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Standard interpolatory subdivision schemes and their underlying interpolating refinable functions are of interest in CAGD, numerical PDEs, and approximation theory. Generalizing these notions, we introduce and study n s -step interpolatory M -subdivision schemes and their interpolating M -refinable functions with n s ∈ N ∪ { ∞ } and a dilation factor M ∈ N \ { 1 } . We completely characterize C m -convergence and smoothness of n s -step interpolatory subdivision schemes and their interpolating M -refinable functions in terms of their masks. Inspired by n s -step interpolatory stationary subdivision schemes, we further introduce the notion of r-mask quasi-stationary subdivision schemes, and then we characterize their C m -convergence and smoothness properties using only their masks. Moreover, combining n s -step interpolatory subdivision schemes with r-mask quasi-stationary subdivision schemes, we can obtain r n s -step interpolatory subdivision schemes. Examples and construction procedures of convergent n s -step interpolatory M -subdivision schemes are provided to illustrate our results with dilation factors M = 2 , 3 , 4 . In addition, for the dyadic dilation M = 2 and r = 2 , 3 , using r masks with only two-ring stencils, we provide examples of C r -convergent r-step interpolatory r-mask quasi-stationary dyadic subdivision schemes. [ABSTRACT FROM AUTHOR]

When constructing multivariate framelets, it is often unavoidable to work with matrices of multivariate trigonometric polynomials and complicated matrix decomposition problems. These problems become even harder when good properties such as high-order vanishing moments are required on the framelets. In this paper, we establish a new method for constructing multivariate dual framelets with high-order vanishing moments. The underlying scheme of our algorithm is the famous Mixed Extension Principle that allows us to derive the high-pass filters (or framelet generators) from a given pair of refinable filters with high-order linear-phase moments. Our method only involves two steps: (1) directly constructing the first few pairs of high-pass filters by using the linear-phase moment conditions of the refinement filters; (2) solving a system of linear equations to obtain the rest of the high-pass filters. Both are easy to implement for scientific computation, regardless of what dimension or dilation matrix we work with. Apart from high-order vanishing moments, we will see that if the refinement filters take coefficients from some subfield of ℂ that is closed under complex conjugation, so do the high-pass filters. Furthermore, our algorithm gives the upper bounds for the number of high-pass filters in arbitrary dimensions. At the end of the paper, we will give several illustrative examples, from which we can also see that the support sizes of the high-pass filters are comparable with those of the refinement filters. [ABSTRACT FROM AUTHOR]

Laws of physical chemistry such as quantum mechanics, laws of chemical kinetics, and thermodynamics have been employed as a potential tool to generate some converging sum rules. Special emphasis has been given to Rayleigh–Schrödinger perturbation theory and the use of delta function potential to generate a number of sum rules. [ABSTRACT FROM AUTHOR]

Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD and for building Hermite wavelets in numerical PDEs. In this paper, we introduce a notion of generalized Hermite (dyadic) subdivision schemes and then we characterize their convergence, smoothness and underlying matrix masks with or without interpolation properties. We also introduce the notion of linear-phase moments for achieving the polynomial-interpolation property. For any given integer m ∈ N , we constructively prove that there always exist convergent smooth generalized Hermite subdivision schemes with linear-phase moments such that their basis vector functions are spline functions in C m (R d) and have linearly independent integer shifts. As by-products, our results resolve convergence, smoothness, and existence of Lagrange, Hermite, or Birkhoff subdivision schemes. Even in dimension one our results significantly generalize and extend many known results on extensively studied univariate Hermite subdivision schemes. To illustrate the theoretical results in this paper, we provide examples of convergent generalized Hermite subdivision schemes with symmetric matrix masks having short support and smooth basis vector functions with or without interpolation property. [ABSTRACT FROM AUTHOR]

