A WKB analysis of the buckling condition for a cylindrical shell of arbitrary thickness subjected to an external pressure

We consider the plane-strain buckling of a cylindrical shellof arbitrary thickness which is made of a Varga material andis subjected to an external hydrostatic pressure on its outersurface. The WKB method is used to solve the eigenvalue problemthat results from the linear bifurcation analysis. We show thatthe circular cross-section buckles into a non-circular shapeat a value of µ₁ which depends on A₁/A₂ and a mode number,where A₁ and A₂ are the undeformed inner and outer radii, andµ₁ is the ratio of the deformed inner radius to A₁. Inthe large mode number limit, we find that the dependence ofµ₁ on A₁/A₂ has a boundary layer structure: it is constantover almost the entire region of 0 < A₁/A₂ < 1 and decreasessharply from this constant value to unity as A₁/A₂ tends tounity. Our asymptotic results for A₁ – 1 = O(1) and A₁– 1 = O(1/n) are shown to agree with the numerical resultsobtained by using the compound matrix method.     

Enhancement of distillate selectivity in Fischer-Tropsch synthesis by using iron and cobalt catalysts in a novel dual-bed reactor ?

Summary An integrated process for producing liquid fuels from synthesis gas via a two-stage Fischer-Tropsch (FT) reaction is disclosed. An iron catalyst was used in the first bed of a fixed-bed reactor followed by a ruthenium promoted cobalt catalyst in the second bed. The activity and selectivity of the dual-bed system were assessed and compared with those using catalysts in a single bed system, separately. The methane selectivity in the dual-bed reactor was about 11% less compared to that of the single-bed system. The C₅⁺ selectivity for the dual-bed reactor was 19.7% higher than that of the single-bed system.     

Resistant starches and health

It was initially hypothesized that resistant starches, i.e., starch that enters the colon, would have protective effects on chronic colonic diseases, including reduction of colon cancer risk and in the treatment of ulcerative colitis. Recent studies have confirmed the ability of resistant starch to increase fecal bulk, increase the molar ratio of butyrate in relation to other short-chain fatty acids, and dilute fecal bile acids. However the ability of resistant starch to reduce luminal concentrations of compounds that are damaging to the colonic mucosa, including fecal ammonia, phenols, and N-nitroso compounds, still requires clear demonstration. As such, the effectiveness of resistant starch in preventing or treating colonic diseases remains to be assessed. Nevertheless, there is a fraction of what has been termed resistant (RS1) starch, which enters the colon and acts as slowly digested or lente carbohydrate in the small intestine. Foods in this class are low glycemic index and have been shown to reduce the risk of chronic disease. They have been associated with systemic physiological effects such as reduced postprandial insulin levels and higher HDL cholesterol levels. Consumption of low glycemic index foods has been shown to be related to reductions in risk of coronary heart disease and Type 2 diabetes. Type 2 diabetes has in turn been related to a higher risk of colon cancer. If carbohydrates have a protective role in colon cancer prevention this may lie partly in the systemic effects of low glycemic index foods. The colonic advantages of different carbohydrates, varying in their glycemic index and resistant starch content, therefore, remain to be determined. However, as recent positive research findings continue to mount, there is reason for optimism over the possible health advantages of those resistant starches, which are slowly digested in the small intestine.     

Magnetic-Field-Orientation Dependent Thermal Entanglement of a Spin-1 Heisenberg Dimer: The Case Study of Dinuclear Nickel Complex with an Uniaxial Single-Ion Anisotropy

The bipartite entanglement in pure and mixed states of a quantum spin-1 Heisenberg dimer with exchange and uniaxial single-ion anisotropies is quantified through the negativity in a presence of the external magnetic field. At zero temperature the negativity shows a marked stepwise dependence on a magnetic field with two abrupt jumps and plateaus, which can be attributed to the quantum antiferromagnetic and quantum ferrimagnetic ground states. The magnetic-field-driven phase transition between the quantum antiferromagnetic and quantum ferrimagnetic ground states manifests itself at nonzero temperatures by a local minimum of the negativity, which is followed by a peculiar field-induced rise of the negativity observable in a range of moderately strong magnetic fields. The rising temperature generally smears out abrupt jumps and plateaus of the negativity, which cannot be distinguished in the relevant dependencies above a certain temperature. It is shown that the thermal entanglement is most persistent against rising temperature at the magnetic field, for which an energy gap between a ground state and a first excited state is highest. Besides, temperature variations of the negativity of the spin-1 Heisenberg dimer with an easy-axis single-ion anisotropy may exhibit a singular point-kink, at which the negativity has discontinuity in its first derivative. The homodinuclear nickel complex [Ni2(Medpt)2(μ-ox)(H2O)2](ClO4)2·2H2O provides a suitable experimental platform of the antiferromagnetic spin-1 Heisenberg dimer, which allowed us to estimate a strength of the bipartite entanglement between two exchange-coupled Ni2+ magnetic ions on the grounds of the interaction constants reported previously from the fitting procedure of the magnetization data. It is verified that the negativity of this dinuclear compound is highly magnetic-field-orientation dependent due to presence of a relatively strong uniaxial single-ion anisotropy.     

