On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation

AbstractIn this paper, we investigate some new nonlinear retarded integral inequalities of Gronwall–Bellman–Pachpatte type. These inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlinear retarded differential and integral equations. An application is also presented to illustrate the usefulness of some of our results in estimation of solution of certain retarded nonlinear differential equations with the initial conditions

The magnetic anisotropy of spin S=1 BaMoP2O8 system

In this work the magnetic anisotropy of low dimensional magnetic compound BaMoP2O8 was studied by using density functional theory and inelastic neutron scattering techniques. Obtained results show that anisotropy of the system has the easy-axis character, where the on-site term plays the leading role in stabilisation of the magnetic ordering.The reported study was funded by RFBR according to the research project № 18-32-00018

Realizing square and diamond lattice S =1/2 Heisenberg antiferromagnet models in the α and β phases of the coordination framework, KTi(C2O4)2⋅xH2O

Provision of a PhD studentship to A.H.A. by the University of Liverpool and the Science and Technology Facilities Council (STFC) is gratefully acknowledged. The work of T.L. was funded by the University of St Andrews and China Scholarship Council (CSC) joint scholarship (201606280032). A.T. was funded by the Federal Ministry of Education and Research through the Sofja Kovalevskaya Award of Alexander von Humboldt Foundation. Work at St Andrews was supported by the Leverhulme Trust (RPG-2013-343).We report the crystal structures and magnetic properties of two pseudopolymorphs of the S=1/2 Ti3+ coordination framework, KTi(C2O4)2⋅xH2O. Single-crystal x-ray and powder neutron diffraction measurements on α−KTi(C2O4)2⋅xH2O confirm its structure in the tetragonal I4/mcm space group with a square planar arrangement of Ti3+ ions. Magnetometry and specific heat measurements reveal weak antiferromagnetic interactions, with J1≈7 K and J2/J1=0.11 indicating a slight frustration of nearest- and next-nearest-neighbor interactions. Below 1.8 K, α−KTi(C2O4)2⋅xH2O undergoes a transition to G-type antiferromagnetic order with magnetic moments aligned along the c axis of the tetragonal structure. The estimated ordered moment of Ti3+ in α−KTi(C2O4)2⋅xH2O is suppressed from its spin-only value to 0.62(3) μB, thus verifying the two-dimensional nature of the magnetic interactions within the system. β−KTi(C2O4)2⋅2H2O, on the other hand, realizes a three-dimensional diamondlike magnetic network of Ti3+ moments within a hexagonal P6222 structure. An antiferromagnetic exchange coupling of J≈54 K—an order of magnitude larger than in α−KTi(C2O4)2⋅xH2O—is extracted from magnetometry and specific heat data. β−KTi(C2O4)2⋅2H2O undergoes Néel ordering at TN=28 K, with the magnetic moments aligned within the ab plane and a slightly reduced ordered moment of 0.79 μB per Ti3+. Through density-functional theory calculations, we address the origin of the large difference in the exchange parameters between the α and β pseudopolymorphs. Given their observed magnetic behaviors, we propose α−KTi(C2O4)2⋅xH2O and β−KTi(C2O4)2⋅2H2O as close to ideal model S =1/2 Heisenberg square and diamond lattice antiferromagnets, respectively.PostprintPeer reviewe

Large easy-axis anisotropy in the one-dimensional magnet BaMo(PO4)(2)

We present an extensive experimental and theoretical study on the low-temperature magnetic properties of the monoclinic anhydrous alum compound BaMo(PO4)(2). The magnetic susceptibility reveals strong antiferromagnetic interactions theta(CW) = -167 K and long-range magnetic order at T-N = 22 K, in agreement with a recent report. Powder neutron diffraction furthermore shows that the order is collinear, with the moments near the ac plane. Neutron spectroscopy reveals a large excitation gap Delta = 15 meV in the low-temperature ordered phase, suggesting a much larger easy-axis spin anisotropy than anticipated. However, the large anisotropy justifies the relatively high ordered moment, Neel temperature, and collinear order observed experimentally and is furthermore reproduced in a first-principles calculations by using a new computational scheme. We therefore propose BaMo(PO4)(2) to host S = 1 antiferromagnetic chains with large easy-axis anisotropy, which has been theoretically predicted to realize novel excitation continua

Realizing Square and Diamond Lattice S=1/2 Heisenberg Antiferromagnet Models in the α and β Phases of the Coordination Framework, KTi(C2 O4)2·x H2O

