Arbitrary Terms Research Articles

THE ENTROPY THEORY OF BOND OPTION PRICING

An informationally efficient price keeps investors as a group in the state of maximum uncertainty about the next price change. The Entropy Pricing Theory (EPT) captures this intuition and suggests that, in informationally efficient markets, perfectly uncertain market beliefs must prevail. When the entropy functional is used to index collective market uncertainty, then the entropy-maximizing consensus beliefs must prevail. The EPT resolves the ambiguity of arbitrage-free valuation in incomplete markets. The EPT produces a new bond option model that is similar to Black–Scholes' with the lognormal distribution replaced by a beta distribution. Unlike alternative models, the beta model is valid for arbitrary term structure dynamics and for arbitrary credit risk of the underlying bonds. Option replication and hedging under the beta model accounts for random changes in the underlying bond price, price volatility and short-term interest rates.

Conserved currents, superpotentials and cosmological perturbations

Conserved currents, superpotentials and cosmological perturbations

Potential Identification by Inverse Scattering Theory

In the context of JWKB (Jeffreys, Wentzel, Kramers, and Brillouin) approximation, we use inverse scattering theory to modify the forbidden region by introducing an arbitrary term in the analytical expression of the potential ν(r) in the case of He-Na elastic scattering given as an example.

Magnetic exchange interaction in clusters of orbitally degenerate ions. I. Effective Hamiltonian

A new effective Hamiltonian is reported for the kinetic exchange between two arbitrary terms 2S A+1 Λ A and 2S B+1 Λ B that can be ground or excited in octahedrally coordinated transition metal ions. This Hamiltonian is applicable to both homo- and heterometallic clusters. For the homonuclear cluster the resonance part of the effective Hamiltonian is also presented for the case when one of the ions is excited. The operator part of the exchange Hamiltonian contains symmetry adapted products of the cubic irreducible tensors acting in orbital spaces Λ A and Λ B and scalar product of site spin operators. The parameters of the Hamiltonian are defined by the relevant intercenter transfer integrals and the fundamental intracenter interactions, namely, crystal field and Racah parameters for the constituent metal ions in their ground, oxidized and reduced electronic configurations. These parameters contain also the reduced matrix elements of the creation (annihilation) operators linking the ground state of the many-electron ions with their reduced and oxidized states (fractional parentage coefficients), W-symbols and 6 j-symbols. The approach is discussed in context of the existing exchange models.

Preface

The ability to simulate one Hamiltonian with another is an important primitive in quantum information processing. In this paper, a simulation method for arbitrary $\sigma_z \otimes \sigma_z$ interaction based on Hadamard matrices (quant-ph/9904100) is generalized for any pairwise interaction. We describe two applications of the generalized framework. First, we obtain a class of protocols for selecting an arbitrary interaction term in an n-qubit Hamiltonian. This class includes the scheme given in quant-ph/0106064v2. Second, we obtain a class of protocols for inverting an arbitrary, possibly unknown n-qubit Hamiltonian, generalizing the result in quant-ph/0106085v1.

A remarkable class of second order differential operators on the Heisenberg group ${\mathbb H}_2$

Let L be a differential operator on \({\mathbb R}^5\) whose principal part is of the form \(\!\sum_{\!j,k=1}^2\! \alpha_{jk}\! X_j Y_k\), where \(X_j=\partial_{x_j}\) and \(Y_j=\partial_{y_j}+x_j\partial_u , j=1,2\), are the usual vector fields generating the Lie algebra of the Heisenberg group \({\mathbb H}_2\). We study the problem of local solvability of these doubly characteristic operators. The whole class of operators splits into three subclasses, depending on the sign of a respective determinant. The operators in the first subclass, when the determinant is negative, are generically non-solvable. The operators in the second subclass, when the determinant is positive, are solvable, for arbitrary left-invariant lower order terms, provided that the coefficient matrix \((\alpha_{j,k})\) is non-degenerate. This fact seems remarkable, since many of these operators have the property that the values taken by their principal symbol are not contained in any proper subcone of the complex plane. Under suitable conditions, solvability even holds in the presence of non-invariant lower order terms.

