Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(S_α(t)), 0<α<1, here dX(τ)=μX(τ)(dτ)^2H+σX(τ)dB_H(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black-Scholes equation and the Black-Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.     

Relativistic comparison theorems for the Klein-Gordon equation with scalar and vector potentials in d-dimensions

Relativistic comparison theorems are established for discrete eigenvalues of Klein-Gordon equation with vector and scalar potentials in d-dimensions. Theorem 1: If V(λ) and S(λ) depend on a parameter λ, ∂S/∂λ?0, S?0, ∂V/∂λ?0, V?0, E>0, then it follows that ∂En/∂λ?0. Theorem 2: If S₂?S₁?0, 0?V₂?V₁, E>0, then the corresponding eigenvalues are ordered as En(2)?En(1). Theorem 3: If 0?V₂?V₁, S₂?|S₁|, En(1)>0, En(2)>0, then En(2)?En(1). Some illustrative examples are given.     

The mixed-spin ternary-alloy in the form of ABpC1−p on the Bethe lattice

The AB_pC_1−p type of mixed ferromagnetic-ferrimagnetic ternary-alloy with A (spin-3/2), B (spin-1) and C (spin-5/2) ions was studied on the Bethe lattice with the odd numbered shells containing only A ions, while the even numbered shells either containing B or C ions randomly. The phase diagrams were obtained on the (R=|J_AC|/J_AB,kT_c/J_AB) and (p, kT_c/J_AB) planes for given values of p and R, respectively, with the coordination numbers z=3, 4, 5 and 6. The explicit dependence of the phase diagrams on z and each shell of the Bethe lattice having only one type of ion lead to some differences when compared with the previous works. The model presents one or two compensation temperatures for appropriate values of the system parameters.     

Interferometry for ellipso-height-topometry: Part 2: Measurement of the ellipsometric data, material identification, and correction of the measured height

Ellipso-height-topometry, EHT, as introduced by Leonhardt, et al. [Interferometry for ellipso-height-topometry, part 1, Optik 113 (2003) 513-519; Topometry for locally changing materials, Opt. Lett. 23 (1998) 1772-1774]; [Ellipso-height topometry, Optik 112 (2001) 413-420] is an extended topometry where topographies of the surface height H(x,y), the ellipsometric parameters Ψ(x,y) and Δ(x,y) (and optionally the intensity distribution I(x,y)) of the surface are measured on the same pixel raster and with high resolution. Thus, we can dispose over a set of (mutually coherent) topographies, and further topographies of quantities of interest can be calculated from this set: the local change in the complex refractive index N(x,y)=n(x,y)−k(x,y)i of bulk surfaces, the thickness distribution t(x,y) of locally changing (discontinuous) films and overlayers, and a correction of the optically measured local height H(x,y). The height error ΔH(x,y) can be calculated from the ellipsometric data and the true height h(x,y)=H(x,y)−ΔH(x,y) is thus obtained. ΔH(x,y) can assume large values when overlayers of oxidations or residues from lubrication oil or from processing are present. Much more information about the surface is gained with this concept.In part 1 of this work a z-scanning interferometric scheme with oblique incidence over the entire object field has been introduced, with the advantages of white-light interferometry, but with the additional capability of measuring material information to supply a complete set of topographies for extended topometry. In addition, very useful coherence properties for interferometry with oblique incidence were presented and discussed which allow to shape the interferogram in a simple way without any additional devices. In this part we derive the theory of the ellipsometric measurement and present first results by complete sets of two different samples.     

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures.The appropriate abstract setting is as follows. There is given a compact metric space (M,d), and M is written as the union of certain closed subsets A₁,…,A_r. For every ρ=1,…,r there is prescribed a strict contraction Γ_ρ:A_ρ→M. A random walk (X_m)_m∈N0 on M is then defined as follows. The starting position is X₀=x₀, where x₀∈M is fixed, and if the walk at the m’th step is at position X_m∈M, then one chooses a ρ among the ρ with X_m∈A_ρ (with equal probability, say) and defines X_m+1 as Γ_ρ(X_m). Associated with the walk is a gainφ(X_m) in every round, where φ:M→R is a continuous function.The aim of the present investigations is the study of the expectation G_m of φ(X_m) as a function of m. Our main result states that the sequence (G_m) is “eventually approximately periodic” provided that all A_ρ are not only closed but also open in M: for every ε there is an l₀∈N such that (G_m) is l₀-periodic up to an error of at most ε for sufficiently large m. In fact it turns out that the behaviour of our process can be described well with a finite Markov chain.In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A₁,A₂, the contractions Γ₁,Γ₂ are rather simple, but the expectations of the gains are not even Cesáro convergent.     

