The Stability of Several Triply Periodic Surfaces

The stability of six triply periodic surfaces of constant mean curvature (CMC) is investigated. The relative energy and curvature values of the surfaces comprising the P (Pm3¯m), I-WP (Im3¯m), and G (I4₁32) families are numerically calculated with K. Brakke's Surface Evolver. Regions where the I-WP surface can exist metastable to a complementary I-WP surface are found. This type of metastability is also found in the F-RD surface. Bifurcation points marking the stability limits of the P, I-WP, and G families are also calculated with Evolver. Modes of instability which may occur in the six CMC families are classified. Bifurcations in the P, G, I-WP, C(P), D, and F-RD families are attributed to fundamental instabilities. Lattices of spheres (LOS) are possible extremal surfaces at the bifurcations. It is determined that both the CMC surfaces and the LOS configurations are unstable to coarsening. Because the variation in curvature is lowest for the G family, it is the most robust of the six families to coarsening when the surfaces are otherwise equivalent.     

Variational Matrix Padé Approximants in Two Body Scattering

The convergence and bounding properties of the variational matrix Padé approximants are investigated for non relativistic two body interactions. Selecting L – 1 discrete values qi, i = 1, …, L – 1 and the physical momentum q₀ the off shell scattering amplitudes are L X L matrices. The [N/N] Padé approximants to the Born series of these matrices are the variational solution of the Schwinger principle and the corresponding physical amplitude has variational properties in the off shell momenta. For positive interactions the best approximants to the phase shift is an absolute minimum on the q_i and monotonic convergence to the exact result for N → ∞ or L → ∞ ca be proved. Similar properties are shown for the bound states using the Ritz variational principle. The required mathematical background is extensively worked out, the extensions to non positive, singular and long range potentials are considered and some numerical examples are presented.     

Simple one-centre calculation of breathing force constants and equilibrium internuclear distances for NH3, H2O and HF

Total molecular energies, breathing force constants and equilibrium internuclear distances are determined for the NH₃, H₂O and HF molecules using a single determinant wave function of the simplified one-centre form s ² s′² p _x ² p _y ² p _z ², where each of the five Slater orbitals, s, s′, p _x , p _y , p _z , is characterized by an effective orbital exponent ζ and an effective principal quantum number n. Five different calculations are performed for each molecule: in (a) the orbitals are centred on the heavy atom, the parameters n are taken to be integral, and the orbitals p _x , p _y and p _z are given the same ζ values (the spherical approximation); in (b) the orbitals p _x , p _y and p _z are allowed to have different ζ values (the ellipsoidal approximation); (c) and (d) are the same as (a) and (b) except that non-integral n values are allowed; (e) is the same as (d) except that the orbital centre also is taken to be a variational parameter. The values obtained are compared with experimental values (the agreement is surprisingly good) and with values from previous one-centre wave functions. The electronic densities for the various spherical approximations are tabulated.     

<Emphasis Type="Italic">R</Emphasis> soliton in the Wess-Zumino model

The Wess-Zumino model involving a renormalizable interaction potential and possessing R symmetry is considered. It is shown that an R soliton, which is a nontopological soliton state, is present in this model. Characteristic properties of the R soliton are discussed. Problems associated with the stability of the R soliton are considered. The results obtained by numerically calculating the energy and the charge of the R soliton are presented for several values of the model parameters. The scalar field configurations in this supersymmetric model are characterized by the presence of fermionic zero modes. Expressions for the fermionic zero modes of the R soliton are obtained, and some of their properties are considered.     

A relativistic mean-field study of magic numbers in light nuclei from neutron to proton drip-lines

In an axially deformed relativistic mean-field calculation of single-particle energy spectra ofN = 8 (Li-Mg) andN = 14,16 (C-Mg) isotonic chain and the one- and two-neutron separation energies of various isotopes of Li-Mg, new magic numbers are found to exist atN = 6 andN = 16 and/orN = 14, which are in addition to theN = 8 andN = 20 magic numbers. In neutron-rich nuclei, the shell gap atN = 6 is larger than atN = 8 and a large gap is observed forN = 16 or 14 for the neutron-rich andN = 14 for proton-rich nuclei. Large shell gaps are also found to exist atN = 14 and 16 orN = 16 alone for nuclei near theβ-stability line. The above results are independent of the parameter sets TM2, NL3 and NL-SH used here. Similarly, new large shell gaps are predicted atZ = 616 and/or 14 for protons.     

Some consequences of neutral current systematics

Two kinds of general consequences of the ΔS=0 weak hadron neutral current independent of a gauge model are presented. Firstly are results which depend on the quark parton model. These involve bounds among neutrino inclusive cross-section and a bound onQ(Z, N) in terms of these inclusive cross-sections. Secondly are results which are independent of the quark-parton model and depend only on the SU(3) structure of the most general ΔS=0 neutral current. These tests of isopin and speciallyU-spin properties of the current are given forv+N→v+hadron+anything,v+N→v+baryon+meson ande ⁺ e ⁻→baryon+anti-baryon. In addition some conjectures are made with regard to the semi-inclusive neutrino-reactions using the quark parton model.     

