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This paper develops the bitensorial formulation of the system of singularities associated with unbounded and bounded Stokes flows. The motivation for this extension is that Stokesian singularities and hydrodynamic fundamental solutions are multi-point functions, and bitensor calculus provides either the proper geometrical setting, in order to avoid inconsistencies and misunderstandings on the role of the different tensorial indices, or a way for compactly deriving hydrodynamic properties. A first relevant result is to provide a clear definition of the singularities (both bounded and unbounded) in Stokes flow, specifying the associated differential equations and boundary conditions. Using this formalism for bounded flows, we show the existence of an integro-differential operator providing the whole system of hydrodynamic singularities by acting on the unbounded Green function (Stokeslet) at its pole and we derive its explicit representation in terms of moments. In the case of an immersed body in a unbounded fluid, we show that, the operator furnishing the disturbance field of a purely $ n $-th order ambient flow, is a generalized $ n $-th order Faxén operator, i.e., it yields the $ n $-th moment on the body if applied to a generic ambient flow, and that a generic disturbance field can be expressed by a summation of the generalized $ n $-th order Faxén operators. Furthermore, we find that the operator providing the disturbance of an ambient flow coincides with the reflection operator for the Stokes solutions in the same flow geometry. We apply this result to the paradigmatic case of fundamental singularities for the Stokes flow bounded by a plane. In this way, we obtain in an alternative and easy way the image system for the Sourcelet and the Rotlet (already derived in the literature) and for the Source Doublet and the Strainlet (presented here for the first time).

We establish boundedness estimates for solutions of generalized porous medium equations of the form $$ \partial_t u+(-\mathfrak{L})[u^m]=0\quad\quad\text{in $\mathbb{R}^N\times(0,T)$}, $$ where $m\geq1$ and $-\mathfrak{L}$ is a linear, symmetric, and nonnegative operator. The wide class of operators we consider includes, but is not limited to, Lévy operators. Our quantitative estimates take the form of precise $L^1$--$L^\infty$-smoothing effects and absolute bounds, and their proofs are based on the interplay between a dual formulation of the problem and estimates on the Green function of $-\mathfrak{L}$ and $I-\mathfrak{L}$. In the linear case $m=1$, it is well-known that the $L^1$--$L^\infty$-smoothing effect, or ultracontractivity, is equivalent to Nash inequalities. This is also equivalent to heat kernel estimates, which imply the Green function estimates that represent a key ingredient in our techniques. We establish a similar scenario in the nonlinear setting $m>1$. First, we can show that operators for which ultracontractivity holds, also provide $L^1$--$L^\infty$-smoothing effects in the nonlinear case. The converse implication is not true in general. A counterexample is given by $0$-order Lévy operators like $-\mathfrak{L}=I-J\ast$. They do not regularize when $m=1$, but we show that surprisingly enough they do so when $m>1$, due to the convex nonlinearity. This reveals a striking property of nonlinear equations: the nonlinearity allows for better regularizing properties, almost independently of the linear operator. Finally, we show that smoothing effects, both linear and nonlinear, imply families of inequalities of Gagliardo-Nirenberg-Sobolev type, and we explore equivalences both in the linear and nonlinear settings through the application of the Moser iteration., 73 pages, 5 figures. v2: Updated according to the referee's suggestions. To appear in "Journal of Functional Analysis"

For k-Riemann–Liouville fractional integral operators, the Hermite–Hadamard inequality is already well-known in the literature. In this regard, this paper presents the Hermite–Hadamard inequalities for k-Riemann–Liouville fractional integral operators by using a novel method based on Green’s function. Additionally, applying these identities to the convex and monotone functions, new Hermite–Hadamard type inequalities are established. Furthermore, a different form of the Hermite–Hadamard inequality is also obtained by using this novel approach. In conclusion, we believe that the approach presented in this paper will inspire more research in this area.

This article has results of four types. We show that the firsteigenvalueλ1(Ω) of the weighted Laplacian of a bounded domain withsmooth boundary can be obtained by S. Sato’s iteration scheme of theGreen operator, taking the limitλ1(Ω) = limk→∞‖Gk(f)‖L2/‖Gk+1(f)‖L2for anyf∈L2(Ω,μ),f >0, (Theorems 2.1 & 2.2). Then, we study theL1(Ω,μ)-moment spectrum of Ω in terms of iterates of the Green oper-atorG, (Theorem 3.2), extendind the work of MacDonald-Meyers [29]to the weighted setting. As corollary, we obtain the first eigenvalue ofa weighted bounded domain in terms of theL1(Ω,μ)-moment spectrum,generalizing the work of Hurtado-Markvorsen-Palmer [25]. Finally, westudy the radial spectrumσrad(Bh(o,r)) of rotationally invariant geodesicballsBh(o,r) of model manifolds. In Theorems 5.4 & 5.6, we prove anidentity relating the radial eigenvalues ofσrad(Bh(o,r)) to an isoperimet-ric quotient, i.e.∑1/λradi=∫V(s)/S(s)ds,V(s) = vol(Bh(o,s)) andS(s) = vol(∂Bh(o,s)). We then consider a proper minimal surfaceM⊂R3and the extrinsic ball Ω =M∩BR3(o,r). We obtain upper and lower es-timates for the series∑λ−2i(Ω) in terms of the volume vol(Ω) and theradiusrof the extrinsic ball Ω, (Theorem 6.1).