Hermite interpolation property is desired in applied and computational mathematics. Hermite and vector subdivision schemes are of interest in CAGD for generating subdivision curves and in computational mathematics for building Hermite wavelets to numerically solve partial differential equations. In contrast to well-studied scalar subdivision schemes, Hermite and vector subdivision schemes employ matrix-valued masks and vector input data, which make their analysis much more complicated and difficult than their scalar counterparts. Under the spectral condition or the spectral chain, analysis of Hermite subdivision schemes through factorization of matrix-valued masks has been extensively studied in the literature and sufficient conditions have been given for the convergence of Hermite subdivision schemes through the contractivity of their derived subdivision schemes. We contribute to the study of Hermite subdivision schemes from a different perspective by investigating vector subdivision operators acting on vector polynomials and by establishing connections among Hermite subdivision schemes, vector cascade algorithms, and refinable vector functions. This approach allows us to characterize and construct all masks for Hermite subdivision schemes, to explain the spectral condition and spectral chain in the literature, to characterize convergence and smoothness of Hermite subdivision schemes using vector cascade algorithms, and to provide simple factorizations of Hermite masks through the normal form of matrix-valued masks such that the Hermite subdivision scheme is convergent if and only if its derived subdivision scheme is contractive. We also constructively prove that there always exist arbitrarily smooth convergent Hermite subdivision schemes, whose basis vector functions are splines and have linearly independent shifts. Several examples of Hermite subdivision schemes with short support and high smoothness are presented to illustrate the results in this paper. [ABSTRACT FROM AUTHOR]

We present a calculation of the masses of the isovector mesons (vector, scalar and pseudoscalar including the established recurrences) using a new method of finite energy QCD sum rules. The method is based on the idea of choosing a suitable integration kernel which minimizes the occurring integral over the cut in the complex energy (squared) plane. We obtain remarkably stable results in a wide range R , where R is the radius of the integration contour. The sum rule predictions agree with the experimental values within the expected accuracy showing that QCD describes single resonances. [ABSTRACT FROM AUTHOR]

In a passive lossy acoustical system, sum rules derived from passivity explicitly relate the broadband response to the spatial dimension of the system, which provide important design criteria as well. In this work, the theory of Herglotz function is applied systematically to derive sum rules for unidimensional scattering problems relying on passive acoustic treatments which are generally made of rigid, motionless and subwavelength structures saturated by air. The rigid-boundary reflection, soft-boundary reflection and transmission problems are analysed. The derived sum rules are applied for guiding the designs of passive absorbers and mufflers: the required minimum space is directly predicted from the target (i.e. the desired absorption or transmission-loss spectra) without any specific design. Besides, it is possible to break this type of sum rules and fundamental constraints in particular cases. This property, if well used, could result in ultra-compact absorbers working at long wavelength up to infinity. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the integrated flavor asymmetry of the sea quarks in the proton, ∫ 0 1 (d ̄ − ū) d x , with the help of the truncated moments approach elaborated in our previous papers. We use the difference between the light sea-quark distributions d ̄ − ū extracted from Drell–Yan (DY) NuSea/E866 measurements of the cross-section ratio σ p d / σ p p and from the recent global analysis of deep inelastic scattering (DIS) F 2 p − n data incorporating the reanalyzed neutron structure function. In our analysis, we also include the most recent DY data from the Fermilab SeaQuest/E906 experiment. [ABSTRACT FROM AUTHOR]

In this paper magnetic dipole moment form factor, G M (2) (Q 2) , describing the radial excitation of decuplet baryons to octet baryons electromagnetic transitions as well as the ratios, R S M = − 1 4 m 2 2 4 m 2 2 Q 2 + (m 2 2 − Q 2 − m 1 2) 2 G C (2) (Q 2) G M (2) (Q 2) and R E M = − G E (2) (Q 2) G M (2) (Q 2) are calculated in the framework of light-cone sum rules. We also estimate the degree of the violation of U-spin symmetry. [ABSTRACT FROM AUTHOR]

Generalized Kramers–Kronig (K–K) type dispersion relations and sum rules are derived in the static limit for the moments of the degenerate four wave mixing susceptibility. The degenerate nonlinear susceptibility is different from a typical use of the conventional K–K dispersion relations, which assume absence of complex poles of a function in the upper half of complex frequency plane, whereas degenerate susceptibility has simultaneous poles in both half planes. In the derivation of the generalized K–K relations the poles and their order are taken into account by utilization of the theorem of residues. The conventional K–K relations can be used to estimate the real and imaginary parts of the second and higher powers of the susceptibility as the effect of the poles is reduced due to a faster convergence of the dispersion relations. The present theory is directly applicable to higher order susceptibilities and can be used in testing of theoretical models describing the degenerate four wave mixing susceptibility in nonlinear optical and terahertz spectroscopy. [ABSTRACT FROM AUTHOR]

The Thomas–Reiche–Kuhn (TRK) sum rule is a fundamental consequence of the position–momentum commutation relation for an atomic electron, and it provides an important constraint on the transition matrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light–matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light–matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light–matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics. [ABSTRACT FROM AUTHOR]

