New Formulas for the Fenchel Subdifferential of the Conjugate Function

Following (López and Volle, J Convex Anal 17, 2010) we provide new formulas for the Fenchel subdifferential of the conjugate of functions defined on locally convex spaces. In particular, this allows deriving expressions for the minimizers set of the lower semicontinuous convex hull of such functions. These formulas are written by means of primal objects related to the subdifferential of the initial function, namely a new enlargement of the Fenchel subdifferential operator.     

Numerical Simulation of MHD Peristaltic Flow with Variable Electrical Conductivity and Joule Dissipation Using Generalized Differential Quadrature Method

In this paper, the MHD peristaltic flow inside wavy walls of an asymmetric channel is investigated, where the walls of the channel are moving with peristaltic wave velocity along the channel length. During this investigation,the electrical conductivity both in Lorentz force and Joule heating is taken to be temperature dependent. Also, the long wavelength and low Reynolds number assumptions are utilized to reduce the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. The new set of obtained equations is then numerically solved using the generalized differential quadrature method(GDQM). This is the first attempt to solve the nonlinear equations arising in the peristaltic flows using this method in combination with the Newton-Raphson technique. Moreover, in order to check the accuracy of the proposed numerical method, our results are compared with the results of built-in Mathematica command NDSolve. Taking Joule heating and viscous dissipation into account, the effects of various parameters appearing in the problem are used to discuss the fluid flow characteristics and heat transfer in the electrically conducting fluids graphically. In presence of variable electrical conductivity, velocity and temperature profiles are highly decreasing in nature when the intensity of the electrical conductivity parameter is strengthened.     

In situ synthesis of silver nanoparticles on densely amine‐functionalized polystyrene: Highly active nanocomposite catalyst for the reduction of methylene blue

In this contribution, polystyrene (PS) bearing nitrogen‐rich ligands as chelation moieties for both Ag⁺ ions and Ag⁽⁰⁾ nanoparticles was prepared through successive chemical modifications of native PS including nitration (treatment with HNO₃/H₂SO₄), reductive amination (treatment with SnCl₂/HCl), Michael addition of methyl acrylate, and grafting of ethyelenediamine. The as‐synthesized PS derivative was further used to support silver nanoparticles through initial chelation of the silver nanoparticle ions precursor and subsequent chemical in situ reduction with sodium borohydride. Chemical structure of the PS derivatives was confirmed after each synthesis step by using complementary characterization methods including infrared and energy‐dispersive X‐ray spectroscopies, elemental analysis, X‐ray diffraction, thermogravimetric analysis, and scanning electron microscopy. The catalytic activity of the PS‐EAD/AgNP nanocomposite was demonstrated using the reduction of methylene blue to leucomethylene blue, as a model reaction. The reaction was monitored by UV‐vis spectrophotometry and achieved with an excess of sodium borohydride allowing for a pseudo‐first‐order analysis of the kinetic reaction parameters. Quantitative reduction of the methylene blue was obtained upon successive catalytic cycles with a rate constant value of 0.4016 minute^?1.     

Sufficient Conditions for Error Bounds and Applications

Our aim in this paper is to present sufficient conditions for error bounds in terms of Fréchet and limiting Fréchet subdifferentials in general Banach spaces. This allows us to develop sufficient conditions in terms of the approximate subdifferential for systems of the form (x, y) C × D, g(x, y, u) = 0, where g takes values in an infinite-dimensional space and u plays the role of a parameter. This symmetric structure offers us the choice of imposing conditions either on C or D. We use these results to prove the nonemptiness and weak-star compactness of Fritz–John and Karush–Kuhn–Tucker multiplier sets, to establish the Lipschitz continuity of the value function and to compute its subdifferential and finally to obtain results on local controllability in control problems of nonconvex unbounded differential inclusions.     

On the Discretization of Truncated Integro-Differential Sweeping Process and Optimal Control

Journal of Optimization Theory and Applications - We consider the Volterra integro-differential equation with a time-dependent prox-regular constraint that changes in an absolutely continuous way...     

