A note on the use of modified Adomian decomposition method for solving singular boundary value problems of higher-order ordinary differential equations

This paper extend the work [Yahya Qaid Hasan, Liu Ming Zhu. Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method. Commun Nonlinear Sci Numer Simul. doi :10.1016/j.cnsns.2008.09.027] to high order of singular boundary value problems. Solution of these problems is considered by proposed modification of Adomian decomposition method. The proposed method can be applied to linear and nonlinear problems. Some examples are presented to show the ability of the method for linear and non-linear ordinary differential equation.     

Are cobaltates conventional? An ARPES viewpoint

Recently discovered class of cobaltate superconductors (Na_0.3CoO₂·nH₂O) is a novel realization of interacting quantum electron system in a triangular network with low-energy degrees of freedom. We employ angle-resolved photoemission spectroscopy to study the quasiparticle parameters in the parent superconductors. Results reveal a large hole-like Fermi surface generated by the crossing of heavy quasiparticles. The measured quasiparticle parameters collectively suggest two orders of magnitude departure from the conventional weak coupling (such as Al) Bardeen-Cooper-Schrieffer electron dynamics paradigm and unveils cobaltates as a rather hidden class of relatively high temperature superconductors. These parameters also form the basis for a microscopic Hamiltonian of the system.     

A framework for quality control and parameter optimization in diffusion tensor imaging: theoretical analysis and validation

In this communication, a theoretical framework for quality control and parameter optimization in diffusion tensor imaging (DTI) is presented and validated. The approach is based on the analytical error propagation of the mean diffusivity (D(av)) obtained directly from the diffusion-weighted data acquired using rotationally invariant and uniformly distributed icosahedral encoding schemes. The error propagation of a recently described and validated cylindrical tensor model is further extrapolated to the spherical tensor case (diffusion anisotropy approximately 0) to relate analytically the precision error in fractional tensor anisotropy (FA) with the mean diffusion-to-noise ratio (DNR). The approach provided simple analytical and empirical quality control measures for optimization of diffusion parameter space in an isotropic medium that can be tested using widely available water phantoms.     

Emergence of Fermi pockets in a new excitonic charge-density-wave melted superconductor

A superconducting state (T(c) approximately 4.2 K) has very recently been observed upon successful doping of the charge-density-wave (CDW) ordered triangular lattice TiSe(2), with copper. Using state-of-the-art photoemission spectroscopy we identify, for the first time, momentum-space locations of doped electrons that form the Fermi sea of the superconductor. With doping, we find that kinematic nesting volume increases, whereas coherence of the CDW collective order sharply drops. In superconducting doping, as chemical potential rises, we observe the emergence of a large density of states in the form of a narrow electron pocket near the L point of the Brillouin zone with d-like character. The k-space spectral evolution directly demonstrates, for the first time, that the CDW order parameter microscopically competes with superconductivity in the same band.     

Fam-Ti catalyzed enantioselective alkynylation of aldehydes

Ferrocenyl-substituted aziridinylmethanol (Fam-1) has been used as a chiral catalyst with titanium for enantioselective alkynylation of aromatic, heteroaromatic, aliphatic, and alpha,beta-unsaturated aldehydes to give the corresponding propargylic alcohols in up to 96% yield and 96% ee. The ligand can be prepared easily and recycled.     

Solid-phase synthesis of symmetrical 5',5'-dinucleoside mono-, di-, tri-, and tetraphosphodiesters

Four classes of phosphitylating reagents were subjected to reactions with aminomethyl polystyrene resin-bound p-acetoxybenzyl alcohol to yield the corresponding polymer-bound mono-, di-, tri-, and tetraphosphitylating reagents. The solid-phase reagents were reacted with unprotected nucleosides (e.g., thymidine, adenosine, 3'-azido-3'-deoxythymidine, cytidine, or inosine) in the presence of 5-(ethylthio)-1H-tetrazole. Polymer-bound nucleosides underwent oxidation with tert-butyl hydroperoxide, deprotection of cyanoethoxy groups with DBU, and the acidic cleavage, respectively, to afford 5',5'-dinucleoside mono-, di-, tri-, and tetraphosphodiesters in 59-78% yield.     