We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [Sum rules via large deviations, J. Funct. Anal. 270(2) (2016) 509–559] for spectral measures of classical ensembles (Gauss–Hermite, Laguerre, Jacobi) and it was extended to spectral matrix measures of the Hermite and Laguerre ensemble in [Sum rules and large deviations for spectral matrix measures, Bernoulli 25(1) (2018) 712–741]. In this paper, we consider the remaining case of spectral matrix measures of the Jacobi ensemble. Our main results are a large deviation principle for such measures and a sum rule for matrix measures with reference measure the Kesten–McKay law. As an important intermediate step, we derive the distribution of matricial canonical moments of the Jacobi ensemble. [ABSTRACT FROM AUTHOR]

We study a 2D system of identical mobile particles on the surface of a cylinder of finite length d and circumference W, immersed in a medium of dielectric constant ε . The two end-circles of the cylinder are like-charged with the fixed uniform charge densities, the particles of opposite charge - e (e being the elementary charge) are coined as "counterions"; the system as a whole is electroneutral. Such a geometry is well defined also for finite numbers of counterions N. Our task is to derive an effective interaction between the end-circles mediated by the counterions in thermal equilibrium at the inverse temperature β . The exact solution of the system at the free-fermion coupling Γ ≡ β e 2 / ε = 2 is used to test the convergence of the pressure as the (even) number of particles increases from N = 2 to ∞ . The pressure as a function of distance d is always positive (effective repulsion between the like-charged circles), decaying monotonously; the numerical results for N = 8 counterions are very close to those in the thermodynamic limit N → ∞ . For the couplings Γ = 2 γ with γ = 1 , 2 , ... , there exists a mapping of the continuous two-dimensional (2D) Coulomb system with N particles onto the one-dimensional (1D) lattice model of N sites with interacting sets of anticommuting variables. This allows one to treat exactly the density profile, two-body density and the pressure for the couplings Γ = 4 and 6, up to N = 8 particles. Our main finding is that the pressure becomes negative at large enough distances d if and only if both like-charged walls carry a nonzero charge density. This indicates a like-attraction in the thermodynamic limit N → ∞ as well, starting from a relatively weak coupling constant Γ in between 2 and 4. As a by-product of the formalism, we derive specific sum rules which have direct impact on characteristics of the long-range decay of 2D two-body densities along the two walls. [ABSTRACT FROM AUTHOR]

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers–Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker–Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai–Zwanzig model and of the Bonilla–Casado–Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively. [ABSTRACT FROM AUTHOR]

As a generalization of orthonormal wavelets in L2(R), tightframelets (also called tight wavelet frames) are of importance in wavelet analysis and applied sciences due to their many desirable properties in applications such as image processing and numerical algorithms. Tight framelets are often derived from particular refinable functions satisfying certain stringent conditions. Consequently, a large family of refinable functions cannot be used to construct tight framelets. This motivates us to introduce the notion of a quasi-tight framelet, which is a dual framelet but behaves almost like a tight framelet. It turns out that the study of quasi-tight framelets is intrinsically linked to the problem of the generalized matrix spectral factorization for matrices of Laurent polynomials. In this paper, we provide a systematic investigation on the generalized matrix spectral factorization problem and compactly supported quasi-tight framelets. As an application of our results on generalized matrix spectral factorization for matrices of Laurent polynomials, we prove in this paper that from any arbitrary compactly supported refinable function in L2(R), we can always construct a compactly supported one-dimensional quasi-tight framelet having the minimum number of generators and the highest possible order of vanishing moments. Our proofs are constructive and supplemented by step-by-step algorithms. Several examples of quasi-tight framelets will be provided to illustrate the theoretical results and algorithms developed in this paper. [ABSTRACT FROM AUTHOR]

X‐ray absorption spectroscopy of thin films is central to a broad range of scientific fields, and is typically detected using indirect techniques. X‐ray excited optical luminescence (XEOL) from the sample's substrate is one such detection method, in which the luminescence signal acts as an effective transmission measurement through the film. This detection method has several advantages that make it versatile compared with others, in particular for insulating samples or when a probing depth larger than 10 nm is required. In this work a systematic performance analysis of this method is presented with the aim of providing guidelines for its advantages and pitfalls, enabling a wider use of this method by the thin film community. The efficiency of XEOL is compared and quantified from a range of commonly used substrates. These measurements demonstrate the equivalence between XEOL and X‐ray transmission measurements for thin films. Moreover, the applicability of XEOL to magnetic studies is shown by employing XMCD sum rules with XEOL‐generated data. Lastly, it is demonstrated that above a certain thickness XEOL shows a saturation‐like effect, which can be modelled and corrected for. [ABSTRACT FROM AUTHOR]

