Fermion mass hierarchy based onN=8 supergravity

A possible mechanism is proposed to realize fermion mass hierarchy based on the superunification model of Ellis et al. In addition to the usual fermion (F)—Higgs (B) coupling, “non-renormalizable” interactions such as(1/(M _p ) ⁿ )(F) ² (B) ⁿ⁺¹ are introduced. It is assumed that three kinds of Higgs scalars respectively develop v.e.v. of orderM _P ,M _X andM _W , corresponding to the symmetry breaking pattern ofSU(8)→SU(5)→SU(3)×SU(3)×U(1)→SU(3)×U(1). As a result, fermions acquire their masses of orderM _w ,M _W (M _X /M _P) andM _W (M _X /M _P )². An example of the model is presented which shows nice feature of hierarchical mass patterns.     

SU(3) ⊗ SU(2) ⊗ U(1) from D = 11 supergravity

In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ? SU(2) ? U(1) as a symmetry of the internal space M₇. These solutions lead, in dimensional reduction, to SU(3) ? SU(2) ? U(1) gauge fields.In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/p which describes the embedding of the stability subgroup SU(2) ? U(1) ? U(1) of M₇ in SU(3) ? SU(2) ? U(1). For all q/p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl $\text{F}{}_{\mathrm{\alpha \beta \gamma \delta }}\text{≠ 0}$. It breaks all sypersymmetries.     

Decay of194Os andL 1 subshell yields atZ=77

The relative intensities of x rays and gammas emitted in the beta decay of¹⁹⁴Os are measured. No evidence for the feeding of a level at 83 keV in¹⁹⁴Ir is found. An upper limit of 1.7×10^?4 was set for theK shell internal ionization probability in the beta decay to the ground state of¹⁹⁴Ir. TheL-conversion coefficient of 43 keV transition is found to be 12.1 and the transition is mainly ofM1 type with an admixture of 1.3%E2 type. TheL ₁ subshell yields atZ=77 are determined to beω ₁=0.16±0.04,f ₁₂=0.11±0.04 andf ₁₃=0.37±0.03.     

Electrical relaxation studies of olivine type nanocrystalline LiMPO4 (M=Ni,Mn and Co) materials

The olivine type LiMPO₄ (M=Ni, Mn and Co) materials were synthesized by solution combustion technique using glycine as fuel. The structural characterizations were explored to confirm the phase formation of materials. The scanning electron microscope was used to identify the morphology of olivine materials. The local structure and chemical bonding between MO₆ octahedral and (PO₄)^3- tetrahedral groups were probed by Raman spectroscopy. Grain and grain boundaries were contributed for ion relaxation and dc conduction in olivine materials. Two orders of enhancement in ionic conductivity was observed in these olivine materials than the reported value. Among all the explored olivine samples, LiMnPO₄ showed highest enhancement in conductivity due to weak Li–O bonding and largest unit cell volume.     

MeanM-subshell fluorescence yields atZ=88, 90, 92, and 94

M x-ray —L x-ray coincidence measurements with high resolution, cooled Si(Li) x-ray detectors were made on transitions following the alpha decays of²²⁸Th,²³²U,²³⁸Pu, and²⁴⁴Cm, in order to determine the meanM-subshell fluorescence yields. The values obtained are:v ₄ ^M =0.032±0.002, andv ₅ ^M =0.024±0.002 atZ=88;v ₁ ^M =0.038±0.003,v ₄ ^M =0.042±0.002, andv ₅ ^M =0.038±0.002 atZ=90;v ₁ ^M =0.047±0.002,v ₄ ^M =0.048±0.002, andv ₅ ^M =0.044±0.002 atZ=92;v ₁ ^M =0.066±0.002,v ₄ ^M =0.062±0.002, andv ₅ ^M =0.063±0.002 atZ=94. The quantityΩ ₁ ^M +f ₁₂ ^MΩ ₂ ^M was measured as (56±10)×10^?4, (62±12)×10^?4, (99±18) ×10^?4, and (93±15)×10^?4 forZ=88, 90, 92, and 94, respectively, which agree well with the calculations of McGuire. The radiativeL ₁-L ₃ transition intensity was measured for the four atomic numbers and found to be consistently less than the calculations of Scofield by about 45 percent.     

