Primes of the form <Emphasis Type="Italic">x</Emphasis><Superscript>2</Superscript> + (<Emphasis Type="Italic">x</Emphasis> + 1)<Superscript>2</Superscript>. Proper divisors of composites of the same form

The aim of the present paper is to characterize prime numbers of the form n = x ² + (x + 1)² and to obtain certain proper divisors of composite numbers of the same form, i.e. divisors d of n such that 1 < d < n.      

New SPE loading material for affinity‐based separation of cyclodextrins from drug:CD complexes in order to overcome Beer's law deviations

Molecular inclusion of guest molecules within CDs is known to alter guest molecule spectrophotometric absorptivity, making their determination, based on spectrophotometric data, inaccurate. Therefore specific analytical methods capable of quantifying the drugs as free molecules must be developed and validated. SPE was selected to simplify sample and avoid more time‐consuming alternatives. A new solid phase was synthesized and characterized by infrared spectrometry, differential scanning calorimetry and elemental analysis. The competitive complexation of adamantane groups immobilized on the silica substrate facilitates drug:CD complex dissociation and elimination of CD from samples. The drug molecules, now free from CD, can be easily analysed by an already available HPLC method. This new SPE loading material was employed in the determination of ketoprofen in its CD complex as a representative example of the utility of this novel material. The calculated analytical errors were reduced from a maximum of 20.79% (without SPE) to a minimum of 3.99%.     

An improved grid method for the computation of the pseudospectra of matrix polynomials

Pseudospectra of matrix polynomials have been systematically investigated in recent years, since they provide important insights into the sensitivity of polynomial eigenvalue problems. An accurate approximation of the pseudospectrum of a matrix polynomial $P\left(\lambda \right)$ by means of the standard grid method is highly demanding computationally. In this paper, we propose an improvement of the grid method, which reduces the computational cost and retains the robustness and the parallelism of the method. In particular, after giving two lower bounds for the distance from a point to the boundary of the pseudospectrum of $P\left(\lambda \right)$, we present two algorithms for the estimation of the pseudospectrum, using exclusion discs. Furthermore, two illustrative examples and an application of pseudospectra on elliptic (quadratic) eigenvalue problems are given.     

A “Discretization” Technique for the Solution of ODEs II

A functional analytic technique was recently presented for finding discrete equivalent counterparts of initial value problems of ODEs and obtaining their real analytic solutions. In the current paper, this technique is extended to boundary value problems of ODEs and to the complex solutions of ODEs. In order to demonstrate this technique, it is applied to the classic Blasius problem of fluid mechanics. Apart from its real solution, its complex solution is also studied. The obtained results indicate that the complex Blasius function exhibits an oscillatory behavior and strengthen a conjecture regarding its singularities in the complex plane.     

Deprotonated and non-deprotonated cobalt(II) complexes of the bis-amide tetradentate ligand N,N′-(dipicolyl)-1,8-naphthylene diamine. Three different modes of coordination by the ligand

The preparation and some properties of the cobalt(II) complexes Co(LH₂)Cl₂·2H₂O, Co(LH₂(NCS)₂ and CoL·H₂O (whereLH₂=N,N-(dipicolyl)-1,8-naphthylenediamine) are reported. On the basis of magnetic moments, visible reflectance and IR data, the structure is proposed to be pseudo-octahedral for Co(LH₂)Cl₂·2 H₂O, pseudo-tetrahedral for Co(LH₂)(NCS)₂ and square planar for CoL·H₂O.

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Deprotonierte und Nicht-deprotonierte Co(II)-Komplexe des vierzähnigen Bisamid-Liganden N,N-(Dipicolyl)-1,8-naphthyldiamin. Drei verschiedene Koordinationstypen

Zusammenfassung Es werden die Darstellung und einige Eigenschaften der Kobalt(II)-Komplexe Co(LH₂)Cl₂·2 H₂O, Co(LH₂)(NCS)₂ und CoL·H₂O [LH₂=N,N-(dipicolyl)-1,8-naphthylendiamin] diskutiert. Auf der Grundlage von magnetischen Momenten, von Daten der sichtbaren Reflektions-und IR-Spektren wird eine pseudooctaedrische Struktur für Co(LH₂)Cl₂·2H₂O, eine pseudotetraedrische für Co(LH₂)(NCS)₂ und eine planar-quadratische für CoL·H₂O vorgeschlagen.