Obliquely propagating magnetosonic waves in multicomponent quantum magnetoplasma

Linear properties of obliquely propagating magnetosonic waves (both fast and slow) in multicomponent (electron-positron-ion (e-p-i) and dust-electron-ion (d-e-i)) quantum magnetoplasma are studied. It is found that the quantum Bohm potential term significantly changes the propagation of fast and slow magnetosonic waves in both e-p-i and d-e-i quantum plasmas. The variation of the dispersion characteristics with the increase/decrease of positron concentration in e-p-i and dust concentration in d-e-i quantum magnetoplasma is explored. Finally, the effect of angle θ (that the ambient magnetic field makes with the x-axis) on the dispersion properties of magnetosonic waves in multicomponent quantum magnetoplasma is investigated. The relevance of the present investigation to the dense astrophysical environments and microelectronic devices is also pointed out.     

Exact solutions for a forced Burgers equation with a linear external force

We investigate the solutions of the Burgers equation , where F(x,t) is an external force and Φ(x,t) represents a forcing term. This equation is first analyzed in the absence of the forcing term by taking F(x,t)=k₁(t)−k₂(t)x into account. For this case, the solution obtained extends the usual one present in the Ornstein-Uhlenbeck process and depending on the choice of k₁(t) and k₂(t) it can present a stationary state or an anomalous spreading. Afterwards, the forcing terms Φ(x,t)=Φ₁(t)+Φ₂(t)x and Φ(x,t)=Φ₃x−Φ₄/x³ are incorporated in the previous analysis and exact solutions are obtained for both cases.     

On stationary convection and oscillatory motions in ferromagnetic convection in a ferrofluid layer

It is shown analytically that the ‘principle of the exchange of stabilities’ (PES), in general, is not valid in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries and hence a sufficient condition is derived for the validity of the PES. Upper bounds for the complex growth rate are then obtained. It is proved that the complex growth rate σ=σ_r+iσ_i (where σ_r and σ_i are, respectively, the real and imaginary parts of σ) of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries lies inside a semicircle in the right half of the σ_rσ_i-plane whose center is at the origin and ²(radius)=RM₁/P_r, where R is the Rayleigh number,M₁ is the magnetic number and P_r is the Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.     

The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τ_N=τ_0Nexp(σ), σ being the ratio of anisotropy energy to thermal energy. The pre-factor, τ_0N, is normally given a value of 10⁻⁹ s, but values ranging from 10⁻⁸ to 10⁻¹² s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ(ω,H)=χ′(ω,H)−iχ″(ω,H), of a magnetic fluid sample, in the MHz-GHz range, in conjunction with the determination of the sample decay function, b(t), the pre-factor τ_0N is determined. b(t) is readily obtained through the inverse Fourier transformation relationship, which exists between b(t) and χ″(ω).     

Thermal relaxation of charm in hadronic matter

The thermal relaxation rate of open-charm (D) mesons in hot and dense hadronic matter is calculated using empirical elastic scattering amplitudes. D-meson interactions with thermal pions are approximated by D^? resonances, while scattering off other hadrons (K, η, ρ, ω, K^?, N, Δ) is evaluated using vacuum scattering amplitudes as available in the literature based on effective Lagrangians and constrained by realistic spectroscopy. The thermal relaxation time of D-mesons in a hot π gas is found to be around 25-50 fm/c for temperatures T=150-180 MeV, which reduces to 10-25 fm/c in a hadron-resonance gas. The latter values, argued to be conservative estimates, imply significant modifications of D-meson spectra in heavy-ion collisions. Close to the critical temperature (Tc), the spatial diffusion coefficient (Ds) is surprisingly similar to recent calculations for charm quarks in the Quark-Gluon Plasma using non-perturbative T-matrix interactions. This suggests a possibly continuous minimum structure of Ds around Tc.     