We report the crystal structures and magnetic properties of two pseudopolymorphs of the S=1/2 Ti3+ coordination framework, KTi(C2O4)2·xH2O. Single-crystal x-ray and powder neutron diffraction measurements on α-KTi(C2O4)2·xH2O confirm its structure in the tetragonal I4/mcm space group with a square planar arrangement of Ti3+ ions. Magnetometry and specific heat measurements reveal weak antiferromagnetic interactions, with J1≈7 K and J2/J1=0.11 indicating a slight frustration of nearest- and next-nearest-neighbor interactions. Below 1.8 K, α-KTi(C2O4)2·xH2O undergoes a transition to G-type antiferromagnetic order with magnetic moments aligned along the c axis of the tetragonal structure. The estimated ordered moment of Ti3+ in α-KTi(C2O4)2·xH2O is suppressed from its spin-only value to 0.62(3)μB, thus verifying the two-dimensional nature of the magnetic interactions within the system. β-KTi(C2O4)2·2H2O, on the other hand, realizes a three-dimensional diamondlike magnetic network of Ti3+ moments within a hexagonal P6222 structure. An antiferromagnetic exchange coupling of J≈54 K - an order of magnitude larger than in α-KTi(C2O4)2·xH2O - is extracted from magnetometry and specific heat data. β-KTi(C2O4)2·2H2O undergoes Néel ordering at TN=28 K, with the magnetic moments aligned within the ab plane and a slightly reduced ordered moment of 0.79μB per Ti3+. Through density-functional theory calculations, we address the origin of the large difference in the exchange parameters between the α and β pseudopolymorphs. Given their observed magnetic behaviors, we propose α-KTi(C2O4)2·xH2O and β-KTi(C2O4)2·2H2O as close to ideal model S=1/2 Heisenberg square and diamond lattice antiferromagnets, respectively. © 2020 American Physical Society.Provision of a Ph.D. studentship to A.H.A. by the University of Liverpool and the Science and Technology Facilities Council (STFC) is gratefully acknowledged. The work of T.L. was funded by the University of St Andrews and China Scholarship Council (CSC) joint scholarship (201606280032). A.T. was funded by the Federal Ministry of Education and Research through the Sofja Kovalevskaya Award of Alexander von Humboldt Foundation. Work at St Andrews was supported by the Leverhulme Trust (RPG-2013-343). The authors are also grateful to the STFC for access to neutron beamtime at ISIS and thank Dr. Gavin Stenning for aiding with SQUID and specific heat measurements at the Materials Characterization Laboratory, ISIS. We thank Dr. Manh Duc Le (ISIS), Dr. Ross Stewart (ISIS), Dr. Craig Robertson (Uni. Liverpool), Dr. Samantha Chong (Uni. Liverpool), and Dr. Hamish Yeung (Uni. Birmingham) for useful discussions

The development of a 16S rRNA gene based PCR for the identification of Streptococcus pneumoniae and comparison with four other species specific PCR assays

<p>Abstract</p> <p>Background</p> <p><it>Streptococcus pneumoniae </it>is one of the most frequently encountered pathogens in humans but its differentiation from closely related but less pathogenic streptococci remains a challenge.</p> <p>Methods</p> <p>This report describes a newly-developed PCR assay (Spne-PCR), amplifying a 217 bp product of the 16S rRNA gene of <it>S. pneumoniae</it>, and its performance compared to other genotypic and phenotypic tests.</p> <p>Results</p> <p>The new PCR assay designed in this study, proved to be specific at 57°C for <it>S. pneumoniae</it>, not amplifying <it>S. pseudopneumoniae </it>or any other streptococcal strain or any strains from other upper airway pathogenic species. PCR assays (psaA, LytA, ply, spn9802-PCR) were previously described for the specific amplification of <it>S. pneumoniae</it>, but <it>psaA</it>-PCR was the only one found not to cross-react with <it>S. pseudopneumoniae</it>.</p> <p>Conclusion</p> <p>Spne-PCR, developed for this study, and psaA-PCR were the only two assays which did not mis-identify <it>S. pseudopneumoniae </it>as <it>S. pneumoniae</it>. Four other PCR assays and the AccuProbe assay were unable to distinguish between these species.</p

Molecular Surveillance of True Nontypeable Haemophilus influenzae: An Evaluation of PCR Screening Assays

BackgroundUnambiguous identification of nontypeable Haemophilus influenzae (NTHi) is not possible by conventional microbiology. Molecular characterisation of phenotypically defined NTHi isolates suggests that up to 40% are Haemophilus haemolyticus (Hh); however, the genetic similarity of NTHi and Hh limits the power of simple molecular techniques such as PCR for species discrimination.Methodology/Principal FindingsHere we assess the ability of previously published and novel PCR-based assays to identify true NTHi. Sixty phenotypic NTHi isolates, classified by a dual 16S rRNA gene PCR algorithm as NTHi (n = 22), Hh (n = 27) or equivocal (n = 11), were further characterised by sequencing of the 16S rRNA and recA genes then interrogated by PCR-based assays targeting the omp P2, omp P6, lgtC, hpd, 16S rRNA, fucK and iga genes. The sequencing data and PCR results were used to define NTHi for this study. Two hpd real time PCR assays (hpd#1 and hpd#3) and the conventional iga PCR assay were equally efficient at differentiating study-defined NTHi from Hh, each with a receiver operator characteristic curve area of 0.90 [0.83; 0.98]. The hpd#1 and hpd#3 assays were completely specific against a panel of common respiratory bacteria, unlike the iga PCR, and the hpd#3 assay was able to detect below 10 copies per reaction.Conclusions/SignificanceOur data suggest an evolutionary continuum between NTHi and Hh and therefore no single gene target could completely differentiate NTHi from Hh. The hpd#3 real time PCR assay proved to be the superior method for discrimination of NTHi from closely related Haemophilus species with the added potential for quantification of H. influenzae directly from specimens. We suggest the hpd#3 assay would be suitable for routine NTHi surveillance and to assess the impact of antibiotics and vaccines, on H. influenzae carriage rates, carriage density, and disease