C (2) N+1 Ruijsenaars–Schneider Models

We define the notion of C ⁽²⁾ _N+1Ruijsenaars–Schneider models and construct their Lax formulation. They are obtained by a particular folding of the A _2N+1 systems. Their commuting Hamiltonians are linear combinations of Koornwinder–van Diejen external fields Ruijsenaars–Schneider models, for specific values of the exponential one-body couplings but with the most general two double-poles structure as opposed to the formerly studied BC _N case. Extensions to the elliptic potentials are briefly discussed.     

On characteristic initial-value and mixed problems

Existence and uniqueness are proved for certain initial-value problems for hyperbolic systems of second-order differential equations, each having the same principal partg ^ab _{a b} (whereg ^ab is indefinite). The initial data are given on two intersecting hypersurfaces H₁ andH ₂ one of which-sayH ₁-is a characteristic surface. The other surface,H ₂, is permitted to be spacelike, timelike, or characteristic. For Einstein's vacuum field equations we restrict ourselves to anH ₂ that is characteristic. Unlike the Cauchy problem, the data have to be necessarily of a considerably higher differentiability class (Sobolev classW ^2m–1) than the solution (Sobolev classW ^m ). On the other hand, in the mixed problem (where one of the surfaces is spacelike) corner conditions have to be fulfilled. The occurrence of constraint equations for Einstein's metric field and for harmonic coordinates can be prevented by solving certain ordinary differential propagation equations.     

The pentad rotation-vibrational states of 12CD4: Wavenumber analysis of infrared and Raman spectra of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands

The so-called pentad of ¹²CD₄ consists of the vibrational states v₁ = 1(symmetry A₁), v₃ = 1(F₂), v₂ = 2(A₁ + E), v₂ = v₄ = 1(F₁ + F₂), and v₄ = 2(A₁ + E + F₂). All states are located in the 1950 to 2250-cm^?1 region and all are strongly interacting. In the present work we have assigned more than 5000 infrared rotation-vibrational transitions and 163 isotropic Raman transitions from the vibrational ground state to the pentad. We have used infrared and Raman spectra of a resolution better than 0.01 cm^?1. From the experimental wavenumbers 2567 pentad rotation-vibrational energy levels with J ≦ 20 have been determined. These levels are reported in the paper. The levels have been used for refinements of the spectroscopic constants of two physically different effective Hamiltonians for the pentad states. For all levels with J ≦ 12 an unweighted standard deviation of 0.004 cm^?1 is obtained for both Hamiltonians, whereas the standard deviation increases more or less rapidly with J above 12 due to the imperfections of the Hamiltonians. The values of the spectroscopic constants of both Hamiltonians (85 and 106, respectively) are reported and the effects of the approximations are discussed.     

Convexity relation for energy in quantum mechanics

The dependence of the ground-state energy E of a quantum-mechanical system on the parameter λ appearing linearly in the Hamiltonian is studied. A variation of the scale makes it possible to supplement the convexity-concavity relation for energy as a function of this parameter with a refined relation between the energies of systems that go over to one another upon a change in the particle charges or masses. This relation follows from the fundamentals of quantum mechanics and is valid for exact energies of the systems being considered. Its application does not require calculating wave functions and makes it possible to determine the boundaries of the ground-state energy level and the boundaries of the region of obvious stability of various systems. The results of applying the theory to m ₁⁺ m ₂⁺ m ₃⁻ and m ₁⁺ m ₂⁺ m ₄⁻ three- and four-particle mesic atoms and molecules featuring particles of various mass are presented.     

Spectroscopic observation of helium-ion- and hydrogen-catalyzed hydrino transitions

Four predictions of Mills’ Grand Unified Theory of Classical Physics (GUTCP) regarding atomic hydrogen undergoing a catalytic reaction with certain atomized elements and ions which resonantly, nonradiatively accept integer multiples of the potential energy of atomic hydrogen, m · 27.2 eV wherein m is an integer, have been confirmed experimentally. Specifically, a catalyst comprises a chemical or physical process with an enthalpy change equal to an integer multiple m of the potential energy of atomic hydrogen, 27.2 eV. For He⁺ m = 2, due to its ionization reaction to He²⁺, and two H atoms formed from H₂ by collision with a third, hot H can also act as a catalyst with m = 2 for this third H. The product is H(1/p), fractional Rydberg states of atomic hydrogen called “hydrino atoms” wherein n = 1/2, 1/3, 1/4, …, 1/p(p≤137 is an integer) replaces the well-known parameter n = integer in the Rydberg equation for hydrogen excited states. The predictions for the hydrino reaction of (1) pumping of the catalyst excited states, (2) characteristic EUV continuum radiation, (3) fast H, and (4) hydrino products were observed in multiple catalyst-hydrogen plasma systems.     