Herein, a ferrimagnetic manganese zinc ferrite (Mn0.5Zn0.5Fe2O4) film with a thickness of 200 nm is prepared without a buffer layer on strontium titanate (001) (SrTiO3) using pulsed laser deposition. Its magnetic properties are investigated using superconducting quantum interference device (SQUID), X‐ray absorption spectroscopy with subsequent X‐ray magnetic circular dichroism (XMCD) and magneto‐optic Kerr effect (MOKE). Hysteresis loops derived from SQUID exhibits bulk‐like properties. This can further be confirmed by bulk‐like XMCD spectra. In remanent magnetization, an in‐plane magnetization with basically no out‐of‐plane component is found. The magnetic moments derived by the sum rule formalism from the XMCD data are in good agreement to the magnetization observed by SQUID and MOKE. XMCD as well as MOKE reveal an in‐plane angular fourfold magnetic anisotropy with the easy direction along [110] for (Mn0.5Zn0.5)Fe2O4 on SrTiO3. The element‐specific magnetic moments from XMCD show a stronger contribution of Fe to the anisotropy than of Mn and distinct contributions of the orbital moments. [ABSTRACT FROM AUTHOR]

We consider the two-dimensional one-component plasma (jellium) of mobile pointlike particles with the same charge e, interacting pairwisely by the logarithmic Coulomb potential and immersed in a fixed neutralizing background charge density. Particles are in thermal equilibrium at the inverse temperature β , the only relevant dimensionless parameter is the coupling constant Γ ≡ β e 2 . In the bulk fluid regime and for any value of the coupling constant Γ = 2 × integer , Šamaj and Percus (J Stat Phys 80:811–824, 1995) have derived an infinite sequence of sum rules for the coefficients of the short-distance expansion of particle pair correlation function. In the context of the equivalent fractional quantum Hall effect, by using specific methods of quantum geometry Haldane (Phys Rev Lett 107:116801, 2011; arXiv:1112.0990v2, 2011) derived a self-dual relation for the Landau-level guiding-center structure factor. In this paper, we establish the relation between the guiding-center structure factor and the pair correlation function of jellium particles. It is shown that the self-dual formula, which provides an exact relation between the pair correlation function and its Fourier component, comes directly from the short-distance symmetry of the bulk jellium. The short-distant symmetry of pair correlations is extended to the semi-infinite geometry of a rectilinear plain hard wall with a fixed surface charge density, constraining particles to a half-space. The symmetry is derived for the original jellium model as well as its simplified version with no background charge (charged wall surface with "counter-ions only"). The obtained results are checked at the exactly solvable free-fermion coupling Γ = 2 . [ABSTRACT FROM AUTHOR]

We present a new sum rule for Clebsch–Gordan coefficients using generalized characters of irreducible representations of the rotation group. The identity is obtained from an integral involving Gegenbauer ultraspherical polynomials. A similar procedure can be applied for other types of integrals of such polynomials and may therefore lead to the derivation of further new relations. [ABSTRACT FROM AUTHOR]

The possibility of physics beyond the Standard Model is studied. The requirement of finiteness of the zero-point energy density and pressure or the requirement of the Lorentz invariance of the zero-point stress-energy tensor in Minkowski space–time, implies regularization sum rules on the number of degrees of freedom and mass of fundamental particles spectrum. The consequences of these sum rules on the existence of particles beyond the Standard Model are studied. If these sum rules are to be satisfied, it is shown that some simple and minimal extensions of the Standard Model such as the two-Higgs-doublet model, right-handed neutrinos, mirror symmetry cannot be complete extensions in their current forms. The only exception is unbroken supersymmetry and may be broken supersymmetry. A comparison between different regularization schemes is also done. It is shown that while all considered regularization schemes give a Lorentz invariant expression for the zero-point stress-energy tensor in Minkowski space, their physical interpretations are quite different. [ABSTRACT FROM AUTHOR]

