tomato pomace contains carotenoids and other chemicals which can be extracted directly into edible oils to improve the health-giving properties of such oils. We report here a novel green solvent, fatty acid ethyl esters (FAEE), which is significantly more effective than sunflower oil and hexane for the extraction of lycopene and beta-carotene from tomato skin waste. FAEE are a non-toxic renewable resource that is environmentally friendly and to our knowledge has never been used as a vegetal extraction fluid. The efficiency of FAEE extraction was significantly improved relative to both sunflower oil and hexane under ultrasound-assisted extraction (UAE) conditions. In addition, FAEE have the additional and significant advantage that once enriched with the extracted nutraceuticals can be used directly as a food additive.     

Sprays metrizable by Finsler functions of constant flag curvature

In this paper we characterize sprays that are metrizable by Finsler functions of constant flag curvature. By solving a particular case of the Finsler metrizability problem, we provide the necessary and sufficient conditions that can be used to decide whether or not a given homogeneous system of second order ordinary differential equations represents the geodesic equations of a Finsler function of constant flag curvature. The conditions we provide are tensorial equations on the Jacobi endomorphism. We identify the class of homogeneous SODE where the Finsler metrizability is equivalent with the metrizability by a Finsler function of constant flag curvature.     

A double smoothing technique for solving unconstrained nondifferentiable convex optimization problems

The aim of this paper is to develop an efficient algorithm for solving a class of unconstrained nondifferentiable convex optimization problems in finite dimensional spaces. To this end we formulate first its Fenchel dual problem and regularize it in two steps into a differentiable strongly convex one with Lipschitz continuous gradient. The doubly regularized dual problem is then solved via a fast gradient method with the aim of accelerating the resulting convergence scheme. The theoretical results are finally applied to an l ₁ regularization problem arising in image processing.