Arbitrary Wave Relativistic Bound State Solutions for the Eckart Potential

The approximately analytical bound state solutions of the l-wave Klein-Gordon and k-state Dirac equations with the mixed Eckart potentials are carried out by a proper approximation to the centrifugal term. The analytical radial wave functions of the l-wave Klein-Gordon and k-state Dirac equations with the mixed Eckart potentials are presented and the corresponding energy equations are derived. Two special cases for k=1 and for k=1 and β=0 are studied briefly. Finally, we also verify the rationality of this approximation.     

Generalized Robertson-Walker metrics and some of their properties. II

The Robertson-Walker (RW) metrics, of dimensionality four and signature –2, are generalized to metrics of dimensionality (n+1) and of arbitrary signature,n (> 1) being an arbitrary integer. In canonical coordinates (t, x ¹,x ², ...,x ⁿ ) these generalized Robertson-Walker (GRW) metrics are functions of the coordinatet. The following statements are proved to be equivalent: The GRW metrics are (a) expressible int-independent form, (b) of constant curvature, (c) Einstein spaces. Furthermore, there are six, and only six, classes of GRW metrics satisfying these three statements. The coordinate transformations which transform these metrics to theirt-independent form are given explicitly. Two of these classes of GRW metrics reduce, in theirt-independent form, to the same flat (generalized Minkowski) metrics, three reduce to the samet-independent metrics which are generalizations of the de Sitter space-time metric, and the last class tot-independent metrics which are generalizations of the anti-de Sitter space-time metric.     

Algebraic Structure and Poisson’s Integral Theory of f(R) Cosmology

In this paper, the algebraic structure and the Poisson’s integral theory of f(R) cosmology are presented. Firstly, the Hamilton canonical equations are derived for the system. Secondly, the contravariant algebraic forms of f(R) cosmology are obtained. Thirdly, the Lie algebraic structure admitted and Poisson’s integral methods are investigated for f(R) cosmology. Further, the first integrals and solution of f(R) cosmology are given. Finally, an example is given to illustrate the results.     

HOW TO EXTEND ANY DYNAMICAL SYSTEM SO THAT IT BECOMES ISOCHRONOUS,ASYMPTOTICALLY ISOCHRONOUS OR MULTI-PERIODIC

We indicate how one can extend any dynamical system (namely, any system of nonlinearly coupled autonomous ordinary differential equations) so that the extended dynamical system thereby obtained is either isochronous or asymptotically isochronous or multi-periodic, namely its generic solutions are either completely periodic with a fixed period or tend asymptotically, in the remote future, to such completely periodic functions or are multi-periodic (or become multi-periodic only asymptotically, in the remote future). In all cases the scale of the periodicity can be arbitrarily assigned. Moreover, the solutions of the extended systems are generally well approximated by those of the original, unmodified, systems, up to a constant rescaling of the independent variable (time), as long as their evolution is considered over time intervals short with respect to the (arbitrarily assigned) periodicities characterizing the extended systems. Several examples are displayed. In some cases the general solution of these dynamical systems is also exhibited; in others, this is impossible inasmuch as the models being manufactured are extensions of dynamical systems displaying chaotic evolutions, such as, for instance, the well-known Lorenz model of 3 nonlinearly coupled ODEs.     

Study of quark distribution amplitudes of 1<Emphasis Type="Italic">S</Emphasis> and 2<Emphasis Type="Italic">S</Emphasis> heavy quarkonium states

In this paper, the quark distribution amplitudes of 1S and 2S heavy quarkonium states are studied in terms of Gaussian-type wave functions. The transverse momenta p _⊥ integrals of the formulae for the decay constant are performed analytically. Then the quark distribution amplitudes are obtained. In addition, the ξ-moments are also calculated. After fixing the relevant parameters appearing in the quark distribution amplitude, the curves of the quark distribution amplitude for 1S and 2S heavy quarkonium states are plotted. Finally, the numerical results of this approach are compared with the other theoretical predictions.     

Analytic Bethe ansatz for fundamental representations of Yangians

We study the analytic Bethe, ansatz in solvable vertex models associated with the YangianY(X _r ) or its quantum affine analogueU _q (X _r ⁽¹⁾ ) forX _r =B _r ,C _r andD _r . Eigenvalue formulas are proposed for the transfer matrices related to all the fundamental representations ofY(X _r ). Under the Bethe ansatz equation, we explicitly prove that they are pole-free, a crucial property in the ansatz. Conjectures are also given on higher representation cases by applying theT-system, the transfer matrix functional relations proposed recently. The eigenvalues are neatly described in terms of Yangian analogues of the semi-standard Young tableaux.     

