On Some Properties of $c$-Frames

In this paper we discuss about $c$-frames, namely continuous frames. Since, $c$-frames are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and $c$-frames to characterize these frames. Also, we will specify (precisely) the synthesis and frame operators of Bochner integrable $c$-frames. Finally, we classify Hilbert-Schmidt operators by $c$-frames and express some new identities for Parseval $c$-frames.     

Multiple solutions for non-homogeneous degenerate Schrödinger equations in cone Sobolev spaces

The present paper deals with the study of semilinear and non-homogeneous Schrödinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and for p ∈ (2, 2?) with respect to non-homogeneous term g(x) ∈ L ₂ ^n/2 (B), which helps to find multiple solutions of our problem. More precisely, we prove the existence of two solutions to the problem 1.1 with negative and positive energy in cone Sobolev space H _2,0 ^1,n/2 (B). Finally, we consider p = 2 and we prove the existence and uniqueness of Fuchsian-Poisson problem.     

Synthesis of 2-(2-Fluorophenyl)-2-methylamino-Cyclohexanone as a New Ketamine Derivative

The main goal of this article is to the present research on the development of ketamine derivatives. The target molecule was a fluoroderivative of ketamine, for which a multistep synthesis has been reported. This novel ketamine derivative, 2-(2-fluorophenyl)-2-methylamino-cyclohexanone, has been called fluoroketamine by our research group. The starting fluorobenzonitrile was reacted with the appropriate Grignard reagent followed by the bromination reaction to obtain α-bromocyclopentyl-(2-fluorophenyl)-ketone. The reaction of the obtained ketone with methylamine at ?40 °C then resulted in the formation of α-hydroxycyclopentyl-(2-flourophenyl)-N-methylamine. Finally, the five-memberd ring cyclopentanol was expanded to the cyclohexylketone by a thermal rearrangement reaction. The HCl salt of the target molecule, which is soluble in water, was obtained by the acidification of the free fluoroketamine with HCl. Preliminary animal tests on mice have shown that the resulting fluoroketamine has some advantages over ketamine in terms of the effective dose and the recovery time.     

Determination of amylose in Iranian rice by multivariate calibration of the surface plasmon resonance spectra of silver nanoparticles

A simple and non-separative analytical method for selective determination of amylose in Iranian rice has been developed. It was based on the reduction of silver ions by amylose and production of Ag nanoparticles, which exhibit surface plasmon resonance (SPR) spectra in the ultraviolet/visible region. The formation of Ag nanoparticles in the presence of amylose was monitored by transmission electron microscopy (TEM) and dynamic light scattering (DLS). The experimental conditions were optimized to obtain the highest yield for nanoparticle formation. Partial least square (PLS) regression as an efficient multivariate spectral calibration method was employed to make a connection between the SPR spectra of the generated Ag nanoparticles and the amylose content (AC) of the rice starch. The number of PLS latent variables was optimized by leave-one-out cross-validation utilizing prediction residual error sum of square (PRESS). The proposed model exhibited a high ability for prediction of amylose concentration in both standard starch samples and real rice samples prepared from different regions of Iran. The relative errors of prediction were almost lower than ±5% for different real samples and the detection limit was 3.23 weight percent of amylose in rice. In comparison to the reference method (Juliano method), the proposed method is simpler and does not need tedious sample preprocessing steps.     

Fuzzy model prediction of Co (III)Al2O3 catalytic behavior in Fischer-Tropsch synthesis

The application of Co(Ⅲ)/Al2O3 catalyst in Fischer-Tropsch synthesis(FTS)was studied in a wide range of synthesis gas conversions and compared with Fuzzy Simulation results.Present study applies fuzzy model to predicting the product composition of CH4,CO2 and CO in Fischer-Tropsch process for natural gas synthesis,in which the input vector was 4-dimension including four variables(operating pressure, operating temperature,time and CO/H2 ratio)of 70 different experiments and the output product is a composition of CO2,CO and CH4. The Mamdani algorithm has been applied to the training of the fuzzy system and the test set was used to evaluate the performance of the system including R2,ARE,AARE and SD.The results demonstrated that the predicted values from the model were in good consistency with the experimental data.The work indicates how fuzzy inference system(FIS),as a promising predicting technique,would be effectively used in FTS.     