     

Insertion reactions of beta-diketiminate-stabilised calcium amides with 1,3-dialkylcarbodiimides

A series of heteroleptic beta-diketiminate-stabilised calcium amides of the form [{ArNC(Me)CHC(Me)NAr}Ca{NR(1)R(2)}(THF)] (Ar = 2,6-diisopropylphenyl; R(1) = H, R(2) = Ar; R(1) = H, R(2) = CH(2)CH(2)OMe; R(1) = R(2) = Ph) react with 1,3-dialkylcarbodiimides, R(3)N[double bond, length as m-dash]C[double bond, length as m-dash]NR(3) (R(3) = Cy, (i)Pr), to yield the corresponding insertion products [{ArNC(Me)CHC(Me)NAr}Ca{(R(3)N)(2)CNR(1)R(2)}(THF)] at room temperature in hydrocarbon solutions. These latter compounds contain both beta-diketiminate and guanidinate ligands bound to calcium. Solid-state data are consistent with the guanidinate ligands adopting a number of binding modes including kappa(2) through kappa(3) coordination, with varying degrees of delocalisation of the non-bound guanidinate nitrogen lone-pair across the pi-framework of the ligand. DFT computational studies have been conducted to address these variations in coordination behaviour.     

Bismaleimides and bisnadimides derived from 2,5-bis(4-aminophenyl)-3,4-diphenylthiophene and their polymerization to heat-resistant matrix resins

Six new structurally different bismaleimides or bisnadimides based on 2,5-bis(4-aminophenyl)-3,4-diphenylthiophene (BADT) were synthesized and characterized by infrared (IR) and proton nuclear magnetic resonance (¹H-NMR) spectroscopy. Chain-extension of several bismaleimides was accomplished by incorporating various imide, amide, and urea groups. The bismaleimide and bisnadimide prepared by reacting BADT with maleic or nadic anhydride, respectively, were soluble in various organic solvents. The monomers were thermally polymerized or by a Michael reaction with certain aromatic diamines. Curing behavior was investigated by differential thermal analysis (DTA). The thermal and thermo-oxidative stability of polymers was evaluated by dynamic thermogravimetric analysis (TGA) and isothermal gravimetric analysis (IGA). The polymers derived from bismaleimide of BADT as well as from the bismaleimides chain-extended by imide groups were stable up to 355–392°C in N₂ or air and afforded anaerobic char yield 66–74% at 800°C. The polymers obtained by curing the bismaleimide-diamine adducts showed a relatively lower thermal stability.     

Ferromagnetic interactions in a 1D alternating linear chain of π-stacked 1,3-diphenyl-7-(thien-2-yl)-1,4-dihydro-1,2,4-benzotriazin-4-yl radicals

X-ray studies show that 1,3-diphenyl-7-(thien-2-yl)-1,4-dihydro-1,2,4-benzotriazin-4-yl (6) adopts a distorted, slipped π-stacked structure of centrosymmetric dimers with alternate short and long interplanar distances (3.48 and 3.52 ?). Cyclic voltammograms of 7-(thien-2-yl)benzotriazin-4-yl 6 show two fully reversible waves that correspond to the -1/0 and 0/+1 processes. EPR and DFT studies on radical 6 indicate that the spin density is mainly delocalized over the triazinyl fragment. Magnetic susceptibility measurements show that radical 6 obeys Curie-Weiss behavior in the 5-300 K region with C=0.378 emu K mol(-1) and θ=+4.72 K, which is consistent with ferromagnetic interactions between S=1/2 radicals. Fitting the magnetic susceptibility revealed the behavior is consistent with an alternating ferromagnetic chain (g=2.0071, J(1) =+7.12 cm(-1), J(2) =+1.28 cm(-1)).