New calculations of α-decay half-lives by the Viola-Seaborg formula

The Viola-Seaborg formula is a well-known formula for α-decay half-lives of heavy nuclei. In this work we obtain new parameters of this formula through a least-square fit to even-even nuclei between Z = 84 and Z = 110 with N greater than 126. On average, the formula can reproduce the half-lives of heavy even-even nuclei within a factor of 1.3. The formula with new parameters works well for the superheavy region which is a hot topic of nuclear physics. The numerical results from the formula are compared with those from the cluster model.     

Local Gromov–Witten invariants of blowups of Fano surfaces

In this paper, using the degeneration formula we obtain a blowup formula of local Gromov–Witten invariants of Fano surfaces. This formula makes it possible to compute the local Gromov–Witten invariants of non-toric Fano surfaces from toric Fano surfaces, such as del Pezzo surfaces. This formula also verified an expectation of Chiang–Klemm–Yau–Zaslow in Section 8.3 of Chiang et al. (1999) [7]     

Empirical investigation of a field theory formula and Black's formula for the price of an interest-rate caplet

The industry standard for pricing an interest-rate caplet is Black's formula. Another distinct price of the same caplet can be derived using a quantum field theory model of the forward interest rates. An empirical study is carried out to compare the two caplet pricing formulae. Historical volatility and correlation of forward interest rates are used to generate the field theory caplet price; another approach is to fit a parametric formula for the effective volatility using market caplet price. The study shows that the field theory model generates the price of a caplet and cap fairly accurately. Black's formula for a caplet is compared with field theory pricing formula. It is seen that the field theory formula for caplet price has many advantages over Black's formula.     

Estimation of van der Waals dipole-quadrupole interactions

A formula has been derived based on a variational approach for the van der Waals dipole-quadrupole interaction coefficient between two atoms or ions. The coefficients for the various ion pairs in the alkali halides have been estimated on the basis of this formula. The results agree quite well with those estimated by Mayer (J. Chem. Phys.1, 270 (1933)) using a perturbation approach. The present formula is shown to have a practical advantage over the perturbation formula.     

Urbaryon Model Approach to Unified Understanding of Large and Small PT Spectra

Single-particle distributions in the entire Peyrou plot at CERN-PS ∼ ISR energies are unifiedly described by the whole-region formula, which incorporates both parton model results at large p_T and all of the Mueller-Regge forms at small p_T. The quantum number dependence of the distributions is explained by the formula as due to the intimate relation between the energy-momentum flow and the quantum-number flow carried by valence urbaryons. A field theoretical basis of the formula is provided by a covariant model of the hadron-urbaryon amplitude which is parametrized in terms of valence urbaryon lines and pair effects. Two-body reactions at all angles are also described by the formula as the exclusive limit of inclusive reactions. The construction of a formula for inclusive two-particle distribution is briefly discussed.     

Acoustic scattering by turbulent fluctuations of pressure and entropy

Detailed analysis is presented of the well-known Tatarskii’s formula, which describes sound wave scattering in a turbulent atmosphere. The adiabaticity of the acoustic fluctuations and incompressibility of the turbulent fluctuations are assumed only. This yields to additional 1 terms in the classical formula (probably, small in the inertial range of turbulence). We show the change of Obukhov’s formula, which describes the connection between turbulent fluctuations of pressure and velocities in a compressible atmosphere, and also demonstrate the effect of the independence of fluctuations of the potential and thermodynamic temperatures. By analogy with the formula for small-scale isotropic temperature fluctuations, which was also obtained by Obukhov, we derive a formula for the fluctuations of entropy and potential density as function of entropy, which describes spatial distribution of the probability density of identical “fluid particles” in the turbulent media.     