Silver,iron, and nickel immobilized on hydroxyapatite‐core‐shell γ‐Fe2O3 MNPs catalyzed one‐pot five‐component reactions for the synthesis of tetrahydropyridines by tandem condensation of amines,aldehydes, and methyl acetoacetate

In this study, Ag, Ni²⁺, and Fe²⁺ immobilized on hydroxyapatite‐core‐shell γ‐Fe₂O₃ nanoparticles (γ‐Fe₂O₃@HAp‐Ag, γ‐Fe₂O₃@HAp‐Ni²⁺, and γ‐Fe₂O₃@HAp‐Fe²⁺) as a new and reusable Lewis acid magnetic nanocatalyst was successfully synthesized and reported for an atom economic, extremely facile, and environmentally benign procedure for the synthesis of highly functionalized tetrahydropyridines derivatives 4a‐t is described by one‐pot five‐component reaction of 2 equiv of aldehydes 1 , 2 equiv of amines 2 , and 1 equiv of methyl acetoacetate 3 in EtOH at room temperature in good to high yields and short reaction time. The presented methodology offers several advantages such as easy work‐up procedure, reusability of the magnetic nanocatalyst, operational simplicity, green synthesis avoiding toxic reagents and solvent, mild reaction conditions, and no tedious column chromatographic separation.     

A New Insight into the Stereoelectronic Control of the Pd0-Catalyzed Allylic Substitution: Application for the Synthesis of Multisubstituted Pyran-2-ones via an Unusual 1,3-Transposition

Pyran-2-ones 3 undergo a novel Pd⁰-catalyzed 1,3-rearrangement to afford isomers 6 . The reaction proceeds via an η²-Pd complex, the pyramidalization of which (confirmed by quantum chemistry calculations) offers a favorable antiperiplanar alignment of the Pd−C and allylic C−O bonds ( C ), thus allowing the formation of an η³-Pd intermediate. Subsequent rotation and rate-limiting recombination with the carboxylate arm then gives isomeric pyran-2-ones 6 . The calculated free energies reproduce the observed kinetics semi-quantitatively.     

Green synthesis of the 1-substituted 1H-1, 2, 3, 4-tetrazoles over bifunctional catalyst based on copper intercalated into Mg/Al hydrotalcite modified magnetite nanoparticles

An effective one-pot, convenient process for the synthesis of 1- substituted 1H-tetrazoles from triethyl orthoformate, amines, and sodium azide is described using copper (II) doped and immobilized on functionalized magnetic hydrotalcite (Fe₃O₄/HT-NH₂ Cu^II) as a novel recyclable catalyst. The application of this catalyst allows the synthesis of a variety of tetrazoles in good to excellent yields in water. The new catalyst was characterized using Fourier transform infrared (FT-IR) spectroscopy, X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), thermogravimetric analysis (TGA), vibration sample magnetometry (VSM) and inductively coupled plasma analysis (ICP-OES). This new procedure offers several advantages such as short operational simplicity, practicability, and applicability to various substrates and the absence of any tedious workup or purification. The loading amount of Cu^II (doped and immobilized) on functionalized magnetic hydrotalcite was indicated to be 4.66 mmol g⁻¹, obtained from the ICP-OES analysis. Also, the excellent catalytic performance, thermal stability, and separation of the catalyst make it an excellent heterogeneous system and a useful alternative to other heterogeneous catalysts. Also, the catalyst could be magnetically separated and reused six times without significant loss of catalytic activity.     

Nanomagnetically modified vitamin B3 (Fe3O4@Niacin): An efficient and reusable green biocatalyst for microwave‐assisted rapid synthesis of 2‐amino‐3‐cyanopyridines in aqueous medium

Superparamagnetic nanoparticles of modified vitamin B₃ (Fe₃O₄@Niacin) represent a new, efficient and green biocatalyst for the one‐pot synthesis of 2‐amino‐3‐cyanopyridine derivatives via four‐component condensation reaction between aldehydes, ketones, malononitrile, and ammonium acetate under microwave irradiation in water. This new magnetic organocatalyst was easily isolated from the reaction mixture by magnetic decantation using an external magnet and reused at least six times without significant degradation in the activity. The catalyst was fully characterized by FT‐IR, XRD, SEM, VSM, UV–Vis, DLS and EDS. Excellent yield, very short reaction time (7–10 min), operational simplicity, easy work‐up procedure, avoidance of hazardous or toxic catalysts and organic solvents are the main advantages of this green methodology which makes it more economic than the other conventional methods.