Multimode q-Oscillator Algebras with q2(k+1) = 1 and Their Bargmann–Fock Representations

A countably infinite class of multimode q-oscillator algebrasA _k;m (k = 1, 2, ..., m = 1, 2, ...) is obtained with the aid of the R-matrix method in quantumgroup theory for q ^2(k+1) = 1. The related Fock spaces are given and they showthat the q-particle systems described by A _k;m obey a generalized Pauli exclusionprinciple. The algebras A _k;m are represented on a kind of q-holomorphic functionspaces B(¯) _k;m which are generalizations of the usual Bargmann–Fock spaceswith many Grassmann variables and have Hilbert space structures with the scalarproduct given by an algebraically defined integral. When taking k = 1 or k , all of the above are reduced to the corresponding results for the usual multimodefermion and boson systems, respectively.     

Spontaneous Symmetry Breaking in Presence of Electric and Magnetic Charges

Starting with the definition of quaternion gauge theory, we have undertaken the study of SU(2) _e ×SU(2) _m ×U(1) _e ×U(1) _m in terms of the simultaneous existence of electric and magnetic charges along with their Yang-Mills counterparts. As such, we have developed the gauge theory in terms of four coupling constants associated with four-gauge symmetry SU(2) _e ×SU(2) _m ×U(1) _e ×U(1) _m . Accordingly, we have made an attempt to obtain the abelian and non-Abelian gauge structures for the particles carrying simultaneously the electric and magnetic charges (namely dyons). Starting from the Lagrangian density of two SU(2)×U(1) gauge theories responsible for the existence of electric and magnetic charges, we have discussed the consistent theory of spontaneous symmetry breaking and Higgs mechanism in order to generate the masses. From the symmetry breaking, we have generated the two electromagnetic fields, the two massive vector W ^± and Z ⁰ bosons fields and the Higgs scalar fields.     

过渡族元素掺杂BaTiO3-Tb1-xDyxFe2-y层状复合材料中的磁电效应

用溶胶-凝胶法制备1.0%mol Mn,Cr,Co掺杂 BaTiO₃(BTO)粉体,在1350℃下烧结成多晶陶瓷样品.X射线衍射和差示扫描量热分析表明,室温下掺杂BaTiO₃具有四方钙钛矿结构;居里点和相变潜热随Cr,Mn,Co掺杂逐渐降低.将掺杂BaTiO₃与Tb_1-xDy_xFe_2-y(TDF)胶合制成双层磁电复合材料,并研究了Cr:BTO-TDF,Mn∶BTO-TDF,Co:BTO-TDF层状复合材料中的磁电效应.实验表明,在340×80 A·m^-1偏置磁场下, Cr:BTO-TDF的横向磁电电压系数达到最大值586 mV·cm^-1·(80 A·m^-1)^-1.在400×80 A·m^-1偏置磁场下,Mn∶BTO-TDF和Co:BTO-TDF的横向磁电电压系数的最大值分别为480 mV·cm^-1·(80 A·m^-1)^-1和445mV·cm^-1·(80 A·m^-1)^-1.研究表明掺杂BaTiO₃-TDF层状复合材料中具有较强的磁电耦合.作为无铅压电材料,掺杂BaTiO₃制备的磁电效应器件颇具应用前景. 关键词： 磁电效应 双层复合材料 3')" href="#">掺杂BaTiO₃ 1-xDy_xFe_2-y')" href="#">Tb_1-xDy_xFe_2-y     

Surface,micellar, and thermodynamic properties of antidepressant drug nortriptyline hydrochloride with TX‐114 in aqueous/urea solutions

This paper deals with a comprehensive study of the mixed micellization and adsorption behavior of mixed systems enclosing an amphiphilic antidepressant drug nortriptyline hydrochloride (NOT) and Triton X‐114 (TX‐114) (nonionic surfactant) in aqueous/urea (500 mmol·kg^?1 and 1000 mmol·kg^?1) solutions by tensiometric method. The NOT is used for the cure of depression. For comparison purpose cmc value of pure drug NOT was also evaluated by conductimetric technique. Different theoretical models like Clint, Rubingh, and Rosen were used to get information about the nature of interaction between the components in bulk and at the interface. Because of the occurrence of urea increase in the surface charge of the micelles was obtained resulting a delay of the micelles formation. The cmc values of the mixed systems of NOT and TX‐114 were found to be in between the cmc values of pure components, which signify nonideal mixed system having attractive interactions in the absence and presence of urea. Various parameters such as micellar mole fractions of TX‐114 (X₁^m, X₁^σ) in solution and at interface, interaction parameter (β^m/β^σ) in solution and at interface, and activity coefficient in solution and at interface were evaluated and discussed using Rubingh's and Rosen's models. Surface excess (Γ_max) increases that means minimum area per head group (A_min) decreases as mole fraction (α₁) of TX‐114 increases in the absence/presence of urea. Different thermodynamic parameters have been calculated and discussed. The ?G⁰_m values achieved are all negative both in the absence and occurrence of urea.     