Effect of variable viscosity and viscous dissipation on the Hagen‐Poiseuille flow and entropy generation

In this article, the steady‐state flow of a Hagen‐Poiseuille modelin a circular pipe is considered and entropy generation due tofluid friction and heat transfer is examined. Because of variationin fluid viscosity, the entropy generation in the flow varies. Inhis model, Arrhenius law is applied for temperature equation‐dependent viscosity, and the influence of viscosity parameters on the entropy generation number and distribution of temperature and velocity is investigated. The governing momentum and energy equations, which are coupled due to the dissipative term in the energy equation, were solved by analytical techniques. The solutions of equations via perturbation method and homotopy perturbation method are obtained and then compared with those of numerical solutions. It is found that the fluid viscosity influences considerably the temperature distribution in the fluid close to the pipe wall, and increasing pipe wall temperature enhances the rate of entropy generation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 529–540, 2011     

The Reaction of (N‐Isocyanimino)triphenylphosphorane with Biacetyl in the Presence of Aromatic Carboxylic Acids: Efficient One‐Pot Three‐Component Reaction for the Synthesis of 3‐(5‐Aryl‐1,3,4‐oxadiazol‐2‐yl)‐3‐hydroxybutan‐2‐one Derivatives

Reactions of biacetyl (=butane‐2,3‐dione) with (N‐isocyanimino)triphenylphosphorane in the presence of aromatic carboxylic acids proceed smoothly at room temperature and under neutral conditions to afford 3‐(5‐aryl‐1,3,4‐oxadiazol‐2‐yl)‐3‐hydroxybutan‐2‐one derivatives in high yields.     

An Efficient One‐Pot,Four‐Component Synthesis of {[(1H‐1,2,3‐Triazol‐4‐yl)methoxy]phenyl}‐1H‐pyrazolo[1,2‐b]phthalazine‐5,10‐dione Derivatives

The 1‐{[(1H‐1,2,3‐Triazol‐4‐yl)methoxy]phenyl}‐1H‐pyrazolo[1,2‐b]phthalazine‐5,10‐dione derivatives 5 were synthesized by a simple and efficient method, i.e., by the four‐component, one‐pot condensation reaction of phthalohydrazide 4 , a (propargyloxy)benzaldehyde 1 , an active methylene compound 3 (malononitrile or ethyl cyanoacetate), and an azide 2 in the presence of Cu(OAc)₂/sodium L ‐ascorbate as catalyst and 1‐methyl‐1H‐imidazolium trifluoroacetate ([Hmim](CF₃COO)) as an ionic‐liquid medium in good to excellent yields (Scheme 1).     

Raman active jagged-shaped gold-coated magnetic particles as a novel multimodal nanoprobe

The creation of novel engineered multimodal nanoparticles (NPs) is a key focus in bionanotechnology and can lead to deep understanding of biological processes at the molecular level. Here, we present a multi-component system made of gold-coupled core-shell SPIONs, as a new nanoprobe with signal enhancement in surface Raman spectroscopy, due to its jagged-shaped gold shell coating.     

Determination of unknown functions in a mathematical model of ductal carcinoma in situ

This study deals with the numerical investigation of a mathematical model of breast cancer at the initial growth stage known as ductal carcinoma in situ. This model considered as an inverse problem and the uniqueness of solution of this inverse problem is proved. To solve this problem, a computational approach is developed based on an iterative procedure and space marching and mollification methods. The stability and convergence results are given to support the method theoretically. Two test problems are considered to demonstrate the efficiency and ability of the proposed numerical approach.