The classical bond-pricing models, as important financial tools, show strong vitality in bond pricing. However, these models also expose their theoretical defects, which leads to inconsistencies with the actual observation results and usually causes prices of bonds be lower than market market. In order change this situation, considering that price underlying is regarded a fractal transmission system, derivative introduced into equation. solve equation, we first convert it an equivalent...

Fe-Zr-B-based amorphous alloys (AAs) show good magnetocaloric effect (MCE) around the ambient temperature, and their maximum magnetic entropy change ([Formula: see text] generally increases with Curie temperature text], which means poor properties near cold end of air conditioner. In this work, by adding 2% (at.%) Ti to replace Zr element in a [Formula: AA, we successfully fabricated ribbon. The ribbon exhibits slightly enhanced glass formability, improved decreased when compared AA. results...

This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the complex Sharma-Tasso-Olver (CSTO) hierarchy. Our main tools include polynomial recursive formalism derive CSTO hierarchy, hyper-elliptic curve with finite number genus, Baker-Akhiezer functions, meromorphic function, Dubrovin-type equations auxiliary divisors, associated trace formulas. By use these tools, explicit representations Baker-Ahhiezer are obtained entire

The coupled Chaffee-Infante reaction diffusion (CCIRD) hierarchy associated with a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mn>3</a:mn> <a:mo>×</a:mo> </a:math> matrix spectral problem is derived by using two sets of the Lenard recursion gradients. Based on characteristic polynomial Lax for CCIRD hierarchy, we introduce trigonal curve <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:msub> <c:mrow> <c:mi mathvariant="script">K</c:mi> </c:mrow>...

&lt;p&gt;In this work, we mainly focused on the pricing formula for fractal barrier options where underlying asset followed sub-mixed fractional Brownian motion with jump, including down-and-out call option, put down-and-in and so on. To start, Black-Scholes type partial differential equation was established by using Itô's a self-financing strategy. Then, transforming to Cauchy problem, obtained explicit formulae options. Finally, effects of price, dimension, Hurst index, jump intensity,...

Starting from a general isospectral problem of fractional order, we propose quadratic-form identity, which the Hamiltonian structure an integrable coupling Ablowitz-Kaup-Newell-Segur hierarchy is derived. The method can be generalized to other couplings.

In this paper a type of 9-dimensional vector loop algebra is constructed, which devoted to establish an isospectral problem. It follows that Liouville integrable coupling system the m-AKNS hierarchy obtained by employing Tu scheme, whose Hamiltonian structure worked out making use constructed quadratic identity. The method given in can be used obtain many other couplings and their structures.

By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave solution Harry presented. Furthermore, numerical solutions diffusion are discussed. Again, through another space-fractional turned into whose two also worked out.

We extend two known dynamical systems obtained by Blaszak, et al. via choosing Casimir functions and utilizing Novikov–Lax equation so that a series of novel including generalized Burgers system, heat equation, on, are followed to be generated. Then we expand some differential operators presented in the paper deduce types expanding models. By taking system as an example, deform its model get half-expanding whose recurrence operator is derived from Lax representation, Hamiltonian structure...

Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation Ut−Vx+[U,V] = 0, but this paper, a new hierarchy possessing bi-Hamiltonian structure is worked out selecting V with spectral potentials. Then its expanding Lax model the simple Hamiltonian operator presented constructing subalgebra loop algebra Ã2. As linear expansions above-mentioned and respect to their dimensional numbers, (2+1)-dimensional forms are derived from equation.

By using a Lie algebra A1, an isospectral Lax pair is introduced from which generalized Giachetti-Johnson hierarchy generated, reduce to the coupled KdV-MKdV equation, furthermore, algebro-geometric solutions of equation are constructed in terms Riemann theta functions.

This paper is dedicated to provide explicit theta function representation of algebro-geometric solutions for the generalized nonlinear Schrödinger hierarchy.Our main tools include zero-curvature equation derive hierarchy, hyper-elliptic curve with genus N , Abel-Jacobi coordinates, meromorphic function, Baker-Akhiezer functions, and Dubrovin-type equations auxiliary divisors.With help these tools, representations Baker-Ahhiezer are obtained whole hierarchy.

A fractional quadratic-form identity is derived from a general isospectral problem of order, which devoted to constructing the Hamiltonian structure an integrable coupling BK hierarchy. The method can be generalized other couplings.

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A (2+1) zero curvature equation is generated from one of the reduced equations self-dual Yang–Mills equations. As its applications, two (2+1)-dimensional integrable couplings famous KN hierarchy are obtained with help a subalgebra Lie R 9 , which can be to Burgers equation. Furthermore, their Hamiltonian structures worked out by taking use quadratic-form identity and variational identity, respectively.

Two different integrable couplings of the modified Tu hierarchy are obtained under zero curvature equation by using two higher dimension Lie algebras. Furthermore, a complex Hamiltonian structures second is presented taking use variational identity.

Some similarity solutions of the time-fractional stationary transonic plane-parallel gas flows (STPPGF) and their generalized space-fractional nonlinear system are obtained by using scalar transformations, including traveling-wave solutions. Two approximated solution formulas ordinary fractional differential equations for generated as well. Finally, a class STPPGF with initial-boundary-value conditions produced applying separated variable method.