Evaluation of N‐hydroxymethylphthalimide in alkaline medium: Novel entry to the tricyclic [1,3]oxazepine core via an intramolecular π and O‐cationic cyclization

Fused isoindolo[1,3]benzo(or thieno)oxazepines 8a,b and one of their positional isomers aromatic tricyclic N,O‐acetals 13b are reported to occur efficiently in a three‐step sequence from N‐hydroxy‐methylphthalimide (6) . The key step of this methodology is the intramolecular arylation of an endocyclic and/or exocyclic N‐acyliminium cation. The mechanism leading to these species, in particular to a tricyclic lactam 13b , is discussed.     

Diastereoselective access to chiral non‐racemic [1,3]oxazolo‐[2,3‐a]isoindol‐5‐one ring systems viaO‐cationic cyclization

Dedicated to Professor Jean Morel for his retirement The title compounds 4 have been prepared from suitable β‐amino‐ alcohol 2 and phthalic anhydride ( 5 ) in a three‐step sequence in moderate to good yields (58‐94%). The key step of this methodology is based on an intramolecular O‐cationic cyclization involving N‐acyliminium species. The high levels of the observed chemoselectivity during the intermolecular or intramolecular cyclization were also discussed.     

Theoretical investigation of the weakly dihydrogen bonded dimers H2 − nXnAlHHArF and H2 − nXnAlHHKrF (n = 0–2; X = F, Cl)

An ab initio computational study of the properties of the dihydrogen-bonded complexes of H_{2 − n}X_nAlH (n = 0–2; X = F, Cl) with the rare gas (Rg) compounds HArF and HKrF was carried out at the MP2(full)/6-311++G(2d,2p) level of theory. For all the studied complexes, we found a low zero-point corrected binding energies. Large red shifts of the H–Rg vibrational stretching frequency in both complexes were predicted. Electrostatic interactions between the individual monomers are also predicted.     

Opuntia dillenii (Ker Gawl.) Haw., Seeds Oil Antidiabetic Potential Using In Vivo,In Vitro,In Situ,and Ex Vivo Approaches to Reveal Its Underlying Mechanism of Action

Opuntia dillenii Ker Gawl. is one of the medicinal plants used for the prevention and treatment of diabetes mellitus (DM) in Morocco. This study aims to investigate the antihyperglycemic effect of Opuntia dillenii seed oil (ODSO), its mechanism of action, and any hypoglycemic risk and toxic effects. The antihyperglycemic effect was assessed using the OGTT test in normal and streptozotocin (STZ)-diabetic rats. The mechanisms of action were explored by studying the effect of ODSO on the intestinal absorption of d-glucose using the intestinal in situ single-pass perfusion technique. An Ussing chamber was used to explore the effects of ODSO on intestinal sodium-glucose cotransporter 1 (SGLT1). Additionally, ODSO’s effect on carbohydrate degrading enzymes, pancreatic α-amylase, and intestinal α-glucosidase was evaluated in vitro and in vivo using STZ-diabetic rats. The acute toxicity test on mice was performed, along with a single-dose hypoglycemic effect test. The results showed that ODSO significantly attenuated the postprandial hyperglycemia in normal and STZ-diabetic rats. Indeed, ODSO significantly decreased the intestinal d-glucose absorption in situ. The ex vivo test (Ussing chamber) showed that the ODSO significantly blocks the SGLT1 (IC₅₀ = 60.24 µg/mL). Moreover, ODSO indu\ced a significant inhibition of intestinal α-glucosidase (IC₅₀ = 278 ± 0.01 µg/mL) and pancreatic α-amylase (IC₅₀ = 0.81 ± 0.09 mg/mL) in vitro. A significant decrease of postprandial hyperglycemia was observed in sucrose/starch-loaded normal and STZ-diabetic ODSO-treated rats. On the other hand, ODSO had no risk of hypoglycemia on the basal glucose levels in normal rats. Therefore, no toxic effect was observed in ODSO-treated mice up to 7 mL/kg. The results of this study suggest that ODSO could be suitable as an antidiabetic functional food.