An improvement of Ozaki’s P-valent conditions

The old result due to[Ozaki,S.:On the theory of multivalent functions Ⅱ.Sci.Rep.Tokyo Bunrika Daigaku Sect.A,45-87(1941)],says that if f(z) = z~p + ∑_(n=p+1~(a_nz~n))~∞ is analytic in a convex domain D and for some real α we have Re{exp(iα)f~((p))(z)} 0 in D,then f(z) is at most p-valent in ED.In this paper,we consider similar problems in the unit disc B = {z ∈ C:|z| 1}.     

On subordination of some analytic functions

We define V (α, β) (α < 1 and β > 1), the new subclass of analytic functions with bounded positive real part, \(V\left( {\alpha ,\beta } \right): = \left\{ {f \in A:\alpha < \operatorname{Re} \left\{ {{{\left( {\frac{z}{{f\left( z \right)}}} \right)}^2}f'\left( z \right)} \right\} < \beta } \right\}\), and study some properties of V (α, β). We also study the class U (γ) (γ > 0): \(u\left( \gamma \right): = \left\{ {f \in A:\left| {{{\left( {\frac{z}{{f\left( z \right)}}} \right)}^2}f'\left( z \right)} \right| - 1 < \gamma } \right\}\), where A is the class of normalized functions.     

A microwave spectroscopic and quantum chemical study of 3-butyne-1-selenol (HSeCH2CH2C[triple bond]CH)

The microwave spectrum of 3-butyne-1-selenol has been studied by means of Stark-modulation microwave spectroscopy and quantum chemical calculations employing the B3LYP/aug-cc-pVTZ and MP2/6-311++G(3df,3pd) methods. Rotational transitions attributable to the H80SeCH2CH2C[triple bond]CH and H78SeCH2CH2C[triple bond]CH isotopologues of two conformers of this molecule were assigned. One of these conformers possesses an antiperiplanar arrangement for the atoms Se-C-C-C, while the other is synclinal and seems to be stabilized by the formation of a weak intramolecular hydrogen bond between the hydrogen atom of the selenol group and the pi electrons of the CC triple bond. The energy difference between these conformers was determined to be 0.2(5) kJ/mol by relative intensity measurements, and the hydrogen-bonded form was slightly lower in energy.     

An application of UV-derivative spectrophotometry and bivariate calibration algorithm for study of photostability of levomepromazine hydrochloride

Derivative spectrophotometry and bivariate calibration algorithm were used for study of run of photooxidation of levomepromazine hydrochloride (LV). The actual concentrations of LV and its main degradation product levomepromazine sulphoxide (LV-SO) were calculated using data provided by applied methods. The direct reading of absorbance values at 302 nm and 334 nm were employed for quantification of LV and LV-SO, respectively, in the case of bivariate method. The derivative spectrophotometric method is based on transformation of zero-order spectra into first derivative. The values of first derivative at 334 nm were used for quantification of LV while at 278 nm for assay of LV-SO. The obtained quantitative data were applied for investigation of kinetics of photodegradation of LV.     

Sterically Less‐Hindered Half‐Titanocene(IV) Phenoxides: Ancillary‐Ligand Effect on Mono‐, Bis‐, and Tris(2‐Alkyl‐/arylphenoxy) Titanium(IV) Chloride Complexes

A series of mono‐, bis‐, and tris(phenoxy)–titanium(IV) chlorides of the type [Cp*Ti(2‐R? PhO)_nCl_3?n] (n=1–3; Cp*=pentamethylcyclopentadienyl) was prepared, in which R=Me, iPr, tBu, and Ph. The formation of each mono‐, bis‐, and tris(2‐alkyl‐/arylphenoxy) series was authenticated by structural studies on representative examples of the phenyl series including [Cp*Ti(2‐Ph? PhO)Cl₂] ( 1 PhCl2 ), [Cp*Ti(2‐Ph? PhO)₂Cl] ( 2 PhCl ), and [Cp*Ti(2‐Ph? PhO)₃] ( 3 Ph ). The metal‐coordination geometry of each compound is best described as pseudotetrahedral with the Cp* ring and the 2‐Ph? PhO and chloride ligands occupying three leg positions in a piano‐stool geometry. The mean Ti? O distances, observed with an increasing number of 2‐Ph? PhO groups, are 1.784(3), 1.802(4), and 1.799(3) Å for 1 PhCl2 , 2 PhCl , and 3 Ph , respectively. All four alkyl/aryl series with Me, iPr, tBu, and Ph substituents were tested for ethylene homopolymerization after activation with Ph₃C⁺[B(C₆F₅)₄]^? and modified methyaluminoxane (7% aluminum in isopar E; mMAO‐7) at 140 °C. The phenyl series showed much higher catalytic activity, which ranged from 43.2 and 65.4 kg (mmol of Ti?h)^?1, than the Me, iPr, and tBu series (19.2 and 36.6 kg (mmol of Ti?h)^?1). Among the phenyl series, the bis(phenoxide) complex of 2 PhCl showed the highest activity of 65.4 kg (mmol of Ti?h)^?1. Therefore, the catalyst precursors of the phenyl series were examined by treating them with a variety of alkylating reagents, such as trimethylaluminum (TMA), triisobutylaluminum (TIBA), and methylaluminoxane (MAO). In all cases, 2 PhCl produced the most catalytically active alkylated species, [Cp*Ti(2‐Ph? PhO)MeCl]. This enhancement was further supported by DFT calculations based on the simplified model with TMA.     