The model under consideration is the classical two-dimensional one-component plasma (jellium) of pointlike particles with charge e, interacting pairwisely via the logarithmic Coulomb potential and immersed in a uniform neutralizing background charge density. The system is in thermal equilibrium at the inverse temperature β , its thermodynamics depends only on the coupling constant Γ = β e 2 . We put into an infinite (homogeneous and translationally invariant) plasma a guest particle of charge Ze with Z > - 2 / Γ in order to prevent from the collapse of the jellium charges onto it. The guest particle induces a screening cloud (the excess charge density) in the plasma. The zeroth and second moments of this screening cloud were derived previously for any fluid value of Γ . In this paper, we propose a formula for the fourth moment of the screening cloud. The derivation is based on the assumption that the fourth moment is, similarly as the second moment, analytic in Z around Z = 0 . An exact treatment of the limit Z → ∞ shows that it is a finite (cube) polynomial in Z. The Γ -dependence of the polynomial coefficients is determined uniquely by considering the limits Z → 0 and Z → ∞ , and the compressibility sum rule for Z = 1 . The formula for the fourth moment of screening cloud is checked in the leading and first correction orders of the Debye–Hückel limit Γ → 0 and at the exactly solvable free-fermion point Γ = 2 . Sufficient conditions for sign oscillations of the induced charge density which follow from the second-moment and fourth-moment sum rules are discussed. [ABSTRACT FROM AUTHOR]

Within the framework of the mechanism proposed in our previous works [Duc and Giao, J. Mod. Phys. 5, 477 (2014); Duc et al., Int. J. Theor. Phys. 54, 1071 (2015); Duc and Giao, Int. J. Theor. Phys. 55, 959 (2016)] for mass and charge creation, we consider the charge and mass spectrum of spinor fields in extradimensions. It is shown that a single spinor field in spacetime with extradimensions corresponds to a set of effective spinor fields in ordinary four-dimensional spacetime with charges and masses obeying the sum rules dictated from some specific assumptions related to the compactification of extradimensions. The obtained results allow us to present an example for unifying six existing flavor quarks, as well as for unifying three existing lepton generators. On the base of the derived charge–mass sum rules, we would predict the existence of some hidden tachyon quarks with fractional charges, as well as some hidden tachyon leptons, neutral or negative charged. [ABSTRACT FROM AUTHOR]

A passive approximation problem is formulated where the target function is an arbitrary complex-valued continuous function defined on an approximation domain consisting of a finite union of closed and bounded intervals on the real axis. The norm used is a weighted Lp-norm where 1 \leq p \leq \infty. The approximating functions are Herglotz functions generated by a measure with H\"older continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are H\"older continuous functions given by the density of the measure and its Hilbert transform, respectively. In practice, it is useful to employ finite B-spline expansions to represent the generating measure. The corresponding approximation problem can then be posed as a finite-dimensional convex optimization problem which is amenable for numerical solution. A constructive proof is given here showing that the convex cone of approximating functions generated by finite uniform B-spline expansions of fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in the convex cone of Herglotz functions which are locally H\"older continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, typical physical application examples are included regarding the passive approximation and optimization of a linear system having metamaterial characteristics, as well as passive realization of optimal absorption of a dielectric small sphere over a finite bandwidth. [ABSTRACT FROM AUTHOR]

We introduce an algebra model to study higher-order sum rules for orthogonal polynomials on the unit circle. We build the relation between the algebra model and sum rules, and prove an equivalent expression on the algebra side for the sum rules involving a Hall-Littlewood type polynomial. By this expression, we recover an earlier result by Golinskii and Zlatoš and prove a new case - half of the Lukic conjecture in the case of a single critical point with arbitrary order. [ABSTRACT FROM AUTHOR]

We consider the A 4 , S 4 and A 5 discrete lepton flavor symmetries broken down to nontrivial residual symmetries in the charged lepton and neutrino sectors in such a way that at least one of them is a Z 2 . Such symmetry breaking patterns lead to predictions for some of the three neutrino mixing angles and/or the Dirac CP violation phase δ of the neutrino mixing matrix. First, we perform a statistical analysis of these predictions, which uses as input the latest global data on the neutrino mixing parameters. We find 14 phenomenologically viable cases. Further, we assess the viability of these cases taking into account the prospective uncertainties in the determination of the mixing angles, planned to be achieved in current and future neutrino oscillation experiments. We find that only six cases would be compatible with the assumed prospective data. We show that this number will be further reduced by a precision measurement of δ. [ABSTRACT FROM AUTHOR]

Several sum rules and other exact relations are employed to determine both the static and the dynamic properties of strongly coupled, partially and completely degenerate one‐component plasmas. Emphasis is placed on the electron gas, both at zero and finite temperatures. The procedure is based on the self‐consistent method of moments, recently developed in Phys. Rev. Lett., 2017, 119, 045001, that provides a neat expression for the loss function valid at strong couplings. An input value of the method in its classical version is the static structure factor, whose accuracy is shown to insignificantly affect the resulting numerical data. Starting from the Cauchy‐Bunyakovsky‐Schwarz inequality, a criterion is proposed to verify the quality of various approaches to the evaluation of the static characteristics of one‐component, strongly coupled plasmas. [ABSTRACT FROM AUTHOR]

