General solutions of the Monge-Ampère equation in n-dimensional space

It is shown that the general solution of a homogeneous Monge-Ampère equation in n-dimensional space is closely connected with the exactly (but only implicitly) integrable system ∂ξ_j/∂x₀ + Σ_k=1ⁿ⁻¹ ξ_k ∂ξ_j/∂x_k = 0 Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Ampère equation.     

The quantum mechanics of affine variables

We study the wrapping of N-type IIB Dp-branes on a compact Riemann surface Σ in genus g>1 by means of the Sen–Witten construction, as a superposition of N′-type IIB Dp′-brane/antibrane pairs, with p′>p. A background Neveu–Schwarz field B deforms the commutative C-algebra of functions on Σ to a non-commutative C-algebra. Our construction provides an explicit example of the N′→∞ limit advocated by Bouwknegt-Mathai and Witten in order to deal with twisted K-theory. We provide the necessary elements to formulate M(atrix) theory on this new C-algebra, by explicitly constructing a family of projective C-modules admitting constant-curvature connections. This allows us to define the g>1 analogue of the BPS spectrum of states in g=1, by means of Donaldson’s formulation of the Narasimhan–Seshadri theorem.     

Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.     

Fabrication and study of a metal-clad planar waveguide based biosensor

A metal-clad planar optical waveguide biosensor having five layer structure has been fabricated to study the detection of Pseudomonas and Pseudomonas-like bacteria. This waveguide is designed to increase the overlap of the evanescent field extension from the sensor face with the micro-scale biological objects in the bulk solution, to place most of the entire volume of the bacteria within the evanescent field. The results presented here leads to a significant optimization of the important design parameters to sense micro-scale biological objects. We have compared our computed results with the results obtained by similar non-metallic clad biosensor. The effect of affinity-layer refractive index on the sensitivity of these planar waveguides is also studied. We have shown this for some special cases by obtaining reflection dips at the particular angle of incidence. Our observations show that the metal-clad planar optical waveguide biosensor having higher affinity refractive index will give better sensitivity than other similar non-metallic clad biosensor. The validation of metal-clad planar optical waveguide sensor for the detection of Pseudomonas aeruginosa bacterium is also made.     

On the pp → ppη(η′) reactions near threshold

The production rate for η′ in pp → ppη′ at rest is calculated in a covariant one boson exchange model, previously applied to study π⁰ and η production in NN collisions. The transition amplitudes for the elementary BN → η′N processes with B being the meson exchanged (B = π, σ, η, , ω and a₀) are taken to be the sum of s- and u-channels with a nucleon in the intermediate states, and an a₀ meson pole in a t-channel. The couplings of the η′ to hadrons are a factor 0.4 weaker than the respective η-hadron couplings, as suggested by a quark model and a singlet-octet mixing angle θ = −23°. The model reproduces near threshold cross sections for the quasielastic processes π⁻p → nη(η′) and pp → ppη(η′) reactions.     

Effect of higher-order electric and magnetic multipolar transitions on Rayleigh light scattering in liquids

We calculate the effect of magnetic dipolar transitions, related with the polarizabilities B″, ′, and ″ and electric-quadrupole transitions, related with the polarizabilities C′, ″, and ′, on dynamical Rayleigh light scattering by isotrophic media. To this aim, we introduce molecular scattering factors of the fourth, fifth and sixth orders related with these polarizabilities. For molecules with 76 magnetic point group symmetries these transitions are found to affect the time-dependent intensities and depolarization ratios of scattered light. Among the 76 groups, the molecules belonging to 23 groups exhibit natural (transmission and Rayleigh) optical activity, whereas the point group m shows Rayleigh activity only. The effects in question result moreover from the contribution of magnetic-dipole and electric-quadrupole transitions. For isotropic molecules, the above transitions lead to partial depolarization of the scattered light wave. Our use of i- and c-tensors as well as Hermitian and anti-Hermitian components permits the extension of our discussion to regions of absorption as well as cases of full symmetry of the molecules.     