Superposition model in electron magnetic resonance spectroscopy – a primer for experimentalists with illustrative applications and literature database

We review applications of the superposition model (SPM) in EMR area, which enables semi-empirical modeling of zero-field splitting (ZFS) parameters (ZFSPs) for transition ions in crystals by separation of geometrical and physical information. Nomenclature used for ZFS and crystal field (CF) Hamiltonians is presented to expose common framework underlying two independent implementations: SPM/ZFS and SPM/CF, which require distinct model parameters. SPM/ZFSP applications in EMR area for S-state 3d⁵ (4f⁷) ions and 3d^N ions with orbital singlet ground state are reviewed. SPM/ZFS methodology for ML_n complexes [central metal (M) ion surrounded by n ligands (L)] with specific symmetry is presented. SPM-related computer packages combined with other methods, role of axis systems in SPM analysis, and structural models for several ion-host systems, are discussed. Extensive survey of SPM/ZFS applications is provided to elucidate usefulness of SPM modeling for interpretation of ZFSPs. This review is geared for EMR practitioners interested in practical utilization of SPM/ZFS (or SPM/CFP) analysis. Database of SPM/ZFS references is compiled for studies of single molecule magnets and single ion magnets based on transition ions. Due to its comprehensiveness, suitable sets of model parameters required for practical utilization SPM/ZFS may be easily located using source references as pointers.     

Generating functions for the affine symplectic group

The generating function notion is used to give a representation of the inhomogeneous symplectic group as group of affine canonical transformations. Then the classical action for linear mechanical systems, the Hamiltonians of which belong to the algebrah sp(2n,R), is deduced; it is explicitely constructed for all the Hamiltonians belonging to some particular subalgebras ofh sp(2n,R). The metaplectic representation ofW Sp(2n,R) onL ²(R) and the solutions of the Schrödinger equation for linear systems are also obtained in terms of generating functions. The Maslov index is explicitly constructed for the quantum corresponding sets of Hamiltonians considered in the classical case.Members of the Centre National de la Recherche Scientifique (France)Recipient of aid from the Ministère de l'Education du Gouvernement du Québec     

Coherent Exchange Cluster Approach for two-dimensional disordered Heisenberg spin systems

The spin wave properties of disordered two-dimensional and quasi two-dimensional Heisenberg spin systems, with an antiferromagnetic ground state (Neèl state) induced by single-ion anisotropy, are discussed within a Coherent Exchange Cluster Approach (Cluster CEA).The configuration averaged Green's functions are described by an effective spin wave Hamiltonian, with two sets of complex and energy dependent coherent exchange integralsJ _lm ¹ (E) andJ _lm ² (E) appropriate to the consideration of two different spins of the binary alloy constituents.J _lm ¹ andJ _lm ² , depending only on the distance of the sitesl andm, are taken to be non zero only for nearest neighbours. The remaining two quantitiesJ ¹(E) andJ ²(E) are determined self-consistently from the requirement that the most important matrix elements of the scatteringT matrix vanish when the configuration averaging has been performed.Numerical results are presented for the antiferromagnetic quasi two-dimensional systems K₂Ni _c Mn_1-c F₄ and Rb₂Fe _c Mn_1-c F₄.Both the density of states and the transverse susceptibilities, determining essentially the neutron scattering cross-sections, are calculated.The density of spin wave states for K₂Ni _c Mn_1-c F₄ is compared for different concentrations with exact computer calculations for finite 30 × 30 arrays. The agreement is excellent.Based on the thesis of H.J. Schlichting, Fachbereich Physik der Universität Hamburg, 1974.     

Nonleptonic Interactions of Kaons in the Quark Confinement Model

Nonleptonic, electromagnetic decays of K-mesons and K°–K̄° transition are treated with the effective Hamiltonians with ΔS = 1, 2. Matrix elements of four-quark operators are calculated in the framework of Quark Confinement Model. The account of the intermediate scalar mesons turns out to allow to explain ΔI = 1/2 rule. The account of intermediate scalar and pseudo-scalar states leads to experimental value of mass difference of K_L°–K_S° mesons. The obtained values for nonleptonic and electromagnetic decay widths as well as mass difference Δm_LS are in good agreement with experimental data.     

Acoustical and excess properties of {1-hexanol + n-hexane, or n-octane, or n-decane} at (298.15, 303.15, and 308.15) K

Densities (ρ) and speeds of sound (u) for the binary mixtures of 1-hexanol with n-hexane, n-octane and n-decane have been measured over the entire composition range at 298.15, 303.15 and 308.15 K. The dynamic viscosities (η) for these systems have been measured at 298.15 K. From experimental data, excess molar volumes (V_m^E), molar isentropic compressibility (K_s,m), excess molar isentropic compressibility (K_s,m^E), deviation in speed of sound (u^D) from their ideal values (u^id) in an ideal mixture, and excess free volumes (V_f^E) have been calculated. The excess functions have also been correlated with the Redlich–Kister polynomial equation. The viscosity data have been analysed in terms of some semi-empirical equations. The theoretical values of speed of sound (u) and isentropic compressibility (κ_S) have also been estimated using the Prigogine–Flory–Patterson (PFP) theory with the van der Waals (vdW) potential energy model and the results have been compared with experimental values. The effect of chain-length of n-alkanes as well as the temperature on the excess properties has also been studied.