We review various applications of dispersion relations (DRs) to the electromagnetic structure of hadrons. We discuss the way DRs allow one to extract information about hadron structure constants by connecting information from complementary scattering processes. We consider the real and virtual Compton scattering processes off the proton, and summarize recent advances in the DR analysis of experimental data to extract the proton polarizabilities, in comparison with alternative studies based on chiral effective field theories. We discuss a multipole analysis of real Compton scattering data, along with a DR fit of the energy-dependent dynamical polarizabilities. Furthermore, we review new sum rules for the double-virtual Compton scattering process off the proton, which allow for model-independent relations between polarizabilities in real and virtual Compton scattering, and moments of nucleon structure functions. Information on double-virtual Compton scattering is used to predict and constrain the polarizability corrections to muonic hydrogen spectroscopy. [ABSTRACT FROM AUTHOR]

This letter presents a method to evaluate the static electric polarizability of 2-D infinitely periodic metal patch arrays with dielectric substrate. Static polarizabilities are used in several design applications for periodic structures such as estimation of the bandwidth limitations for frequency-selective structures or prediction of the radiation properties for antenna arrays. The main features of the proposed method are its numerical efficiency and a deep insight into the physics of the fields interacting with the structure. We provide derivation and analysis of the method, and its verification against two another commercial solver-based approaches for various structure geometries. Additionally, we suggest the guidelines for applying the method to bandwidth optimization of frequency-selective structures and illustrate this with an example. [ABSTRACT FROM AUTHOR]

Abstract: Spinterface engineering has shown quite important roles in organic spintronics as it can improve spin injection or extraction. In this study, 11,11,12,12‐tetracyanonaptho‐2,6‐quinodimethane (TNAP) is introduced as an interfacial layer for a prototype interface of Fe/TNAP. An element‐specific investigation of the electronic and magnetic structures of Fe/TNAP system by use of near edge X‐Ray absorption fine structure (NEXAFS) and X‐ray magnetic circular dichroism (XMCD) is reported. Strong hybridization between TNAP and Fe and induced magnetization of N atoms in TNAP molecule are observed. XMCD sum rule analysis demonstrates that the adsorption of TNAP reduces the spin moment of Fe by 12%. In addition, induced magnetization in N K‐edge of TNAP is also found with other commonly used ferromagnets in organic spintronics, such as La0.7Sr0.3MnO3 and permalloy, which makes TNAP a very promising molecule for spinterface engineering in organic spintronics. [ABSTRACT FROM AUTHOR]

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The strong coupling constants not only are important to understand the strong interactions of the heavy baryons, but can also help us reveal the nature and structure of these baryons. Additionally, researchers indeed have made great efforts to calculate some of the strong coupling constants, , , , , , , , , , , , , , , , etc. In this paper, we analyze the strong vertices and using the three-point QCD sum rules under the Dirac structure of . We perform our analysis by considering the contributions of the perturbative part and the condensate terms of and . After the form factors are calculated, they are then fitted into analytical functions which are used to get the strong coupling constants for these two vertices. The final results are and . [ABSTRACT FROM AUTHOR]

We study a mixture of two superfluids with density–density and current–current (Andreev–Bashkin) interspecies interactions. The Andreev–Bashkin coupling gives rise to a dissipationless drag (or entrainment) between the two superfluids. Within the quantum hydrodynamics approximation, we study the relations between speeds of sound, susceptibilities and static structure factors, in a generic model in which the density and spin dynamics decouple. Due to translational invariance, the density channel does not feel the drag. The spin channel, instead, does not satisfy the usual Bijl–Feynman relation, since the f-sum rule is not exhausted by the spin phonons. The very same effect on one dimensional Bose mixtures and their Luttinger liquid description is analysed within perturbation theory. Using diffusion quantum Monte Carlo simulations of a system of dipolar gases in a double layer configuration, we confirm the general results. Given the recent advances in measuring the counterflow instability, we also study the effect of the entrainment on the dynamical stability of a superfluid mixture with non-zero relative velocity. [ABSTRACT FROM AUTHOR]