Dynamics of uniform quantum gases, I: Density and current correlations

A unified approach valid for any wavenumber q, frequency ω, and temperature T is presented for uniform ideal quantum gases allowing for a comprehensive study of number density and particle-current density response functions. Exact analytical expressions are obtained for spectral functions in terms of polylogarithms. Also, particle-number and particle-current static susceptibilities are presented which, for fugacity less than unity, additionally involve Kummer functions. The q- and T-dependent transverse-current static susceptibility is used to show explicitly that current correlations are of long range in a Bose-condensed uniform ideal gas but for bosons at T>T_c and for Fermi and Boltzmann gases at all temperatures these correlations are of short range. Contact repulsive interactions for systems of neutral quantum particles are considered within the random phase approximation. The expressions for particle-number and transverse-current susceptibilities are utilized to discuss the existence or nonexistence of superfluidity in the systems under consideration.     

Study of the structure and refractive parameters of diethylamine and triethylamine

The refractive index (n) and thermal coefficient of the refractive index (dn/dt) are measured at four wavelengths for the diethylamine and triethylamine. The measurements are carried out using the Bellingham+Stanley model 60/ED high-accuracy Abbe refractometer. The optical permittivity (ε) and its variation with temperature are calculated. Applying the Cauchy equation, the following refractive properties are obtained: the optical dispersion dn/dλ, the dielectric dispersion dε/dλ, the variation of -dn/dT, dε/dT, as a function of wavelength (λ), and Cauchy's constants against temperature. Additionally, molar refractivity versus temperature and wavelength are determined.     

Representations ofSO(p+q) andO(p) with an application to the shapes of8,9Li

It is easy to show that the symmetry groups governing a system ofZ protons andN neutrons areSO(p+q) andO(p), wherep, q are related toZ, N and the symmetry groups are transitive on a Grassmann manifoldG _p,q. In this paper the general representations ofSO(p+q) andO(p) are found and used to describe the geodesics onG _p,q for the nuclear manifolds of the neutron rich-elements^8,9Li.     

［Mg(NH2)2］n(n=1—5)团簇的密度泛函理论研究

用密度泛函理论的杂化密度泛函B3LYP方法在6-31G^*基组水平上对［Mg(NH₂)₂］_n(n=1—5)团簇各种可能的构型进行几何结构优化,预测了各团簇的最稳定结构.对最稳定结构的振动特性、成键特性、电荷特性等进行了理论研究.结果表明：团簇易形成链状结构,Mg—N键长为0.190—0.234 nm,N—H键长为0.101—0.103 nm,H—N—H键角为100.2°—107.5°;团簇中M 关键词： 2)₂］_n(n=1—5)团簇')" href="#">［Mg(NH₂)₂］_n(n=1—5)团簇 密度泛函理论 结构与性质 储氢材料     

Anisotropic dc conductivity of pentagonal quasicrystals

The dc conductivity in the system with a fivefold rotational symmetry in theX-Y plane (QC plane) but having periodicity along theZ direction (C axis) are theoretically investigated from Kubo formula using the recursion method. Numerical results are suggestive of a metallic behavior for the dc conductivity in theQC plane as well as along theC direction, but these two kinds of dc conductivity are anisotropic in magnitude.     

Beauty-conserving strangeness-changing rare semileptonic decays ofB s meson

The beauty-conserving strangeness-changing decays ofB _s meson are examined. In the charm sector, charm-conserving strangeness changing (Δc = 0, Δs ≠ 0) decays are Cabibbo suppressed and are governed by the CKM elementV _us which is much smaller than the CKM diagonal elementV _cs, so may be of little interest. On the other hand, in theb-sector, beauty-conserving strangeness changing (Δb = 0, Δs ≠ 0) decays are CKM allowed as the CKM matrix elementV _us governing such decays is much larger thanV _bc orV _bu which govern respectively theb →c orb →u transitions. The phase space available, however, is too small for the decays considered here. The numerical estimates for the decay widths of two such modes ofB _s meson are presented.     

Superspinors and Graded Lorentz Groups in Three,Four and Five Dimensions

Three superalgebras osp(1; 2; F) (F = R, C, H) and corresponding three supergroups are considered. The transformation laws of spinors with anticommuting components for 3-dimensional (O(2, 1) ≃ Sp(2; R)), 4-dimensional (O(3, 1) ≃ Sp(2, C)) and 5-dimensional (O(4, 1) ≃ Sp(2; H)) Lorentz group are extended in a supersymmetric way by introducing nonlinear realizations of the supergroups OSp(1, 2; F). The affine Grassmann spinors in all three cases are obtained by suitable “flat” limit of the nonlinear realization. Different gradings and different contractions of osp(1,2; F) (F = R, C, H) superalgebras are considered.     

Novel solvable many-body problems

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type (“acceleration equals forces”) which determine the motion of points in the complex plane. These models are solvable, namely their con?guration at any time can be obtained from the initial data by algebraic operations, amounting to the determination of the zeros of a known time-dependent polynomial in the independent variable z. Some of these models are multiply periodic, isochronous or asymptotically isochronous; others display scattering phenomena.