Eisenstein type series for Calabi–Yau varieties

In this article we introduce an ordinary differential equation associated to the one parameter family of Calabi–Yau varieties which is mirror dual to the universal family of smooth quintic three folds. It is satisfied by seven functions written in the q-expansion form and the Yukawa coupling turns out to be rational in these functions. We prove that these functions are algebraically independent over the field of complex numbers, and hence, the algebra generated by such functions can be interpreted as the theory of (quasi) modular forms attached to the one parameter family of Calabi–Yau varieties. Our result is a reformulation and realization of a problem of Griffiths around seventies on the existence of automorphic functions for the moduli of polarized Hodge structures. It is a generalization of the Ramanujan differential equation satisfied by three Eisenstein series.     

Definable nilpotent and soluble envelopes in groups without the independence property

We prove that in a group without the independence property a nilpotent subgroup is always contained in a definable nilpotent subgroup of the same nilpotency class. The analogue for the soluble case is also shown when the subgroup is normal in the ambient group.     

A non-metric perfectly normal hereditarily indecomposable continuum

We construct an example of a non-metric perfectly normal hereditarily indecomposable continuum. The example is constructed as an inverse limit of non-metric analogues of solenoids. Theorems needed to insure perfect normality are stated and proven. It is shown that the example cannot be embedded in a countable product of Hausdorff arcs.     

Partial Synthesis of Coenzyme B12 from Cobyric Acid

Here we report the direct chemical synthesis of coenzyme B₁₂ (AdoCbl) from Co_β ‐5′‐deoxyadenosylcobyric acid (AdoCby) and the preparation of the latter from crystalline CN ,H₂O‐cobyric acid (CN ,H₂OC by). AdoCby is a suggested common key intermediate in the biosynthesis of AdoCbl and of other cobamides in microorganisms. AdoCby was thoroughly characterized by spectroscopic means, including homo‐nuclear and hetero‐nuclear NMR , as such data are not available in published work. AdoCbl was prepared from AdoCby in one‐step in over 85% yield, by covalent attachment in aqueous solution of the integral B₁₂‐nucleotide moiety using 1‐ethyl‐3‐(3‐dimethylaminopropyl)‐carbodiimide (EDC ·HC l) and N‐hydroxybenzotriazole (HOB t) as coupling reagents. By the same procedure crystalline vitamin B₁₂ (CNC bl) was also prepared in 92% yield from CN ,H₂OC by. Coordination of the B₁₂‐nucleotide base at the Co_α ‐face of AdoCby or of CN ,H₂OC by was indicated to assist in the efficient covalent coupling at the activated f‐side chain function to furnish the complete corrinoids AdoCbl and CNC bl.     

Outer operators for the noncommutative symmetric hardy spaces associated with finite subdiagonal algebra

In this article, we extended main results on outer operators of [6] to the symmetric Hardy spaces, when associated subdiagonal algebra is finite.     

A Disposable Homemade Screen Printed Electrochemical Sensor for Vitamin B1 Determination in Multivitamin Ampoules: Potentiometric and Surface Morphology Studies

Thiamine chloride hydrochloride (TCH) is one of the B‐complex vitamins which resemble a very biologically important group of biomolecules. The first screen‐printed graphite ion‐selective sensor for the determination of TCH was prepared and characterized. The sensor is based on TCH‐tetraphenylborate as electrode material. A number of parameters such as the type of solvent mediator, weight percent of the ion‐exchanger, test solution temperature and possible interferences were extensively studied. Moreover, the surface morphology of the prepared sensor was studied using scanning electron microscopy. The sensor shows a Nernstian slope of 30.60±0.07 mV/decade, a low LOD of 5.08×10⁻⁶ mol/L and a wide applicability range of 5.96×10⁻⁶‐1.00×10⁻² mol/L. The sensing graphite ink remains usable for at least one month. Fast potentiometric response was obtained within 5 s and remains stable for at least 60 s. The sensor was applied to the analysis of TCH in pure solutions and multivitamin ampoules from the Egyptian market using the standard addition method and high recovery values of 97–102 % were obtained. Low %RSD values (0.27‐1.30) indicate high precision of the proposed sensor. Our sensor provides the advantages of disposability, simple preparation procedures, sensitivity and easy storage and transportation.     

Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all solutions in terms of the law of the driving noise.     

Structural and optical characterization of CdS nanoparticles prepared by chemical precipitation method

In the present study we have synthesized CdS semiconducting quantum dots by the chemical precipitation method using Thioglycerol as the capping agent. X-ray powder diffraction (XRD) and transmission electron microscopy (TEM) are employed to characterize the size, morphology and crystalline structure of the as-prepared material. The synthesized QPs have a mixture of cubical and hexagonal crystal symmetry with 12 nm average diameter. Ultraviolet-visible (UV-vis) absorption spectroscopy is used to calculate the band gap of the material and blue shift in absorption edge. Confinement of the optical phonon modes in the QPs is studied by Raman spectroscopy, while FTIR for identification of chemical bonds in the nanomaterial. Multiple cadmium and sulphur defects were observed by employing the photoluminescence (PL) method.