红色LiMBO3 : Re3+(Re=Eu,Sm) 发光材料的特性

采用固相法制备了红色LiM(M=Ca, Sr, Ba)BO₃ : Re³⁺(Re=Eu, Sm)发光材料,研究了材料的发光性能。研究发现LiM(M=Ca, Sr, Ba)BO₃ : Eu³⁺材料呈现多峰发射,最强发射分别位于610,615,613 nm处,分别监测这三个最强峰,所得激发光谱峰值位于369,400,470 nm。LiM(M=Ca, Sr, Ba)BO₃ : Sm³⁺材料也呈多峰发射,分别对应Sm³⁺的⁴G_5/2→⁶H_5/2、⁴G_5/2→⁶H_7/2和⁴G_5/2→⁶H_9/2跃迁发射;分别监测602,599,597 nm三个最强发射峰,所得激发光谱峰值位于374,405 nm。研究了激活剂浓度对材料发射强度的影响,结果随激活剂浓度的增大,发射强度先增强后减弱,即,存在浓度猝灭效应。实验表明,加入电荷补偿剂Li⁺、Na⁺或K⁺均可提高LiM(M=Ca, Sr, Ba)BO₃ : Re³⁺(Re=Eu, Sm)材料的发射强度。     

Non-abelian D = 11 supermembrane

We obtain a U(M) action for super membranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. The worldvolume action has (LCG) N = 8 supersymmetry arid it corresponds to M parallel supermembranes minimally immersed on the target M g × T ² (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N = 8 SYM in the IR phase for any number of M2-branes.     

Local and itinerant magnetism and superconductivity in R Rh2si2 (R = rare earth)

Magnetization and Mossbauer studies reveal that R Rh₂Si₂ (R = rare earth) have two magnetic phase transitions, one corresponding to the ordering of the rare earth (T^N = 27?130K) and the other to the itinerant electron ordering of the Rh sublattice (T^M= 5?17K). LaRh₂si₂ has also been studied by resistivity, specific heat and a.c. susceptibility measurements. All studies indicate that LaRh₂Si₂ orders magnetically at T^M= 7K and becomes superconducting, type II, at T^c= 3.8±0.2K.     

A classification of compactifying solutions for d =11 supergravity

Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail.The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry.The existence of a spin structure on homogeneous manifolds $\text{G}\text{H}$ is discussed and related to topological properties of $\text{G}\text{H}$. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.     

Brownian motion on a manifold as a limit of Brownian motions with drift

Let ?ⁿ be n-dimensional Euclidean space and let M ? ?ⁿ be a smooth compact m-dimensional Riemannian manifold (without boundary) embedded in ?ⁿ. By a Brownian motion on M we mean a Markovian process whose transition semigroup is defined by the generator ?½Δ_M, where Δ_M stands for the Laplace-Beltrami operator on M (see, e.g., [2]). This note extends a series of papers in which a measure generated by a Brownian motion on M on the space of trajectories (with values in M) can be represented as the weak limit of measures on the space of trajectories in the ambient space ?ⁿ (see [7–10]). Namely, we claim that a sequence of diffusion processes on ?n which are Brownian motions with drift (in the direction of the manifold) with infinitely increasing modulus converges in distribution to a Brownian motion on the manifold.     

Solid solution formation in the systems CuMIIIX2-AgMIIIX2 where MIII=Al,Ga, In and X2=S,Se

A study of solid solution formation in the systems CuAlX₂-AgAlX₂, CuGaX₂-AgGaX₂ and CuInX₂-AgInX₂, where X=S, Se, has shown that when M^III=Al and Ga, CuM^IIIX₂ and AgM^IIIX₂ were not completely miscible. The CuInX₂-AgInX₂ system, however, showed complete solid solubility. The limits of solid solubility are explained in terms of the c/a ratio, and the internal atomic coordinate u. The lattice constant a is a linear function of composition, while c bows upwards. This behavior is also discussed in terms of trends in 2-c/a.     

ΔB = 2 transitions in supersymmetric theories

We carry out a systematic analysis of ΔB = 2 interactions in supersymmetric theories. The selection rules in ΔB = 2 transition depend on the relative value of M (the mass scale that characterizes the ΔB = 2 interactions) and Λ_s (the super-symmetry-breaking scale). In particular, if M ? 10⁴GeV and Λ_s ～ 10²GeV, the effective ΔB = 2 interactions induce NN annihilation in a nucleus yielding two kaons in the final state while processes with only one or zero kaons are suppressed by mixing angles. On the other hand, if M ? 10⁴GeV, then supersymmetry does not imply any additional selection rules beyond those of ordinary (non-supersymmetric) theories.     

A family of angle-moments proportional to r-n,n = 1,2,…, in free space

The moments M_n(r) ≡ 1/2 ∝^2π₀ dθ sinⁿ θ I(r,θ) of the intensity I(r, θ) in free space surrounding a spherical object emitting radiation with an arbitrary directional dependence are shown to be exactly proportional to r^-(n+1), n = 0, 1,….     

Spontaneous compactification in generalized Candelas-Weinberg models

In their recent work on the dimensional reduction, Candelas and Weinberg considered a model which is compactified into a direct product space of the Minkowski space (M₄) and an N-dimensional sphere (S_N). In the present paper we investigate generalized models of their type which are compactified into M₄ × S_M × S_N and M₄ × S_M × CP₂. The compactification is caused by the quantum loop effect due to a large number of matter fields. The conditions for the vacuum stability are studied. Numerical computation of the loop effect is undertaken, and it is shown that some of the models of the type M₄ × S_M × S_N admit a stable solution which has finite circumferences of both of the extra spaces and positive coupling constants of the Einstein-Yang-Mills theory in four dimensions.     