A calculation of the non-singlet part of spin dependent structure function, $xg_{1}^{NS}(x,Q^{2})$ and associated sum rule, the Bjorken Sum rule up to next-next-to-leading order(NNLO) is presented. We use a unified approach incorporating Regge theory and the theoretical framework of perturbative Quantum Chromodynamics. Using a Regge behaved model with Q dependent intercept as the initial input, we have solved the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation up to NNLO at small- x for $xg_{1}^{NS}(x,Q^{2})$ and the solutions are utilised to calculate the polarised Bjorken sum rule(BSR). We have also extracted the higher twist contribution to BSR based on a simple parametrisation. These results for both of $xg_{1}^{NS}(x,Q^{2})$ and BSR, along with higher twist corrections are observed to be consistent with the available data taken from SMC, E143, HERMES, COMPASS and JLab experiments. In addition, our results are also compared with that of other theoretical and phenomenological analysis based on different models and a very good agreement is also observed in this regard. Further a very good consistency between our calculated results and theoretical QCD predictions of BSR is also achieved. [ABSTRACT FROM AUTHOR]

This work is a companion paper of [F. Gamboa, J. Nagel and A. Rouault, Sum rules via large deviations, J. Funct. Anal. 270 (2016) 509-559] and [F. Gamboa, J. Nagel and A. Rouault, Sum rules and large deviations for spectral matrix measures, preprint (2016), ] (see also [J. Breuer, B. Simon and O. Zeitouni, Large deviations and sum rules for spectral theory - A pedagogical approach, to appear in J. Spectr. Theory, preprint (2016), ]). We continue to explore the connections between large deviations for random objects issued from random matrix theory and sum rules. Here, we are concerned essentially with measures on the unit circle whose support is an arc that is possibly proper. We particularly focus on two-matrix models. The first one is the Gross-Witten (GW) ensemble. In the gapped regime, we give a probabilistic interpretation of a Simon sum rule. The second matrix model is the Hua-Pickrell (HP) ensemble. Unlike the GW ensemble the potential is here infinite at one point. Surprisingly, but as in [F. Gamboa, J. Nagel and A. Rouault, Sum rules via large deviations, J. Funct. Anal. 270 (2016) 509-559], we obtain a completely new sum rule for the deviation to the equilibrium measure of the HP ensemble. The case of spectral matrix measures is also studied. Indeed, in the case of HP ensemble, we extend our earlier works on large deviation for spectral matrix measure [F. Gamboa, J. Nagel and A. Rouault, Sum rules and large deviations for spectral matrix measures, preprint (2016), ] and get here also a completely new sum rule. [ABSTRACT FROM AUTHOR]

We present generalized evolution equations and factorization in terms of the truncated Mellin moments (TMM) of the parton distributions and structure functions. We illustrate the x and Q2 dependence of TMM in the polarized case. Using the TMM approach we compare the integrals of g1 with HERMES and COMPASS data from the limited x-ranges. [ABSTRACT FROM AUTHOR]

In classical semi-infinite Coulomb fluids, two-point correlation functions exhibit a slow inverse-power law decay along a uniformly charged wall. In this work, we concentrate on the corresponding amplitude function which depends on the distances of the two points from the wall. Recently Šamaj (J Stat Phys 161:227-249 ), applying a technique of anticommuting variables to a 2D system of charged rectilinear wall with 'counter-ions only', we derived a relation between the amplitude function and the density profile which holds for any temperature. In this paper, using the Möbius conformal transformation of particle coordinates in a disc, a new relation between the amplitude function and the density profile is found for that model. In all exactly solvable cases, the amplitude function factorizes itself in the two distances from the wall. Presupposing this factorization property at any temperature and using specific sum rules for semi-infinite geometries, a relation between the amplitude function of the charge-charge structure function and the charge profile is derived for many-component Coulomb fluids in any dimension. [ABSTRACT FROM AUTHOR]

We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge. We derive a sum rule for the fourth moment of equilibrium charge correlations. Our method relies on the study of the system response to the potential created by a weak external charge distribution with slow spatial variations. The induced particle densities, and the resulting induced charge density, are then computed within density functional theory, where the free energy is expanded in powers of the density gradients. The comparison with the predictions of linear response theory provides a thermodynamical expression for the fourth moment of charge correlations, which involves the isothermal compressibility as well as suitably defined partial compressibilities. The familiar Stillinger-Lovett condition is also recovered as a by-product of our method, suggesting that the fourth moment sum rule should hold in any conducting phase. This is explicitly checked in the low density regime, within the Abe-Meeron diagrammatical expansions. Beyond its own interest, the fourth-moment sum rule should be useful for both analyzing and understanding recently observed behaviours near the ionic critical point. [ABSTRACT FROM AUTHOR]