Chiral anomaly andCPTinvariance in an implicit momentum space regularization framework

This is the second in a series of two contributions in which we set out to establish a novel momentum space framework to treat field theoretical infinities in perturbative calculations when parity-violating objects occur. Since no analytic continuation on the space-time dimension is effected, this framework can be particularly useful to treat dimension-specific theories. Moreover arbitrary local terms stemming from the underlying infinities of the model can be properly parametrized. We (re)analyse the undeterminacy of the radiatively generated CPT violating Chern-Simons term within an extended version of $QED_4$ and calculate the Adler-Bardeen-Bell-Jackiw triangle anomaly to show that our framework is consistent and general to handle the subtleties involved when a radiative corretion is finite.

New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams

For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the epsilon-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the epsilon-expansion can be calculated. For more complicated cases, only a few higher terms in epsilon are obtained. Apart from the one-loop two- and three-point diagrams, the examples include two-loop (mainly on-shell) propagator-type diagrams and three-loop vacuum diagrams. As a by-product, some new relations involving Clausen function, generalized log-sine integrals and certain Euler--Zagier sums are established, and some useful results for the hypergeometric functions of argument 1/4 are presented.

Merostachys Spreng. (Poaceae, Bambusoideae, Bambuseae): A New Species from Brazil and Critical Notes on "Group Speciosa"

Summary. Merostachys brevigluma, a new species from Brazil and the related species M. speciosa Spreng., M. neesii Rupr., and M. kunthii Rupr. are described, illustrated, compared and discussed. Sprengel (1825) described the species Merostachys speciosa; five years later Kunth (1830) took up Sprengel's name of which he said, "Although I have not seen Sprengel's plant I am sure that it is identical with one I have before me, which was sent to me by Beyrich". However, the specimen on which Kunth based his description of M. speciosa, although very similar to Sprengel's M. speciosa, was a different plant. According to Beyrich who collected it, the specimen came from a plant with the habit of Bambusa, and reached a height of 20 - 30 ft. Ruprecht (1839) recognised that the Beyrich collection was different from Sprengel's description of M. speciosa and described it as a new species, M. kunthii. A similar situation arose with Nees (1829), who took up Sprengel's name for an unidentified collection at Berlin. Once again, Ruprecht (1839) decided that this was not the same as Sprengel's plant, and described it as another new species, M. neesii. These were the initial steps in a series of misinterpretations centred around these three names. We have three species, M. speciosa Spreng., M. kunthii Rupr. and M. neesii Rupr. and the confusion over their taxonomy has persisted. These species were described and redescribed under different names. The use of imprecise and arbitrary terms such as 'ligule', 'numerous rootlets', 'cilia of the ligule', 'herbaceous beard' and 'cirrhose-ciliate ligule' for the oral setae, and 'crassitie pennae gallinaceae' and 'crassite pennae columbineae' for branch thickness, no doubt did much to create the mutual hostility which can be seen in their published polemics. Moreover, Nees (1829) mentioned in Note III (p. 531) the existence of another specimen in the Berlin Herbarium, collected by Sellow in Paraguay, at the summit of the mountain called Cabo do Butucaray. He wrote that "it was similar to this" and "that it could be a juvenile state of it (though it lacks flowers); it differs, however, in the culms being still rougher, the leaf sheaths herbaceously bearded at the mouth, the leaves glaucescent and very serrulate-scabrous on the margin". The species Nees quoted as "this", McClure (unpublished translations and notes on Merostachys) determined as M. speciosa Spreng. and says in his notes: "The reason why the plant

Codimension-onepersistence beyond all orders of homoclinic orbits to singularsaddle centres in reversible systems