The application of fractional derivatives in stochastic models driven by fractional Brownian motion

In this paper, in order to establish connection between fractional derivative and fractional Brownian motion (FBM), we first prove the validity of the fractional Taylor formula proposed by Guy Jumarie. Then, by using the properties of this Taylor formula, we derive a fractional Itô formula for H∈[1/2,1), which coincides in form with the one proposed by Duncan for some special cases, whose formula is based on the Wick Product. Lastly, we apply this fractional Itô formula to the option pricing problem when the underlying of the option contract is supposed to be driven by a geometric fractional Brownian motion. The case that the drift, volatility and risk-free interest rate are all dependent on t is also discussed.     

Refinement of a formula for decay after weak coherent excitation of a sphere

A new formula has been given recently by A.A. Svidzinsky and M.O. Scully to describe the temporal evolution of the excitation function in a large sphere satisfying the Markov condition after excitation by a single photon. This formula is based on a physically reasonable Ansatz from which differential equations are inferred for the undetermined radial functions in the Ansatz. The solution to these differential equations leads to the formula for β. Numerical calculations from this formula yield a value ∼10% for the maximum probability of occupancy of secondary excited states.In this paper, we refine the formula of Svidzinsky and Scully by allowing the radial functions in the Ansatz to depend on the angular index l of the spherical Bessel functions. By using the Debye formula for the asymptotic behavior of j_l(u) for large l as well as u, we obtain differential equations in each angular sector, similar to theirs but with a dependence on l. The solution to these equations yields our improved formula, from which we calculate 17.1% for the maximum probability of secondary excited states.     

A simple formula for the average gate fidelity of a quantum dynamical operation

This Letter presents a simple formula for the average fidelity between a unitary quantum gate and a general quantum operation on a qudit, generalizing the formula for qubits found by Bowdrey et al. [Phys. Lett. A 294 (2002) 258]. This formula may be useful for experimental determination of average gate fidelity. We also give a simplified proof of a formula due to Horodecki et al. [Phys. Rev. A 60 (1999) 1888], connecting average gate fidelity to entanglement fidelity.     

The relation between the waveguide and overlap implementations of Kaplan's domain wall fermions

Recently, Narayanan and Neuberger proposed that the fermion determinant for a lattice chiral gauge theory be defined by an overlap formula. The motivation for that formula comes from Kaplan's five-dimensional lattice domain wall fermions. In the case that the target continuum theory contains 4n chiral families, we show that the effective action defined by overlap formula is identical to the effective action of a modified waveguide model that has extra bosonic ghost fields. This raises serious questions about the viability of the overlap formula for defining chiral gauge theories on the lattice.     

Prediction of double-pomeron cross sections from single-diffraction measurements

A particular case of a Mueller formula describing the absence of long-range two-particle correlations is used to predict double-pomeron cross sections from available data on single-diffraction dissociation. Although success of the formula in this application would immediately verify the double-pomeron hypothesis, the converse is not true because the formula may be invalidated by prominent low-energy resonances (such as the f₀) in the pomeron-pomeron total cross section. Low-statistics experiments at s = 200 and 400 GeV² are in order of magnitude agreement with the formula.     

On Gammelgaard’s Formula for a Star Product with Separation of Variables

We show that Gammelgaard’s formula expressing a star product with separation of variables on a pseudo-Kähler manifold in terms of directed graphs without cycles is equivalent to an inversion formula for an operator on a formal Fock space. We prove this inversion formula directly and thus offer an alternative approach to Gammelgaard’s formula which gives more insight into the question why the directed graphs in his formula have no cycles.     

A Structural Entropy Measurement Principle of Propositional Formulas in Conjunctive Normal Form

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.     

Absolute Electron Impact Cross Sections for Single Ionization of Metastable Atoms of H,He, Ne,Ar, Kr,Xe and Rn

Cross sections for single ionization of metastable atoms of H, He, Ne, Ar, Kr, Xe and Rn by electrons with impact energy E (threshold < E < 200 eV) are determined using a recently developed semiclassical formula. The formula consists of an energy dependent term (classical binary encounter approximation) and a term containing the weighted sum of the squared radii of maximum charge density of the outer electron subshells (Born Bethe approximation). Although this formula was originally devised and applied for ground state atoms, a comparison of the present calculations with previous calculations and measurements indicates that this formula can also be used successfully in case of metastable atoms.     

