Existence of nonnegative solutions for parabolic problem on Dirichlet forms

In this work, we investigate perturbed parabolic problem on measure spaces. For strongly local Dirichlet form, we obtain some results on existence and uniqueness of nonnegative solution. We also presented some examples as an applications.     

A Diophantine duality applied to the KAM and Nekhoroshev theorems

In this paper, we use geometry of numbers to relate two dual Diophantine problems. This allows us to focus on simultaneous approximations rather than small linear forms. As a consequence, we develop a new approach to the perturbation theory for quasi-periodic solutions dealing only with periodic approximations and avoiding classical small divisors estimates. We obtain two results of stability, in the spirit of the KAM and Nekhoroshev theorems, in the model case of a perturbation of a constant vector field on the $n$ -dimensional torus. Our first result, which is a Nekhoroshev type theorem, is the construction of a “partial” normal form, that is a normal form with a small remainder whose size depends on the Diophantine properties of the vector. Then, assuming our vector satisfies the Bruno–Rüssmann condition, we construct an “inverted” normal form, recovering the classical KAM theorem of Kolmogorov, Arnold and Moser for constant vector fields on torus.     

Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to “Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians”, in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrableGevrey Hamiltonians at a quasiperiodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.     

New Composite Sorbent for Removal of Sulfate Ions from Simulated and Real Groundwater in the Batch and Continuous Tests

The evaluation of groundwater quality in the Dammam formation, Faddak farm, Karbala Governorate, Iraq proved that the sulfate (SO₄²⁻) concentrations have high values; so, this water is not suitable for livestock, poultry and irrigation purposes. For reclamation of this water, manufacturing of new sorbent for permeable reactive barrier was required through precipitation of Mg and Fe hydroxides nanoparticles on the activated carbon (AC) surface with best Mg/Fe molar ratio of 7.5/2.5. Mixture of 50% coated AC and 50% scrap iron was applied to eliminate SO₄²⁻ from contaminated water with efficiency of 59% and maximum capacity of adsorption equals to 9.5 mg/g for a time period of 1 h, sorbent dosage 40 g/L, and initial pH = 5 at 50 mg/L initial SO₄²⁻ concentration and 200 rpm shaking speed. Characterization analyses certified that the plantation of Mg and Fe nanoparticles onto AC was achieved. Continuous tests showed that the longevity of composite sorbent is increased with thicker bed and lower influent concentration and flow rate. Computer solution (COMSOL) software was well simulated for continuous measurements. The reclamation of real contaminated groundwater was achieved in column set-up with efficiency of 70% when flow rate was 5 mL/min, bed depth was 50 cm and inlet SO₄²⁻ concentration was 2301 mg/L.     

Low Voltage Digitally Controlled CMOS Current Conveyor

In this paper, a digitally controlled current conveyo(DCCC) is presented. The proposed DCCC is based on rail-to-rail folded cascode implementation with a current division network (CDN). The CDN is used to provide control on the current gain of the DCCC. The CDN uses a novel current division technique based on differential pairs. The proposed DCCC can operate from ±1.5 V supply voltages. Applications of the proposed DCCC such as variable gain amplifiers (VGA) and digitally tunedfilters have been investigated. PSpice simulations based on the AMI 1.2 µm N-well level 3 parameters are in agreement with the presented work.     

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.     

Spectral Studies On Some 2-Quinolones

Spectral properties of some 2-Quinolones were investigate-ed. IR and ¹H NMR were applied to characterize the ligands. The hydrogen bond property is of important parameter for controlling the behaviour of the compounds. The N[sbnd]H, O[sbnd]H, C[dbnd]O, C[sbnd]H, and C[sbnd]N fundamental functional groups are characterized. The electronic transitions are assigned. The data are explained on the basis of molecular structure and substituents effects. The acid-base equilibria and the phenomena of tautomerism for these compounds are explained and discussed. The acid exponents (pK_OH, and pK_NH) are evaluated.     

Cyanoacetamide Intermediate in Heterocyclic Synthesis: Synthesis and Biological Evaluation of Hitherto New Dioxoisoindoline Heterocyclic Derivatives

Innovative poly‐substituted heterocyclic rings incorporating dioxoisoindoline ( 2 – 25 ) were synthesized through the reaction of dioxoisoindoline derivative 2 as starting compound with various types of reagents. All compounds were characterized by appropriate means of (¹H‐NMR, ¹³C‐NMR, IR, and mass). The prepared compounds were evaluated as antimicrobial agents against Escherichia coli, Staphylococcus aureus, and Candida albicans microorganisms. The tested compounds exhibited low to moderate antibacterial activities and promising results as antifungal agents.     

Synthesis of Some New Thiazolo[3,2‐a]pyrimidine Derivatives and Their Applications as Disperse Dyes

A series of novel thiazolo[3,2‐a]pyrimidine derivatives were synthesized by using β‐ketoanilides 1a–c as starting materials and as key intermediates for preparation of new pyrimidinecompounds 3a–e and fused heterocyclic pyrimidine derivatives 5a–c . The new compounds were transformed to disperse dyes 6a,b and 7 . The chemical structures were elucidated by spectroscopic and elemental analyses and found to be in good agreement with the proposed structures. The versatility of compounds 6a,b and 7 for textile dyeing as disperse dyes was reported. The synthesized dyes were applied to polyester fabrics by using high temperature dyeing method at 120°C. The dye uptake expressed as color strength (k/s) of the dyed samples has been measured. Moreover, the color strength was examined in detail. In addition, the position of color in CIELAB coordinates (L*, a*, b*, h, and C*) was assessed. The color fastness of the dyed samples gave excellent results for washing and rubbing; however, the light fastness was moderate. Raman spectra of dyed samples unequivocally excluded ring dyeing and found to match with the proposed structures.