B→ηlν decays and the flavor-singlet form factors

We study semileptonic decays B→η^(′)lν, taking into account the flavor-singlet contribution (F^singlet₊) to the B→η^(′) form factors, which arises from the two-gluon emission in a decaying B meson. It has been recently pointed out that, in addition to large weak annihilation effects, the unknown value of F^singlet₊ prevents accurate theoretical estimates in the analysis of B→η′K decays in QCD factorization. We present a certain method to determine F^singlet₊ with a reasonable accuracy, using B→η^(′)lν and B→πlν decays. We also investigate the possible effect of F^singlet₊ on the estimated branching ratios (BRs) for B→η^(′)lν and find that the BR for B→η′lν is particularly sensitive to the effect of F^singlet₊.     

Scaling limit of deeply virtual compton scattering

I outline a perturbative QCD approach to the analysis of the deeply virtual Compton scattering process γ^*p → γp′ in the limit of vanishing momentum transfer t = (p′ − p)². The DVCS amplitude in this limit exhibits a scaling behavior described by two-argument distributions F(x,y) which specify the fractions of the initial momentum p and the momentum transfer r ≡ p′ − p carried by the constituents of the nucleon. The kernel R(x,y;ξ,η) governing the evolution of the non-forward distributions F(x,y) has a remarkable property: it produces the GLAPD evolution kernel P(x/ξ) when integrated over y and reduces to the Brodsky-Lepage evolution kernel V(y,η) after the x-integration. This property is used to construct the solution of the one-loop evolution equation for the flavor non-singlet part of the non-forward quark distribution.     

Pion–nucleon amplitude near threshold: the sigma-term and scattering lengths beyond few loops

The pion–nucleon amplitude is considered in the vicinity of the elastic scattering threshold within a relativistic dynamical model dressing the πNN and πNΔ vertices self-consistently with an infinite number of meson loops. The dressing is formulated as solution of a system of coupled integral equations incorporating unitarity, crossing symmetry and analyticity constraints. The calculated scattering lengths and the sigma-term agree with recent data analyses. The dressing is important in this model both below and at threshold. The contribution of the Δ resonance is discussed, including effects of the consistent dressing of the πNΔ vertex. A comparison with the approaches of chiral perturbation theory and the Bethe–Salpeter equation is outlined.     

The Boltzmann equation for very hard particles

The nonlinear Boltzmann equation is solved analytically for general initial distributions in a (spatially homogeneous) system of very hard particles (VHP) with two translational degrees of freedom and with a transition probability for binary collisions (vw →v′w′) proportional to δ(v² + w² − v′² −w′²).

The scattering cross-section corresponding to this model increases as the square root of the collision energy (hence the name VHP-model). As the total energy of the system is finite, essentially no highly energetic particles are present to probe the unphysical high-energy behavior of the cross-section.

The VHP-model is extended to a multicomponent mixture of particles, and solved by the same technique, viz. Laplace transformation. An analogous discrete variable model is solved by a generating function method.

Finally the solutions of the nonlinear and linearized Boltzmann equation are compared. Their large-energy behavior at a fixed (large) time is different; their large-time behavior at a fixed energy is the same.     

Anisotropic dielectric properties of PbYb1/2Ta1/2O3 single crystals

PbYb_1/2Ta_1/2O₃ single crystals were obtained for the first time. They were grown by the flux method. The PbOPbF₂B₂O₃ system was used as a solvent. Dielectric investigations were carried out in 1 0 0_c, 1 1 0_c and 1 1 1_c pseudocubic directions. These studies pointed to anisotropy of dielectric properties. Frequency-independent ε′(T) and ε″(T) maxima related to the antiferroelectric–paraelectric (AFE—PE) phase transition are observed for all directions at 562 K. The frequency-dependent ε′(T) and ε″(T) maxima near 400 K related to the ferroelectric (FE)–AFE phase transition are observed only in 1 1 1_c direction. The hysteresis loops were observed in this direction only. These results point that ferroelectric relaxor properties appear only in 1 1 1_c direction. We propose to consider the ferroelectric phase as ferrielectric one.     

Photoproduction of Θ and other pentaquark states

We present constraints on the relative photoproduction cross sections of positive parity pentaquark states, Σ₅, Λ₅, and N₅, based on a minimum phenomenology gained in and their baryon–meson couplings as in the work of Close and Dudek. The possibility of anomalous signals in γp→K⁰_S(Θ⁺;Σ_d⁺) is discussed. We emphasize the importance of comparing with “conventional” states such as γN→KΣ(1660).     

