The hysteresis loops of FM/AFM two-layer Bethe lattice

The distinct hysteresis loops (HLs) of ferromagnetic/antiferromagnetic (FM/AFM) two-layer Bethe lattice with the Ising spins of the top layer having only FM interactions and the bottom ones having only AFM interactions with the interlayer coupling is either FM or AFM type are studied by using a pairwise approach. The sublattice magnetizations are studied by increasing and decreasing the external magnetic field (H) to obtain the HLs. The shapes of the HLs are strongly dependent on the competitions among the system parameters and on the phase configurations. The HLs are formed only when the AFM-type interactions are involved. The small loops of hysteresis are also formed because of the reentrant behavior in the FM region.     

Spin-1 Blume-Capel model with longitudinal random crystal and transverse magnetic fields：A mean-field approach

The spin-1 Blume-Capel model with transverse and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the crystal field is either turned on with probability p or turned off with probability 1 p on the sites of a square lattice. Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ=Ω/J and p at zero h. Thus, the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.     

Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Brownian motion, and can be numerically computed using the classical finite difference methods. We prove the convergence of this numerical scheme and present examples to illustrate its performance.     

Lubricant properties of Moringa oil using thermal and tribological techniques

The increasing application of biobased lubricants could significantly reduce environmental pollution and contribute to the replacement of petroleum base oils. Vegetable oils are recognized as rapidly biodegradable and are thus promising candidates for use as base fluids in formulation of environment friendly lubricants. Although many vegetable oils have excellent lubricity, they often have poor oxidation and low temperature stability. Here in, we report the lubricant potential of Moringa oil, which has 74% oleic acid content and thus possess improved oxidation stability over many other natural oils. For comparison, Jatropha oil, cottonseed oil, canola oil and sunflower oil were also studied. Among these oils, Moringa oil exhibits the highest thermo-oxidative stability measured using PDSC and TG. Canola oil demonstrated superior low temperature stability as measured using cryogenic DSC, pour point and cloud point measurements. The friction and wear properties were measured using HFRR. Overall, it was concluded that Moringa oil has potential in formulation of industrial fluids for high temperature applications. Names are necessary to report factually on available data; however, the USDA neither guarantees nor warrants the standard of the product, and the use of the name by USDA implies no approval of the product to the exclusion of others that may also be suitable.     

A Lagrangian relaxation approach to large-scale flow interception problems

The paper presents a tight Lagrangian bound and an efficient dual heuristic for the flow interception problem. The proposed Lagrangian relaxation decomposes the problem into two subproblems that are easy to solve. Information from one of the subproblems is used within a dual heuristic to construct feasible solutions and is used to generate valid cuts that strengthen the relaxation. Both the heuristic and the relaxation are integrated into a cutting plane method where the Lagrangian bound is calculated using a subgradient algorithm. In the course of the algorithm, a valid cut is added and integrated efficiently in the second subproblem and is updated whenever the heuristic solution improves. The algorithm is tested on randomly generated test problems with up to 500 vertices, 12,483 paths, and 43 facilities. The algorithm finds a proven optimal solution in more than 75% of the cases, while the feasible solution is on average within 0.06% from the upper bound.     

On the Continuity of Stochastic Exit Time Control Problems

We determine a weaker sufficient condition than that of Theorem 5.2.1 in Fleming and Soner (2006) for the continuity of the value functions of stochastic exit time control problems.     

Synthesis of a series of triple-bridged cyclotriphosphazene hexa-alkoxy derivatives and investigation of their structural and mesomorphic properties

Triple diamino-bridged cyclotriphosphazene (1) was reacted in a 1:8 stoichiometry with the sodium derivatives of long-chain diols [1-octanol, 1-decanol, 1-dodecanol, 1-hexadecanol] tetrahydrofuran (THF) at room temperature to form hexa-substituted cyclotriphosphazene derivatives (2, 3, 4 and 5, respectively), whose mesomorphic behaviours were investigated for their possible applications as liquid crystals. The cylindrical-type cyclotriphosphazene derivatives (2–5) were characterised by mass and elemental analyses and by Fourier transform infrared spectroscopy (FT-IR), ¹H and ³¹P {¹H} NMR spectroscopies. The thermal and mesomorphic properties were investigated by differential scanning calorimetry and by polarising optical microscopy, respectively. It was found that liquid crystal materials could be obtained from compounds 3 and 4 with alkoxy chains rather than using aromatic ring(s) as mesogens as published previously.     

Some general univalence criteria for a family of integral operators

The main object of the present paper is to discuss some extensions of univalence conditions for a family of integral operators. Several other closely-related results are also considered. Many known univalence conditions are shown to follow upon specializing the parameters involved in our main results.     

A theory of high frequency vibrations of piezoelectric cyrstal bars

This paper presents a higher order, linear theory of piezoelectric crystal bars as in the same spirit as that of Mindlin. First, a power series representation in aerial coordinates is employed for both the mechanical displacement and electric potential fields. Next, with the help of a variational theorem deduced from Hamilton's principle, together with these series, the theory is established consistently. A hierarchy of 1-dimensional approximate equations of motion, charge equations of electrostatics, initial and boundary conditions, strain-displacement and electric field-electric potential relations, and macroscopic constitutive equations constitutes the theory, and it governs all the types of motions of piezoelectric crystal bars of uniform cross-section. Further, special cases of interest are pointed out. The solutions of the initial mixed boundary-value problems defined by this theory are proven to be unique.