Macromolecules, when immersed in a polar solvent like water, become charged by a fixed surface charge density which is compensated by 'counter-ions' moving out of the surface. Such classical particle systems exhibit poor screening properties at any temperature and the trivial bulk regime (far away from the charged surface) with no particles, so the validity of standard Coulomb sum rules is questionable. In the present paper, we concentrate on the two-dimensional version of the model with the logarithmic interaction potential. We go from the finite disc to the semi-infinite planar geometry. The system is exactly solvable for two values of the coupling constant $$\varGamma $$ : in the Poisson-Boltzmann mean-field limit $$\varGamma \rightarrow 0$$ and at the free-fermion point $$\varGamma =2$$ . We show that the finite-size expansion of the free energy does not contain universal term as is usual for Coulomb fluids. For the coupling constant being an arbitrary positive even integer, using an anticommuting representation of the partition function and many-body densities we derive a sequence of sum rules. As a result, the contact density of counter-ions at the wall is available for the disc. The amplitude function, which characterizes the asymptotic inverse-power law behavior of the two-body density along the wall, is found to be related to the particle density profile. The dielectric susceptibility tensor, calculated exactly for an arbitrary coupling and the particle number, exhibits the anticipated disc value in the thermodynamic limit, in spite of zero contribution from the bulk region. Some of the results obtained in the Poisson-Boltzmann limit are generalized to an arbitrary Euclidean dimension. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that the consideration of the braneworld consistency conditions within the framework of bulk modified gravities allows for the existence of thick branes in the five-dimensional case with compact extra dimension. On studying the specific consistency conditions in the Brans-Dicke gravity, we were able to show that the brane generating scalar field potential is relevant for relaxing the gravitational constraints. [ABSTRACT FROM AUTHOR]

The helicity-dependent coherent π0-photoproduction in the reaction γd → π0d near the η-threshold is investigated. The calculations are performed within an approach which includes the reaction amplitudes of the impulse approximation (IA), two-step process with intermediate πN- and ηN-rescattering, and the higher order terms in the multiple scattering series for the intermediate ηNN interaction. The contribution of γd → π0d to the deuteron spin asymmetry is calculated and its contribution to the Gerasimov-Drell-Hearn (GDH) integral is explicitly evaluated by integration up to a photon energy of 900 MeV. In addition, the helicity E-asymmetry is calculated. The results revealed that the doubly polarized differential cross-sections and the helicity E-asymmetry are sensitive to the interference of rescattering effects, specially at photon energies 600-800 MeV and extreme backward pion angles. The sensitivity of the obtained results for the GDH integral to the choice of NN potential model governing the deuteron wave function is discussed. We find that the deviation among results obtained for the deuteron GDH integral using different deuteron wave functions is quite large. [ABSTRACT FROM AUTHOR]

The masses and decay constants of the light tensor mesons were calculated with quantum numbers in the framework of the QCD sum rules in the standard model. The non perturbative contributions up to dimension-5 are considered as important terms of the operator product expansion. [ABSTRACT FROM AUTHOR]

Quasi-1D quantum structures with spectra scaling faster than the square of the eigenmode number (superscaling) can generate intrinsic, off-resonant optical nonlinearities near the fundamental physical limits, independent of the details of the potential energy along the structure. The scaling of spectra is determined by the topology of the structure, while the magnitudes of the transition moments are set by the geometry of the structure. This paper presents a comprehensive study of the geometrical optimization of superscaling quasi-1D structures and provides heuristics for designing molecules to maximize intrinsic response. A main result is that designers of conjugated structures should attach short side groups at least a third of the way along the bridge, not near its end as is conventionally done. A second result is that once a side group is properly placed, additional side groups do not further enhance the response. [ABSTRACT FROM AUTHOR]

Using the fact that the neutrino mixing matrix , where Ue and Uν result from the diagonalization of the charged lepton and neutrino mass matrices, we analyze the predictions based on the sum rules which the Dirac phase δ present in U satisfies when Uν has a form dictated by, or associated with, discrete flavor symmetries and Ue has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to Uν, so that the reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 have values compatible with the current data. [ABSTRACT FROM AUTHOR]

The dynamic structure factor of dense two-component plasmas is studied within the method of moments. A new model for the Nevanlinna parameter function is suggested. Our results on the dynamic structure factor satisfy the sum rules and other exact relations automatically, independently of the choice of a mathematically consistent model of the latter. A quantitative agreement is obtained with the molecular dynamics simulation data. Our approach permits to correct and complement the results of alternative approaches. [ABSTRACT FROM AUTHOR]