Phase transition in Ising, XY and Heisenberg magnetic films

The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ_c is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J_b, J_s and J_⊥, respectively. It is found that τ_c increases with the exchange interactions of surface. The magnetic phase diagrams (τ_c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T_c(l) from the bulk value (T_c(∞)/T_c(l) − 1) can be described by a power law l^−λ, where λ = 1/υ is the inverse of the correlation length exponent.     

Scaling form of zero-field-cooled and field-cooled susceptibility in superparamagnet

The scaling form of the normalized ZFC and FC susceptibility of superparamagnets (SPMs) is presented as a function of the normalized temperature y(=k_BT/K_u〈V〉), normalized magnetic field h (=H/H_K), and the width σ of the log-normal distribution of the volumes of nanoparticles, based on the superparamagnetic blocking model with no interaction between the nanoparticles. Here 〈V〉 is the average volume, K_u is the anisotropy energy, and H_K is the anisotropy field. Main features of the experimental results reported in many SPMs can be well explained in terms of the present model. The normalized FC susceptibility monotonically increases as the normalized temperature y decreases. The normalized ZFC susceptibility exhibits a peak at the normalized blocking temperature y_b(=k_BT_b/K_u〈V〉), forming the y_b vs h diagram. For large , y_b starts to increase with increasing h, showing a peak at h=h_b, and decreases with further increasing h. The maximum of y_b at h=h_b is due to the nonlinearity of the Langevin function. For small σ, y_b monotonically decreases with increasing h. The derivative of the normalized FC magnetization with respect to h shows a peak at h=0 for small y. This is closely related to the pinched form of M_FC vs H curve around H=0 observed in SPMs.     

Exact solutions for a diffusion equation with a nonlinear external force

This work is devoted to investigate the solutions of the one-dimensional diffusion equation by taking the nonlinear external force F(x,t;ρ)=−k(t)x+K/x+κx|x|^α−1η[ρ(x,t)] into account. Our investigation is first performed by considering the case α=0 and η=1, which results in a Burgers like equation with a spatial and time dependent external force. After, we consider the case α≠0 and η=α+1 and show that the solution found may be expressed in terms of the q-exponential functions present in the Tsallis formalism. In addition, we also discuss the stationary solution for α and η arbitraries.     

Pseudoscalar quarkonium exclusive decays to vector meson pair

The pseudoscalar quarkonia exclusive decays to light mesons still poses a challenge to the theoretical understanding of quarkonium properties in decay. In this work, we evaluate the processes of pseudoscalar heavy quarkonium decays into vector meson pairs, especially the helicity suppressed processes of ηb→J/ψJ/ψ and ηc→VV. In the framework of NRQCD, the branching fraction of Br[ηb→J/ψJ/ψ] are evaluated at the next-to-leading order of perturbative QCD; and within the light-cone distribution formalism, we calculate also the higher twist effects in these processes. Numerical results show that the higher twist terms contribute more than what from the NLO QCD corrections in the process of ηb→J/ψJ/ψ. It is found that the experimental results on ηc→VV are hard to be understood by merely the quark model and perturbative QCD calculation.     

Logistic equation of arbitrary order

The paper is concerned with the new logistic equation of arbitrary order which describes the performance of complex executive systems X vs. number of tasks N, operating at limited resources K, at non-extensive, heterogeneous self-organization processes characterized by parameter f. In contrast to the classical logistic equation which exclusively relates to the special case of sub-extensive homogeneous self-organization processes at f=1, the proposed model concerns both homogeneous and heterogeneous processes in sub-extensive and super-extensive areas. The parameter of arbitrary order f, where −∞<f<+∞, depends on both the coefficient of external resource utilization u=N/K, where 0<u<1, and the internal microscopic character of realized processes related to the depth of feedback β. The coefficient β directly influences self-organization of processes by the change of microscopic parameters V_i, S_i, i and Z, where V_i is the number of references (visit) to the ith component of the system during the service of each task, S_i is the time of serving the task by the ith component, and Z is the think time of a given process. In the general case of complex system, parameters V_i, S_i, i and Z can have values in the range from 0 to +∞. In this way the new equation includes all possible cases of a complex executive system’s operation. Furthermore, it allows us to define the optimal matching point between X and N with f as the parameter. It also helps to balance the load in complex systems and to equip artificial systems with self-optimization mechanisms similar to those observed in natural systems.     

