We prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state-dependent delay in an abstract space. Sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using the Krasnoselskii–Schaefer type fixed point theorem with the fractional power of operators. An example is provided to illustrate the main results.

Approximate controllability of partial neutral functional differential systems of fractional order with state-dependent delay

Reported are the syntheses, crystal structures, and magnetic susceptibilities of two series of closely related rare-earth metal–lithium germanides RE2Li2Ge3 and RE3Li4Ge4 (RE = La–Nd, Sm). All titl...

Closely related rare-earth metal germanides RE2Li2Ge3 and RE3Li4Ge4 (RE = La-Nd, Sm): synthesis, crystal chemistry, and magnetic properties.

Calcium phosphate based biomaterials are widely used in dentistry and as a bone substitutes in orthopedic applications. Calcium pyrophosphate (CPP) – a type of calcium phosphate and a shortest linear polyphosphate can also be used as a bone graft. Successive applications of theses materials depend on the degree of bio-resorption, mechanical strength and bio-compatibility. Zinc improves the bone activity of osteoblast, promotes the bone regeneration and also stimulates enzyme activity. In the present study Zn doped calcium pyrophosphate dihydrate (Zn-CPPD) nanoparticles were synthesized using surfactant mediated approach with varying [Zn]/[Ca] molar ratio as 0% (pure CPPD), 2%, 5% and, 10%. The crystalline nature and the average crystallite size was studied by Powder XRD. Zinc doping was confirmed by EDAX. The TEM study indicated that pure and Zn doped CPPD nanoparticles were in the range from 4 nm to 40 nm. The presence of various bonds was confirmed by FT-IR spectroscopy. The amount of water of hydration and the thermal stability was studied by thermo-gravimetry. Formation of other phases on heating CPPD at C and C were identified by the powder XRD. Substitution of Zn content significantly affects the crystallinity and thermal stability of nanoparticles. The results are discussed.

Synthesis and characterization of pure and zinc doped calcium pyrophosphate dihydrate nanoparticles

The magnetism of Sm3Ag4Sn4 and Gd3Ag4Sn4

We review the complementary roles that 119Sn Mossbauer spectroscopy and neutron diffraction are playing in developing a complete description of magnetic ordering in the R3 Cu4Sn4 and R3Ag4Sn4 intermetallic compound series. We show that the two techniques yield consistent pictures of the order, and in many cases both are essential to obtaining a complete description. The recent neutron diffraction work on Sm3Cu4Sn4, Sm3Ag4Sn4 and Gd3Ag4Sn4 is highlighted.

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USING NEUTRON DIFFRACTION AND MÖSSBAUER SPECTROSCOPY TO STUDY MAGNETIC ORDERING IN THE R3T4Sn4 FAMILY OF COMPOUNDS

Natural gadolinium is the strongest neutron-absorbing element and neutron diffraction studies of Gd-containing materials rely on the use of either enriched Gd isotopes or short neutron wavelengths where the absorption is weaker but, unfortunately, the neutron flux is also weak. We have employed a new sample-mounting technique to obtain neutron powder diffraction patterns from the intermetallic compound Gd3Ag4Sn4 containing natural Gd, at a neutron wavelength of ∼ 2.37 ˚ A where there is much greater flux. Here, we report the magnetic structure of Gd3Ag4Sn4. The magnetic ordering temperature is 28.8(2) K. At 2.8 K the Gd(4e) sublattice is antiferromagnetically ordered along the crystal c-axis, commensurate with the crystal lattice. The Gd(2d) sublattice is also ordered along the c-axis but its magnetic structure is incommensurate with the crystal lattice. (Some figures in this article are in colour only in the electronic version)

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Neutron powder diffraction determination of the magnetic structure of Gd(3)Ag(4)Sn(4).

We have studied the complex magnetic ordering of the Dy sublattices in orthorhombic Dy3Ag4Sn4 by high-resolution neutron diffraction and 119 Sn Mossbauer spectroscopy. Magnetic ordering in this compound occurs over two transitions. At 16 K the Dy(2d) site orders in a doubled commensurate antiferromagnetic structure described by a propagation vector (0 1 0) ,w ith moments aligned along (100). The Dy(4e) site orders incommensurately with ap ropagation vector (0 0.628(1) 0) and moments in the (001) plane. Below the second transition at 14 K both Dy site ordering modes are commensurate antiferromagnetic with the propagation vector (0 1 0) and unchanged ordering directions. The 119 Sn Mossbauer spectra comprise thre em agnetically split sextets in the area ratio 50%:25%:25% due to transferred hyperfine fields at the 119 Sn nuclei from the surrounding magnetic Dy neighbours. This spectral decomposition deviates from the area ratio 50%:50% expected on the basis of the crystal structure and is in perfect agreement with the magnetic structure of Dy3Ag4Sn4 deduced from neutron diffraction data. (Some figures in this article are in colour only in the electronic version)

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Complex antiferromagnetic order in Dy3Ag4Sn4

Tb3Ag4Sn4 has been studied using both bulk magnetization and Sn119 Mossbauer spectroscopy We find evidence for a first-order magnetostructural transition at 28K, followed by a spin reorientation at 13K Three tin sites with hyperfine fields of 80, 42, and 35T are observed at 2K with area ratios of 2:1:1 Magnetization at 5K is linear up to 9T, indicating antiferromagnetic ordering

M. Napoletano

Papers

USING NEUTRON DIFFRACTION AND MÖSSBAUER SPECTROSCOPY TO STUDY MAGNETIC ORDERING IN THE R3T4Sn4 FAMILY OF COMPOUNDS

Neutron powder diffraction determination of the magnetic structure of Gd(3)Ag(4)Sn(4).

Complex antiferromagnetic order in Dy3Ag4Sn4

Complex magnetic ordering in Tb3Ag4Sn4

Magnetic properties of the new rare earth intermetallic compound Pr5AgSn3