New Sobolev-Weinstein Spaces and Applications

In this paper, we consider the generalized Weinstein operator $\Delta_{W}^{d,\alpha,n}$, we introduce new Sobolev-Weinstein spaces denoted $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1}),$ $s\in\mathbb{R},$ associated with the generalized Weinstein operator and we investigate their properties. Next, as application, we study the extremal functions on the spaces $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1})$ using the theory of reproducing kernels.     

Coupled coincidence point results on generalized distance in ordered cone metric spaces

In this paper, we establish some coupled coincidence point results in the setting of partially ordered cone metric spaces via $c$ -distance. We also proved some related coupled common fixed point theorems for such mappings. Our results generalize, extend, and unify several well-known comparable results in the literature regarding this topic. We present some examples to illustrate the concepts and results.     

Common tripled fixed point results in cone metric type spaces

In this paper, we prove some common tripled fixed point and tripled coincidence point results for contractive conditions in a cone metric type space. Our results extend, unify and generalize well-known results in the literature, in particular the recent results of Aydi et al. (Fixed Point Theory Appl 2012:134, 2012). Some examples are also presented to validate our obtained results and new concepts.     

Local nonlinear dynamics of MEMS arches actuated by fringing-field electrostatic actuation

Nonlinear Dynamics - The nonlinear dynamic behavior of a resonant MEMS arch microbeam actuated by fringing electric actuation is investigated in this paper. The arch microbeam is loaded with DC and...     

Synthesis of α-Alkylidene-β-Ethoxycarbonyl Cyclopentanones and -γ-Butyrolactones

Synthesis of (E,Z)-α-Alkylidene-β-ethoxycarbonyl cyclopentanones 5 and (E,Z)-α-alkylidene-γ-butyrolactones 7 by condensing phosphonates 3 or 6 with a variety of aldehydes in the presence of aqueous potassium carbonate (6-10M) as base is reported.     

Action des Hydrazines Fluoroalkylées Sur Les α-Cetophosphonates: Synthèse des Hydrazones α-Phosphonylées N-Fluoroalkylées

In the present work, we study the reaction of fluorinated hydrazines H ₂ N-NHR _F with α-ketophosphonates 1, which lead to N-fluoroalkylated α-phosphonylated hydrazones 2. The stereochemistry of the hydrazones 2 was determined by multinuclear NMR experiments ( ¹ H, ¹³ C, ¹⁹ F, and ³¹ P) and IR spectroscopy.     

First synthesis of (±)-bis-homosarkomycin ethyl ester

A five step synthesis of (±)-bis-homosarkomycin ethyl ester 6 has been achieved starting from commercially available ethyl phosphonoacetate and ethyl 5-bromovalerate. The successful synthetic approach to 6 uses α-methylene pimelate 3 as a key intermediate.     

MEIR-KEELER TYPE CONTRACTIONS FOR TRIPLED FIXED POINTS

In 2011,Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces.In our paper,we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.     

Synthesis,crystal structure and spectral characteristics of highly fluorescent chalcone-based coumarin in solution and in polymer matrix

A new coumarin chalcone 3-((2E)-3-(2-hydroxyphenyl) prop-2-enoyl)-4-hydroxy-2(H)-chromen-2-one was synthesized using the Claisen Schmidt reaction by the condensation of 3-acetyl-4-hydroxycoumarin and 2-hydroxybenzaldehyde using a mild organic base. This novel compound was characterized by ¹H NMR, FT-IR and UV–vis spectroscopy. Single crystal X-ray diffraction investigation at low temperature (T=120 K) shows that this compound exhibits an intramolecular O3–H…O hydrogen bond, the coumarin ring and the phenyl group are nearly coplanar and the crystal packing is stabilized by intermolecular O3–H…O contacts and π–π stacking interactions. This ortho-hydroxyphenyl-4-hydroxycoumarin chalcone exhibits a strong blue-green emission under visible light excitation at 470 nm. The fluorescence behaviors of this compound doped in poly(methyl methacrylate) (PMMA) were investigated.