Affine scaling algorithm fails for semidefinite programming

In this paper, we introduce an affine scaling algorithm for semidefinite programming (SDP), and give an example of a semidefinite program such that the affine scaling algorithm converges to a non-optimal point. Both our program and its dual have interior feasible solutions and unique optimal solutions which satisfy strict complementarity, and they are non-degenerate everywhere.     

Asymptotic stability for quasi-linear systems whose linear approximation is not assumed to be uniformly attractive

Sufficient conditions are obtained for uniform stability and asymptotic stability of the zero solution of two-dimensional quasi-linear systems under the assumption that the zero solution of linear approximation is not always uniformly attractive. A class of quasi-linear systems considered in this paper includes a planar system equivalent to the damped pendulum x′??+ h(t)x??+ sin x = 0, where h(t) is permitted to change sign. Some suitable examples are included to illustrate the main results.     

Intra-abdominal fat area is a predictor for new onset of individual components of metabolic syndrome: MEtabolic syndRome and abdominaL ObesiTy (MERLOT study)

Objective: To investigate the significance of intra-abdominal fat area (IAFA) on new onset of individual components of the metabolic syndrome: high blood pressure, dyslipidemia, or hyperglycemia. Methods: We conducted a longitudinal study using checkup data of a hospital from 1994 to 2010. Of 25,255 subjects, we examined 1,380 Japanese, who underwent computed tomography to measure IAFA and had no metabolic syndrome components at baseline. Results: During 3.6 years of the mean follow-up period, one of metabolic syndrome components occurred in 752 subjects. Of three components, high blood pressure was more prevalent. The multiple Cox regression analysis disclosed that IAFA is significantly associated with onset of metabolic syndrome components (HR: 1.05 per 10 cm², 95%CI: 1.03–1.07). This finding was independent of BMI, and significant even in non-obese individuals with body mass index <25 kg/m². Conclusions: MERLOT study demonstrates that IAFA is an independent predictor for new onset of individual components of the metabolic syndrome, even in non-obese healthy Japanese.     

Magnetization reversal in a preferred oriented (111) L1(0) FePt grown on a soft magnetic metallic glass for tilted magnetic recording

L1(0) FePt is an important material for the fabrication of high density perpendicular recording media, but the ultrahigh coercivity of L1(0) FePt restricts its use. Tilting of the magnetic easy axis and the introduction of a soft magnetic underlayer can solve this problem. However, high temperature processing and the requirement of epitaxial growth conditions for obtaining an L1(0) FePt phase are the main hurdles to be overcome. Here, we introduce a bilayered magnetic structure ((111) L1(0) FePt/glassy Fe(71)Nb(4)Hf(3)Y(2)B(20)/SiO(2)/Si) in which the magnetic easy axis of L1(0) FePt is tilted by ~36° from the film plane and epitaxial growth conditions are not required. The soft magnetic underlayer not only promotes the growth of L1(0) FePt with the preferred orientation but also provides an easy cost-effective micro/nanopatterning of recording bits. A detailed magnetic characterization of the bilayered structure in which the thickness of (111) L1(0) FePt with the soft magnetic Fe(71)Nb(4)Hf(3)Y(2)B(20) glassy underlayer varied from 5 to 60 nm is carried out in an effort to understand the magnetization switching mechanism. The magnetization switching behavior is almost the same for bilayered structures in which FePt layer thickness is >10 nm (greater than the domain wall thickness of FePt). For FePt film ~10 nm thick, magnetization reversal takes place in a very narrow field range. Magnetization reversal first takes place in the soft magnetic underlayer. On further increase in the reverse magnetic field, the domain wall in the soft magnetic layer compresses at the interface of the hard and soft layers. Once the domain wall energy becomes sufficiently large to overcome the nucleation energy of the domain wall in L1(0) FePt, the magnetization of the whole bilayer is reversed. This process takes place quickly because the domain walls in the hard layer do not need to move, and the formation of a narrower domain wall may not be favorable energetically. Our results showed that the present bilayered structure is very promising for the fabrication of tilted bit-patterned magnetic recording media.     

Induction in linear logic

Linear logic, introduced by Girardet al., has a great power of expression, but no method for induction. This paper proposes a method of induction using knowledge represented by linear logical formulas. In linear logic, the number of propositions is controlled by logical operators. When a background theory and a hypothesis prove an example, the number of propositions on each side must be equivalent.     

Organic high-spin systems: Synthesis,electrochemical and spectroscopic studies of π-extended tetraaryl m-phenylenediamines

Three highly π-extended tetraaryl-1,3-phenylenediamines for charged high-spin molecular systems were successfully synthesized using Suzuki coupling. Their electrochemical and spectroscopic properties were also examined. They showed blue fluorescence. The dications derived from highly π-extended tetraaryl-1,3-phenylenediamines were generated and characterized by electron transfer stopped-flow method.     

Toroidal surgeries on hyperbolic knots

For a hyperbolic knot in , a toroidal surgery is Dehn surgery which yields a -manifold containing an incompressible torus. It is known that a toroidal surgery on is an integer or a half-integer. In this paper, we prove that all integers occur among the toroidal slopes of hyperbolic knots with bridge index at most three and tunnel number one.

     

Supramolecular graphyne: a C(sp)-H...N hydrogen-bonded unique network structure of 2,4,6-triethynyl-1,3,5-triazine

The crystallization of 2,4,6-triethynyl-1,3,5-triazine (2) leads to a pi-stacked layered structure of a C(sp)-H...N hydrogen-bonded unique hexagonal network structure, which may be regarded as a supramolecular analogue of a hitherto unknown graphyne network: in-plane intermolecular interactions are short and linear H...N contacts (2.31 and 2.34 A) and the interlayer separation is 3.23 A.