Phosphorylation and ATP-binding induced conformational changes in the PrkC,Ser/Thr kinase from <Emphasis Type="Italic">B. subtilis</Emphasis>

Recent studies on the PrkC, serine-threonine kinase show that that the enzyme is located at the inner membrane of endospores and is responsible for triggering spore germination. The activity of the protein increases considerably after phosphorylation of four threonine residues placed on the activation loop and one serine placed in the C-terminal lobe of the PrkC. The molecular relationship between phosphorylation of these residues and enzyme activity is not known. In this work molecular dynamics simulation is performed on four forms of the protein kinase PrkC from B. subtilis—phosphorylated or unphosphorylated; with or without ATP bound—in order to gain insight into phosphorylation and ATP binding on the conformational changes and functions of the protein kinase. Our results show how phosphorylation, as well as the presence of ATP, is important for the activity of the enzyme through its molecular interaction with the catalytic core residues. Three of four threonine residues were found to be involved in the interactions with conservative motifs important for the enzyme activity. Two of the threonine residues (T167 and T165) are involved in ionic interactions with an arginine cluster from αC-helix. The third residue (T163) plays a crucial role, interacting with His-Arg-Asp triad (HRD). Last of the threonine residues (T162), as well as the serine (S214), were indicated to play a role in the substrate recognition or dimerization of the enzyme. The presence of ATP in the unphosphorylated model induced conformational instability of the activation loop and Asp-Phe-Gly motif (DFG). Based on our calculations we put forward a hypothesis suggesting that the ATP binds after phosphorylation of the activation loop to create a fully active conformation in the closed position.     

A concise synthesis of (±) and a total synthesis of (+)-epiquinamide

A total synthesis of the quinolizidine alkaloid (+)-epiquinamide 1 has been achieved starting from (−)-pipecolinic acid 3. The key step is the highly diastereoselective addition of a TBDMS-protected propargyl alcohol to a chiral aldehyde derived from 3 to give erythro alkynol 19, which is then easily transformed into the desired bicyclic skeleton.     

On a sufficient condition for function to be p-valent close-to-convex

The Ramanujan Journal - The property of close-to-convexity of analytic function, that generalizes that of starlikeness, was introduced by Kaplan in 1952. He also gave the geometric interpretation...     

On Ozaki's condition for p-valency

Let f be an analytic function in a convex domain $D?\mathbb{C}$. A well-known theorem of Ozaki states that if f is analytic in D, and is given by $f(z)=z^p+{\sum }_{n=p+1}^{\infty }{a}_n{z}^n$ for $z\in D$, and

$\mathfrak{Re}\{{\mathrm{e}}^{\mathrm{i}\alpha }{f}^{(p)}(z)\}>0,(z\in D),$

for some real α, then f is at most p-valent in D. Ozaki's condition is a generalization of the well-known Noshiro–Warschawski univalence condition. The purpose of this paper is to provide some related sufficient conditions for functions analytic in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ to be p-valent in $\mathbb{D}$, and to give an improvement to Ozaki's sufficient condition for p-valence when $z\in \mathbb{D}$.     

Biomimetic synthesis of leukotriene A

A biogenetically patterned conversion of $\text{1}$ into $\text{2}$ is described. This transformation has been found to be non-stereospecific with respect to the geometry of the newly generated double bond at C9(10).