The persistence from a singular limit is studied ofhomoclinic orbits to a saddle-centre equilibrium infour-dimensional reversible vector fields.The linearization is assumed tohave eigenvalues ±iω, ±λ, λ,ω>0,with the singular limit being λ→0.Recent work by Lombardi has shown the generic non-persistence of such homoclinic solutions under perturbations thatbreak the integrability of a normal form due to a splitting term(Melnikov function) that is exponentially small in λ/ω.A plausible argument is presented which extends Lombardi's analysisto suggest persistence in a codimension-one sense. Specifically,keeping nonlinear terms fixed but treating λ and ω asindependent parameters, then, under the correct sign of anormal-form coefficient b2, each term in the calculablepart of the Melnikov function has a countable sequence of signchanges as a function ofω. This calculable part of the Melnikov function is only theleading-order term under an additional assumption of closenessto integrability. In that case, a zero of this functionimplies anω-value at which a curve of homoclinic orbits bifurcates fromλ = 0 in the parameter plane. The large-ω asymptotics ofthis sequence of bifurcation points is determined solely by the valueof b2.This heuristic result is supported by careful numerical experiments ona class of fourth-order reversible equations with arbitrary quadraticnonlinear terms. The implications of the results are discussed for solitarywater waves of elevation in the presence of surface tension and forrecently discovered embedded solitons in a variety of(non-integrable) nonlinear optical models.

Quantum computation using decoherence-free states of the physical operator algebra

The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction Hamiltonian, and the system Hamiltonian is the sum of arbitrary terms either commuting with or belonging to the physical algebra, then its states are decoherence free. One of the considered examples shows that, for a uniform collective coupling to the environment, the smallest number of physical qubits encoding a decoherence free logical qubit is reduced from four to three.

A Complete Categorization of When Generalized Tribonacci Sequences Can Be Avoided by Additive Partitions

A set or sequence $U$ in the natural numbers is defined to be avoidable if ${\bf N}$ can be partitioned into two sets $A$ and $B$ such that no element of $U$ is the sum of two distinct elements of $A$ or of two distinct elements of $B$. In 1980, Hoggatt [5] studied the Tribonacci sequence $T=\{t_n\}$ where $t_1=1$, $t_2=1$, $t_3=2$, and $t_n=t_{n-1}+t_{n-2}+t_{n-3}$ for $n\ge 4$, and showed that it was avoidable. Dumitriu [3] continued this research, investigating Tribonacci sequences with arbitrary initial terms, and achieving partial results. In this paper we give a complete answer to the question of when a generalized Tribonacci sequence is avoidable.

M-solid varieties generated by lattices

Following W. Taylor, we define an identity $ \varepsilon $ to be hypersatisfied by a variety V iff, whenever the operation symbols of V are replaced by arbitrary terms (of appropriate arity) in the operations of V, then the resulting identity is satisfied by V in the usual sense. Whenever the identity $ \varepsilon $ is hypersatisfied by a variety V, we shall say that $ \varepsilon $ is a hyperidentity of V, or a V hyperidentity. When the terms being substituted are restricted to a submonoid M of all the possible choices, $ \varepsilon $ is called an M-hyperidentity, and a variety V is M-solid if each identity is an M-hyperidentity. In this paper we examine the solid varieties whose identities are lattice M-hyperidentities. The M-solid varieties generated by the variety of lattices in this way provide new insight on the construction and representation of various known classes of non-commutative lattices.

Some remarks on the ϵ-expansion of dimensionally regulated Feynman diagrams

Some problems related to the construction of the ϵ-expansion of dimensionally regulated Feynman integrals are discussed. For certain classes of diagrams, an arbitrary term of the ϵ-expansion can be expressed in terms of log-sine integrals related to the polylogarithms. It is shown how the analytic continuation of these functions can be constructed in terms of the generalized Nielsen polylogarithms.

Invariants, Patterns and Weights for Ordering Terms

We prove that any simplification order over arbitrary terms is an extension of an order by weight, by considering a related monadic term algebra called the spine. We show that any total ground-stable simplification order on the spine lifts to an order on the full term algebra. Conversely, under certain restrictions, a simplification ordering on the term algebra defines a weight function on the spine, which in turn can be lifted to a weight order on the original ground terms which contains the original order. We investigate the Knuth–Bendix and polynomial orders in this light. We provide a general framework for ordering terms by counting embedded patterns, which gives rise to many new orderings. We examine the recursive path order in this context.

