A complex number  is called an extended eigenvalue for an operator  on a Hilbert space H if there exists a nonzero operator  such that: such  is called an extended eigenoperator corresponding to. The goal of this paper is to calculate extended eigenvalues and extended eigenoperators for the weighted unilateral (Forward   and Backward) shift operators. We also find an extended eigenvalues for weighted bilateral shift operator. Moreover, the closedness of extended eigenvalues for the weighted unilateral (Forward and Backward) shift operators under multiplication is proven.

Tridentate Schiff base ligand L2 and its complexes with nickel(II), cobalt (II), copper (II), manganese (II) and mercury (II) ions have been synthesized by the condensation of 4Aminoantipyrine, Benzoin, then the ligand (L1) and 3-amino benzoic acid. The ligand and its complexes were described by 1H-&13C-NMR, UV-visible, FT-IR, (only ligand), molar conductance elemental, analysis and magnetic susceptibility, calculations. It has been set that the ligand acts as (N, N, O) neutral tridentate forming chelates with stoichimetry (metal: ligand) (1:1). all metal complexes is suggested Octahedral configuration. Most of the prepared compounds show antibacterial activity to (Staphylococcus aureus),(Escherichia coli), (Bacillussubtilis) and (Ps

This research includes the synthesis of new series of heterocyclic compounds. Reaction of 2-nitro benzylidene)thiosemicarbazide(1) with ethyl chloro acetate gave (2-nitro benzylidene amino)-2-thioxomidazolidine-4-one(2) ,treatment(2) with methyl iodide to give(3)which was reacted with hydrazine to give 2-hydrazinyl-1-[(2-nitrobenzylidene)amino]- 1H-imidazol-5(4H)-one, andreation of compound(2) with aromatic aldehydes to give 5arylidene -3-({2-nitro benzylidene}amino)2-thioxo-3,5-dihydro-4H-imidazole-4-one(5a,5b), which was reacted with ethyl aceto acetate to give 4-aryl-1-[2-nitrobenzylidene, amino -6oxo-2-thioxo octa hydro-1H-benzo[d]imidazole-5-carboxylate and followed synthesis of βlactamederivtives(9a,9b) by treatment derivatives(

     A spectrophotometric method is proposed for the determination of some drugs containing amino group such as mesalazine, metoclopramide and dopamine in pharmaceutical formulations. It was simple, precise, accurate, rapid, and based on the oxidation of each drug with chromate as an oxidizing agent in the presence of 1N hydrochloric acid. Then indigo carmine is reacted with residual chromate in the presence of a catalysis factor (sodium oxalate). Increasing in absorbance's value of the color system is proportional to the amount of the three drugs which is measured at the selected wavelength of 610 nm.

The proposed method is obeying Beer's law in the ranges of (1-40, 2-44 and 2-52) ppm for the concentration of

the physical paraneters of oxadizole derivaties as donor molecules have been measured the charge transfer and methanol as solvent have been estimated from the electonic spectra

The main purpose of this paper is to study feebly open and feebly closed mappings and we proved several results about that by using some concepts of topological feebly open and feebly closed sets , semi open (- closed ) set , gs-(sg-) closed set and composition of mappings.

The reduced electric quadrupole transition strengths B(E2) from the first excited
2+ state to the ground 0+ state of some even-even Neon isotopes (18,20,22,24,26,28Ne)
have been calculated. All studied isotopes composed of 16O nucleus that is
considered as an inert core and the other valence particles considered to move over
the sd-shell model space within 1d5/2, 2s1/2 and 1d3/2 orbits.
The configuration mixing shell model with limiting number of orbitals in the
model space outside the inert core fail to reproduce the measured electric transition
strengths. Therefore, and for the purpose of enhancing the calculations, the
discarded space has been included through a microscopic theory which considers a
particle-

Background: It is well known that mycotic antigens have an important
role in atopy and the induction of asthma. Now one of the important
subjects is the relation between respiratory bacterial and viral
infections in the inflammatory reactions accompanied with bronchial
asthma viruses Bacteria or their metabolites act as trigger for asthma
or increase it's intensity .
Objectives: To show the relation between asthma and some viral
infections serologically.
Methods: Direct ELISA test was employed to detect lgG specific for
Respiratory Syncytial virus (Rsv) parainfluenza virus type (p13) and
influenza virus in sera of (100) asthmatic patients of two age groups.
(10-17) and(18-50) years old. Serum samples from

  The chalcones 1( a,b) were prepared by the reaction of  2- acetyl benzofuran with two aromatic aldehydes in the presence of alkaline media. These chalcones are used as starting material to obtain the  desired heterocyclic: pyrazolin, isoxazoline, pyrimidinthion, pyrimidinone, cyclohexanone and indazole derivatives. The structure of newly synthesized heterocyclic compounds were established on the basis of  their melting points, elemental analysis(C.H.N), FTIR and 1HMNR (for some of them) spectral data . The synthesized compounds have been screened for their antibacterial activities, they exhibited good antibacterial activity against Escherichia coli (G-) and Staphylococus aureus (G+) .