Modal attenuation in metal-clad graded-index slab optical waveguides

The paper presents the influence of refractive profile shape on the distribution of modal attenuation in planar metal-clad optical waveguide structures. A calculation method has been presented in which we applied the Snyder–Love expression on modal attenuation coefficients and matrix method 4 × 4 for the analysis of planar waveguides. The obtained results are almost identical with the exact results for refractive profiles: the parabolic, exponential, Gaussian and linear ones. It has been demonstrated that the applied calculation method can be used in waveguides of any profiles of the refractive index.     

Electrical properties of pure and Li2O-doped CuO/Fe2O3 system precalcined at different temperatures

The electrical properties of pure and Li₂O-doped CuO/Fe₂O₃ solids were investigated. Pure and variously doped solids were subjected to thermal treatment at 1073–1273 K and the amount of dopant was varied between 0.84 to 3.36 mol%. The effect of precalcination temperature and amount of Li₂O added on the electrical conductivity σ, activation energy E_a and dielectric constant * were studied. The variation of ′ and ″ as a function of frequency for pure and variously doped solids precalcined at different temperatures was also investigated. The results obtained were discussed.     

用转移矩阵法研究LNN型非线性平面光波导

用转移矩阵法数值分析了芯区和衬底为非线性介质、覆盖层为线性介质结构平面光波导的传播特性,包括TM的模场分布和功率与有效折射率之间关系的分析.解析地表达了模式本征方程和功率分布,对非线性介质中电场强度与介质非线性系数的关系进行了研究.计算结果表明,TM的模场分布和功率与有效折射率及介质的非线性系数有关.     

Graduation of electron spectrometer intensity scale. Part 2. How to do it

Graduation function G(E′) absolute values have been determined experimentally for the first time for the intensity scale of an ordinary Auger electron spectrometer. The determination of G(E′) includes creation of an original standard signal and measurement of the consequent reaction of the spectrometer using a “giant rectangular modulation” operation mode, integration of the measurand, and use of an original G(E′) definition. The experimental values of G(E′) are presented in the correct dimensional units for a pass energy range E′ = 150–1000 eV. A non-monotonous behaviour of G(E′), a strong dependence of G(E′) on the multiplier entrance bias voltage, and a discrepancy between the graduation functions of spectrometers of the same type with CMA are demonstrated. Possibilities are predicted for a similar G(E′) determination for other types of spectromer.     

Upper bound on all products of R-parity violating couplings λ′ and λ″ from proton decay

We prove that any product of R-parity violating couplings λ′ (L-violating) and λ″ (B-violating) can be strongly restricted by proton decay data. For any pair λ′ and λ″ the decay exists at least at one loop level. For squark masses below 1 TeV we find the conservative bounds |λ′ · λ″| < 10⁻⁹ in absence of squark flavor mixing, and |λ′ · λ″| < 10⁻¹¹ when this mixing is taken into account. We study the dependence of the bounds on the flavor basis in which R-parity breaking couplings are determined.     

Search for narrow NNπ resonances in exclusive pp→ppππ measurements

Narrow structures in the range of a few MeV have been searched for in ppπ⁺ and ppπ⁻ invariant mass spectra (M_ppπ⁺ and M_ppπ⁻) obtained from exclusive measurements of the pp→ppπ⁺π⁻ reaction at T_p=725,750 and 775 MeV using the PROMICE/WASA detector at CELSIUS. The selected reaction is particularly well suited for the search for dibaryon resonances decoupled from NN and/or NΔ. In the mass range 2020 MeV/c²<m_dibaryon<2085 MeV/c² no narrow structures could be identified on the 3σ level of statistical significance neither in M_ppπ⁻ nor in M_ppπ⁺ giving an upper limit (95% C.L.) for dibaryon production in this reaction of σ<20 nb.     

Supersymmetric contributions to direct CP violation in K→ππγ decays

We analyze the supersymmetric contributions to direct–CP–violating observables in K→ππγ decays induced by gluino–mediated magnetic–penguin operators. We find that ε′_+−γ and the differential width asymmetry of K^±→π^±π⁰γ decays could be substantially enhanced with respect to their Standard Model values, especially in the scenario where ε′/ε is dominated by supersymmetric contributions. These observables could therefore provide a useful tool to search for New Physics effects in |ΔS|=1 transitions, complementary to ε′/ε and rare decays.