Simplicial minisuperspace models in the presence of a massive scalar field with arbitrary scalar coupling R2

We consider a simplicial minisuperspace model based on a cone over the 4 triangulation of the 3-sphere, in the presence of a massive scalar field, , with arbitrary scalar coupling term R2. By restricting all the interior edge lengths and all the boundary edge lengths to be equivalent and the scalar field to be homogeneous on the 3-space, we obtain a two-dimensional minisuperspace model {si,i} for what is one of the most relevant triangulations of the spatial universe. We solve the two classical equations and find that there are both real Euclidean and Lorentzian classical solutions for any size of the boundary 3-space, 4. After studying the analytic properties of the action in the space of complex edge lengths we then obtain steepest descents contours of constant imaginary action passing through Lorentzian classical geometries giving the dominant contribution and yielding a convergent wavefunction of the universe. We also show that the semi-classical wavefunctions for the Euclidean solutions associated with large boundary 3-spaces are exponentially suppressed.

Explicit results for all orders of theɛexpansion of certain massive and massless diagrams

An arbitrary term of the $\ensuremath{\varepsilon}$ expansion of a dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using a magic connection between these diagrams and two-loop massive vacuum diagrams, the $\ensuremath{\varepsilon}$ expansion of the latter is also obtained, for arbitrary values of the masses. The problem of analytic continuation is also discussed.

A Hyperbase for Binary Lattice Hyperidentities

We define an identity e to be i>hypersatisfied by a variety V if, whenever the operation symbols of V, are replaced by arbitrary terms (of appropriate arity) in the operations of V, the resulting identity is satisfied by V in the usual sense. Whenever the identity e is hypersatisfied by a variety V, we shall say that e is a i>V hyperidentity. For example, the identity i>x + i>x ⋅ i>y e i>x ⋅(i>x + i>y) is hypersatisfied by the variety L of all lattices. A proof of this consists of a case-by-case examination of { + , ⋅} ⊆{i>x, i>y, i>x ∨ i>y, i>x ∧ i>y}, the set of all binary lattice terms. In an earlier work, we exhibited a hyperbase Σi>L for the set of all binary lattice (or, equivalently, quasilattice) hyperidentities of type 〈2, 2, …〉. In this paper we provide a greatly refined hyperbase Σi>L. The proof that Σi>L is a hyperbase was obtained by using the automated reasoning program Otter 3.0.4.

The Cauchy stress tensor for a material subject to an isotropic internal constraint

The Cauchy stress tensor, T_ij, is considered for an elastic material which is subject to any internal isotropic constraint, apart from the constraint of incompressibility. For a given strain, it is seen that if in a given basis one of the eigenvectors of the stress tensor has a zero component, say the αth component, and if the arbitrary scalar term in the stress may be chosen so that T_αβ(α≠β) shear stress component is zero, then the stress tensor has a double eigenvalue. This means that there is a great simplification in the stress field. The given strain may be maintained experimentally by a simple tension superimposed upon a hydrostatic stress field. Examples are presented for Bell-constrained and Ericksen-constrained materials.

A FULLY COUPLED THERMO-MECHANICAL MICROMECHANICS MODEL

The development for a micromechanical model with full thermomechanical coupling, which is based on the combined effects of the mechanical and energy equations, is presented. The model is based on a combined approximate kinematic and thermal analysis of a repeating unit cell in a triply periodic array of inclusions. The unit cell is considered to consist of different subregions that can be composed of any desired material. The behavior of the material within the different subregions can be modeled using elastic, plastic, viscoelastic, viscoplastic, or damage constitutive models. The analysis satisfies the equations of motion and the energy equation for the different subregions of the unit cell in an average sense. The interfacial continuity conditions for the velocities, stresses, temperature, and thermal fluxes between the different subregions are also satisfied in an average sense. Arbitrary heat source terms are included in the energy equation to allow for the analysis of reactive materials. The resulting system of governing equations exhibits full coupling between the deformations and the thermal effects. The proposed model is analytical and provides closed-form expressions for the effective macroscopic kinematic and thermal behavior of a particulate composite. The influence of the thermomechanical coupling on behavior at both the macroscopic and microscopic levels is considered. The presence of the coupling can lead to significant localization of the thermal and deformation responses within different regions of the unit cell. It is shown that the presence of inelastic deformations in conjunction with thermomechanical coupling effects can result in appreciable deviation from an isothermal, inelastic analysis.