Using Lie’s classical method of group invariants, new solutions are found for the valuation of zero-coupon bonds. In finding the solutions, the model for the underlying short-term interest rate assumes a realistic time-dependent, mean-reverting drift form and a power-law volatility.

We obtain iso-spectral Euler-Bernoulli beams by using factorization and Lie symmetry techniques. The canonical Euler-Bernoulli beam operator is factorized as the product of a second-order linear differential operator and its adjoint. The factors are then reversed to obtain iso-spectral beams. The factorization is possible provided the coefficients of the factors satisfy a system of non-linear o...

Abstract. We investigate symmetry reduction of optimal control problems for left-invariant control systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a discrete-time setting as well as the standard continuous-time formulation. Specifically, we recast the optimal control problem as a constrained variation...

In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior in the Golden Gate Bridge in San Francisco. We perform a complete Lie symmetry group classification by using the equivalence transformation group ...

Abbreviations CT: Coordinate transformation FIR: Finite impulse response HFP: Harmonic function pair ILS: Innnitesimal linear symmetry GHT: Generalized Hough transform GLS: Generalized linear symmetry SNR: Signal to noise ratio 1 Abstract A theory for detecting general curve families by means of symmetry measurements in the coordinate transformed originals is presented. Symmetries are modeled b...

Lie Group Action. A process by which a Lie group, acting as a symmetry, moves points in a space. When points in the space that are related by a group element are identified, one obtains the quotient space. Free Action. An action that moves every point under any nontrivial group element. Proper Action. An action that obeys a compactness condition. Momentum Mapping. A dynamically conserved quanti...

We develop algebraic methods for finding loop corrections to the N = 4 SYM dilatation generator, within the noncompact psu(1, 1|2) sector. This sector gives a ’t Hooft coupling λ-dependent representation of psu(1, 1|2)× psu(1|1)2. At first working independently of the representation, we present an all-order algebraic ansatz for the λ-dependence of this Lie algebra’s generators. The ansatz solve...

: Singular systems play an important role in many fields, and some new fractional operators, which are general, have been proposed recently. Therefore, singular on the basis of mixed derivatives including integer order derivative generalized operators studied. Firstly, Lagrange equations within established, primary constraints presented for systems. Then constrained Hamilton constructed by intr...