The interaction of cationic polymers and their bisphosphonate derivatives with hydroxyapatite

Conjugating proteins with bisphosphonates (BPs), a class of molecules with exceptional affinity to hydroxyapatite (HA), is a feasible means to impart bone affinity to protein-based therapeutic agents. To increase the targeting effectiveness while minimizing protein modification, a polymeric linker containing multiple copies of BPs could be constructed for protein conjugation and targeting to bone. Towards this goal, poly(L-lysine) (PLL) and poly(ethylenimine) (PEI) were utilized as the polymeric backbones to incorporate a BP, namely 2-(3-mercaptopropylsulfanyl)-ethyl-1,1-bisphosphonic acid (thiolBP), by using N-hydroxysuccinimidyl polyethylene glycol maleimide and succinimidyl-4-(N-maleimidomethyl)-cyclohexane-1-carboxylate, respectively. In vitro and in vivo mineral affinity of the polymer-BP conjugates were determined in comparison with the unmodified polymers. The in vitro results indicated strong binding of the cationic polymers to HA in their unmodified form. BP conjugation did not enhance the inherent mineral affinity of the polymers; in contrast, certain modifications negatively affected the polymers' binding to the HA. In vivo results from a subcutaneous implant model in rats also showed no significant difference in mineral affinity of the BP modified and unmodified PEI. We conclude that thiolBP conjugation to the cationic polymers PLL and PEI was not beneficial for increasing the mineral affinity of the polymeric molecules. The strong interaction between the cationic polymers and HA may make the polymers suitable for imparting mineral affinity to bone-acting therapeutics.     

Synthesis and some reactions of 4‐(ethoxycarbonyl)‐1,5‐diphenyl‐1H‐pyrazole‐3‐carboxylic acid

1,5‐Diphenyl‐1H‐pyrazole‐3,4‐dicarboxylic acid‐4‐ethyl ester 2 , obtained from the 4‐ethoxycarbonyl‐5‐phenyl‐2,3‐furandione 1 and N‐benzylidene‐N′‐phenyl hydrazine, was converted via reactions of its acid chloride 3 with various alcohols or N‐nucleophiles into the corresponding ester 5 or amide derivatives 6 , respectively. In addition, 2 was decarboxylated to give ethyl 1,5‐diphenylpyrazole‐4‐carboxylate 4 . Nitrile 7 derivative of 2 was also obtained by dehydration of 6a in a mixture of SOCl₂ and DMF. While cyclocondensation reaction of 2 with hydrazine hydrate leads to the formation of pyrazolo[3,4‐d]pyridazine‐4,7‐dione 8 , the reaction of 3 with anhydrous hydrazine provided a new bis pyrazole derivative 9 .     

A study on chemical behaviors of some 4‐pyrones synthesized by one‐step reactions towards various amines

Cycloaddition of acetylbenzoyl ketene generated in situ as an intermediate during one‐step reaction between excess benzoylacetone and oxalylchloride to C=C double bond of cyclic enol form of benzoylacetone gave 3‐acetyl‐5‐benzoyl‐6‐methyl‐2‐phenyl‐4(4H)‐pyrone 1a . Condensation reactions of 1a together with 3,5‐dibenzoyl‐2,6‐diphenyl‐4(4H)‐pyrone 1b and 3‐benzoyl‐5‐ethoxycarbonyl‐2,6‐diphenyl‐4(4H)‐pyrone 1c with two‐fold excess primary amines provided a series of 3‐benzoyl‐1‐alkyl‐5‐(1‐alkylimino‐ethyl)‐6‐phenyl‐2‐methyl‐4(1H)‐pyridinone 2 , 3,5‐dibenzoyl‐1‐alkyl‐2,6‐diphenyl‐4(1H)‐pyridinone 3a‐c and 3‐benzoyl‐1‐alkyl‐5‐ethoxycarbonyl‐2,6‐diphenyl‐4(1H)‐pyridinone 3d,e derivatives, respectively. In addition, while prolonged reaction of n‐pentylamine with unsymmetrical pyrone derivative 1a gives a symmetrical pyridinone derivative namely 3,5‐dibenzoyl‐2,6‐dimethyl‐1‐pentyl‐4(1H)‐pyridinone 5 , much prolonged action n‐pentylamine and then aqueous n‐pentylamine on 1b resulted in degradation of the 4‐pyrone ring to give dibenzoylmethane.