A Closed Formula for the Asymptotic Expansion of the Bergman Kernel

We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl invariants. The proof relies on a combinatorial interpretation of a recursive formula due to M. Engliš and A. Loi.     

Phase-integral calculation of quantal matrix elements between unbound states,without the use of wavefunctions

The paper deals with the calculation of diagonal as well as off-diagonal matrix elements between unbound states pertaining to a radial Schrödinger equation. For the case that the effective potential, i.e. the potential with the centrifugal barrier included, is real and that only a single generalized classical turning point exists, we derive, on the basis of a phase-integral method, a new, general formula for the calculation of such matrix elements without the use of wavefunctions. The formula applies to an arbitrary order of the phase-integral approximations used. While conventional methods may present difficulties when the radial wavefunctions oscillate rapidly in space, this formula, in which the wavefunctions do not appear, is expected to be more accurate the more rapidly the wavefunctions oscillate. The formula is tested numerically for a Lennard-Jones potential and is found to yield extremely accurate results.

When specialized to the first-order approximation, our formula goes over into a formula derived previously by other authors. They derived the formula by introducing the first-order JWKB approximation for the wave-functions in the integral defining the matrix element and simplifying the resulting expression by using simple qualitative arguments. The remarkably good accuracy of this first-order formula has puzzled previous authors. So has also the fact that attempts to improve it, by including quantities neglected on the basis of the simple qualitative arguments, and by using Airy functions or uniform approximations for the wavefunctions through the turning points, have failed. Our derivation throws light on the question of the accuracy to be expected, and it explains why already the first-order formula is remarkably accurate and why no improvement is gained in the attempts mentioned.     

超导临界温度理论(Ⅲ)

本文定出超导临界温度T_c级数公式(1)的前几项系数。对于形式为α²F(ω)=(λω)/2[a₁δ(ω-ω₁)+(1-a₁)δ(ω-ω₂)]的双δ型有效声子谱及若干具体材料的谱,将级数公式计算的T_c与Allen-Dynes公式(以下简称A-D公式)及Eliashberg方程的数值解作了比较。计算表明,当级数(1)收敛时,级数公式计算的结果较A-D公式更接近于数值解。此外,本文还给出了一个近似的T_c级数公式,得到了估计该T_c级数收敛半径的方法,并计算了若干材料的收敛半径值。因此,可估计级数公式(1)的适用范围。 关键词：     

Fringe formula for projection type moiré topography

The rays that form moiré fringes in projection type moiré topography are discussed. It is shown that the nodal-ray formula conventionally used in projection type moiré topography gives erroneous results for an object located close to the lenses. An alternative formula based on principal rays is proposed and compared with the conventional nodal ray formula. The principal ray formula proposed can be applied to a wide class of optical systems, including a telecentric system.     

电子阻止本领Se(E)的z振荡及其计算

本文应用Hartree-Fock-Slater势能代替Thomas-Fermi势能,得出电子阻止本领S_e(E)的归一化关系式;同时,结合有效原子序数概念,得出能量对S_e(E)影响的关系式,利用前一关系式,定量计算了S_e(E)随离子和靶原子的原子序数z变化的振荡关系,计算结果与实验值相当符合,利用后一关系式,定量计算了多种离子-靶体系的S_e(E),与文献[1]的关系式比较,本文结果更好地符合实验值,而且有更广的能量适用范 关键词：     

A modified Euler–Maclaurin formula in 1D and 2D with applications in statistical physics

The Euler–Maclaurin summation formula is generalized to a modified form by expanding the periodic Bernoulli polynomials as its Fourier series and taking cuts, which includes both the Euler–Maclaurin summation formula and the Poisson summation formula as special cases. By making use of the modified formula, a possible numerical summation method is obtained and the remainder can be controlled. The modified formula is also generalized from one dimension to two dimensions. Approximate expressions of partition functions of a classical particle in square well in 1D and 2D and that of a quantum rotator are obtained with error estimation.