Compensation temperatures and magnetic susceptibility of a mixed ferro-ferrimagnetic ternary alloy

We study the compensation behaviour and magnetic susceptibility of a mixed ferro-ferrimagnetic ternary alloy of the type ABpC1−p on a cubic lattice by the use of Monte Carlo simulations. We consider that the A and X (X=B or C) ions are alternately connected and have different Ising spins SA=3/2, SB=2, and SC=5/2, respectively. In particular, we find that the magnetic susceptibility may exhibit an outstanding behaviour in a vicinity of the critical and compensation temperatures. The relation of the studied model to ternary Prussian blue analogs is also discussed.     

Magnetic phase diagrams of the CrB- and FeB-type HoSi compounds

The temperature magnetic phase diagrams of the dimorphic HoSi compound were studied by neutron diffraction. The sample comprises 35.5% CrB- (Cmcm) and 64.5% FeB-type (Pnma) of structure. Both phases order antiferromagnetically below T_N=25 K and undergo first-order magnetic transitions at T_ic=16.5 K. Their T-phase diagrams comprise a low temperature (LT) 2.7 K−T_ic and a high temperature (HT) range T_ic−T_N with distinct wave vectors.The LT magnetic ordering of the CrB-type HoSi with the wave vector q₁=(1/2, 0, 1/2) corresponds to a uniaxial magnetic structure, with the Ho moments along the shortest axis c. At 2.7 K the ordered moment value is 8.6(2) μ_B/Ho atom. The HT ordering, described by the wave vector q₂=(q_2x, 0, q_2z) with a T-variable length, corresponds to an amplitude modulated structure.The magnetic ordering of the FeB-type HoSi requires two symmetry independent vectors q₃=(0, q_3y, q_3z) for the LT- and q₄=(q_4x, q_4y, 0) for the HT range. Both vectors correspond to sine wave modulated structures with the Ho magnetic moments confined along the shortest axis b. The q₃ vector has an almost invariable length vs. T close to ≈(0, 9/17, 1/11). At 2.7 K the amplitude of the wave is 10.9(1) μ_B/Ho atom. At T_icq₃ jumps to the wave vector q₄=(q_4x, q_4y, 0) with a T-variable length. At 17 K q₄=(0.092(1), 0.538(3), 0). Around T_ic there is a narrow coexistence range of the q₃ and q₄ competing phases. Various models are discussed and compared with the isomorphic RSi (R=rare earth) compounds counterparts of HoSi, a comparison that has led us to briefly review the magnetic structures available in the literature for this interesting class of compounds.     

Hard exclusive photoproduction of Φ and J/Ψ mesons

We calculate the leading-order perturbative contribution to γp→M_Vp, with M_V being a Φ or J/Ψ meson, in the kinematic region of large energy and scattering angle.     

The single-particle potential of nuclear matter in the LOCV framework

The density and momentum dependence of single-particle potential (SPP) and effective mass of symmetric nuclear matter are studied in the framework of lowest order constrained variational (LOCV) method. The Reid68, the Reid68-Δ and the ₁₈Av interactions are considered as the input nucleon-nucleon potentials. It is shown that the SPP of nuclear matter, at fixed density, is an increasing function of nucleon momentum, and it has different behavior for the Reid type potentials with respect to ₁₈Av interaction. We find good agreements between our LOCV SPP and those coming from others many-body techniques such as the (Dirac-)Brueckner-Hartree-Foch ((D)BHF), the fermion hypernetted chain (FHNC), mean field (MF), etc. On the other hand SPP dramatically depends on the density at low and high nucleon momentums. While the effective mass of nuclear matter increases as we increase the nucleon momentum, it decreases at the Fermi surface. Again, good agreements are observed between our calculated effective mass and those coming from the methods mentioned above.