The Klein-Gordon operator in conformal space

We consider the Minkowski space M₄ as a local chart of a compact differentiable pseudo-Riemannian manifold M⁴_c, on which the whole conformal group $\text{O(2, 4)}\text{Z}{}_2$ acts continuously. We investigate the conditions under which functions or differential operators on the space M₄ can be uniquely continued to the conformal manifold M⁴_c. This is done by using methods well-known in the theory of differentiable manifolds. In particular, we show that the Klein-Gordon operator □+m² can be uniquely continued to the space M⁴_c and we discuss the conformal invariance of the Klein-Gordon equation on the manifold M⁴_c.     

A steeply-rising potential in tensor gauge theory

Massive tensor gauge mesons produce a steeply rising “potential” of the type M²r² in a non-perturbative classical solution of an Einstein-like equation. Such a potential is shown to give rising Regge trajectories.     

Toward isovector M1 transitions in odd-odd N = Z nuclei

IsovectorM1 transitions between low-lying T=1 and T=0 states in odd-odd N = Z nuclei are discussed. The data on low-spin states in the odd-odd nuclei ⁴⁶V and ⁵⁰Mn investigated with the ⁴⁶Ti(p, nγ)⁴⁶V and ⁵⁰Cr(p, nγ)⁵⁰Mn fusion evaporation reactions at the FN-TANDEM accelerator in Cologne are reported. A simple explanation of the enhancement of the M1 transitions is given in terms of quasideuteron configurations. The fragmentation of the strong M1 transitions is shown to be due to the coupling of the two-particle configurations to the rotating core.     

Pseudo-supersymmetry, consistent sphere reduction and Killing spinors for the bosonic string

Certain supergravity theories admit a remarkable consistent dimensional reduction in which the internal space is a sphere. Examples include type IIB supergravity reduced on S⁵, and eleven-dimensional supergravity reduced on S⁴ or S⁷. Consistency means that any solution of the dimensionally-reduced theory lifts to give a solution in the higher dimension. Although supersymmetry seems to play a role in the consistency of these reductions, it cannot be the whole story since consistent sphere reductions of non-supersymmetric theories are also known, such as the reduction of the effective action of the bosonic string in any dimension D on either a 3-sphere or a (D−3)-sphere, retaining the gauge bosons of SO(4) or SO(D−2) respectively. We show that although there is no supersymmetry, there is nevertheless a natural Killing spinor equation for the D-dimensional bosonic string. A projection of the full integrability condition for these Killing spinors gives rise to the bosonic equations of motion (just as happens in the supergravity examples). Thus it appears that by extending the notion of supersymmetry to “pseudo-supersymmetry” in this way, one may be able to obtain a broader understanding of a relation between Killing spinors and consistent sphere reductions.     

A Class of Super Dense Stars Models Using Charged Analogues of Hajj-Boutros Type Relativistic Fluid Solutions

We present a spherically symmetric solution of the general relativistic field equations in isotropic coordinates for perfect charged fluid, compatible with a super dense star modeling. The solution is well behaved for all the values of Schwarzschild parameter u lying in the range 0 < u < 0.1727 for the maximum value of charge parameter K = 0.08163. The maximum mass of the fluid distribution is calculated by using stellar surface density as ρ _b = 4.6888×10¹⁴g cm^?3. Corresponding to K = 0.08 and u _max = 0.1732, the resulting well behaved solution has a maximum mass M = 0.9324M _⊙ and radius R = 8.00 and by assuming ρ _b = 2×10¹⁴g cm^?3 the solution results a stellar configuration with maximum mass M = 1.43M _⊙ and radius R _b = 12.25 km. The maximum mass is found increasing with increasing K up to 0.08. The well behaved class of relativistic stellar models obtained in this work might has astrophysical significance in the study of internal structure of compact star such as neutron star or self-bound strange quark star like Her X-1.     

Geometry of multidimensional universes

LetG be a compact group of transformation (global symmetry group) of a manifoldE (multidimensional universe) with all orbits of the same type (one stratum). We studyG invariant metrics onE and show that there is one-to-one correspondence between those metrics and triples (g _μv,A _μ ^ä ,h _αβ), whereg _μv is a (pseudo-) Riemannian metric on the space of orbits (space-time),A _μ ^ä is a Yang-Mills field for the gauge groupN|H, whereN is the normalizer of the isotropy groupH inG, andh _αβ are certain scalar fields characterizing geometry of the orbits (internal spaces). The scalar curvature ofE is expressed in terms of the component fields onM. Examples and model building recipes are also given. The results generalize those of non-abelian Kaluza-Klein theories to the case where internal spaces are not necessarily group manifolds.