In this paper, we present the q-Lidstone polynomials which are q-Bernoulli polynomials generated by the third Jackson q-Bessel function, based on the Green’s function of a certain q-difference equation. Also, we provide the q-Fourier series expansions of these polynomials and derive some results related to them.

In this paper, we consider the definition of “useful” Csiszár divergence and “useful” Zipf-Mandelbrot law associated with the real utility distribution to give the results for majorizatioQn inequalities by using monotonic sequences. We obtain the equivalent statements between continuous convex functions and Green functions via majorization inequalities, “useful” Csiszár functional and “useful” Zipf-Mandelbrot law. By considering “useful” Csiszár divergence in the integral case, we give the results for integral majorization inequality. Towards the end, some applications are given.

This paper deals with structural static or stability analysis of straight beams, when the bending-torsion coupling is considered. A practical case is the lateral buckling analysis of high cross-section beams which involves the coupled bending deflection and twist. Simple rectangular cross-section or thin walled open profile symmetric cross-section beams can buckle laterally when they are subjected to bending with respect to the stiffer plane. Bending-torsion coupling occurs also for some composite beams. The presented approximate integral method uses flexibility influence functions (Green functions) and a matrix formulation, leading to an eigenvalue problem in the case of stability analysis. The formulation can be also used for static or dynamic analysis. Some numerical examples are presented in comparison with the results of other methods.

This paper gives extensions and improvements of Sherman’s inequality forn-convex functions obtained by using new identities which involve Green’s functions and Fink’s identity. Moreover, extensions and improvements of Majorization inequality as well as Jensen’s inequality are obtained as direct consequences. New inequalities between geometric, logarithmic and arithmetic means are also established.

This work gives sufficient conditions for the solvability of the fourth order coupled system { u ( 4 ) ( t ) = f ( t , u ( t ) , u ′ ( t ) , u ″ ( t ) , u ‴ ( t ) , v ( t ) , v ′ ( t ) , v ″ ( t ) , v ‴ ( t ) ) v ( 4 ) ( t ) = h ( t , u ( t ) , u ′ ( t ) , u ″ ( t ) , u ‴ ( t ) , v ( t ) , v ′ ( t ) , v ″ ( t ) , v ‴ ( t ) ) with f , h : [ 0 , 1 ] × R 8 → R some L 1 - Caratheodory functions, and the boundary conditions { u ( 0 ) = u ′ ( 0 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 v ( 0 ) = v ′ ( 0 ) = v ″ ( 0 ) = v ″ ( 1 ) = 0 . To the best of our knowledge, it is the first time in the literature where two beam equations are considered with full nonlinearities, that is, with dependence on all derivatives of u and v . An application to the study of the bending of two elastic coupled clamped beams is considered.

This work presents a Green's function approach, originally implemented in graphene with well-defined edges, to the surface of a strong 3D Topological Insulator (TI) with a sequence of proximitized superconducting (S) and ferromagnetic (F) surfaces. This consists of the derivation of the Green's functions for each region by the asymptotic solutions method, and their coupling by a tight-binding Hamiltonian with the Dyson equation to obtain the full Green's functions of the system. These functions allow the direct calculation of the momentum-resolved spectral density of states, the identification of subgap interface states, and the derivation of the differential conductance for a wide variety of configurations of the junctions. We illustrate the application of this method for some simple systems with two and three regions, finding the characteristic chiral state of the Quantum Anomalous Hall Effect (QAHE) at the NF interfaces, and chiral Majorana modes at the NS interfaces. Finally, we discuss some geometrical effects present in three-region junctions such as weak Fabry-P\'erot resonances and Andreev bound states., Comment: 14 pages, 6 figures

In this paper we use a potential-theoretic approach to establish various representation theorems and Poisson-Jensen-type formulas for subharmonic functions in sub-Riemannian settings. We also characterize the Radon measures in \begin{document}$ \mathbb{R}^N $\end{document} which are the Riesz-measures of bounded-above subharmonic functions in the whole space \begin{document}$ \mathbb{R}^N $\end{document}.

En este trabajo analizamos el transporte electrónico en conductores rectangulares en las que se insertan nanoporos que restringen el flujo de portadores. Al colocar moléculas en los nanoporos se observa que existen resonancias y antiresonancias en los coeficientes de transmisión cuando las orientaciones de las moléculas son paralelas o perpendiculares al flujo de portadores. El conductor es descrito mediante el método de enlaces fuertes (tight-binding), el cálculo de los coeficientes de transmisión a través del sistema se realiza mediante la fórmula de Landauer en el régimen balístico a bajas temperaturas y las funciones de Green fuera del equilibrio nos permite determinar la influencia de los contactos semi-infinitos sobre el conductor con nanoporos mediante un algoritmo recursivo. La presencia de moléculas en las partes centrales de los nanoporos también son descritos por sítios en la aproximación de enlaces fuertes., In this work, we analyze the electron transport in rectangular conductors in which we insert a nanopore which restrict the carrier flux. Actually, to setup molecules at middle of the nanopore, we observe resonances and anti-resonances in the transmission coefficient when the molecule orientation is parallel or perpendicular to carrier flux. In our case, the conductor is described by a tight binding approximation, the transmission coefficients through the system are calculated by Landauer formula considering a ballistic regime at low temperatures and the out of equilibrium Green functions to permit us calculate the coupling of the leads with conductor including the nanopore and the molecules, recursively. The presence of the molecules at middle of the nanopore are described, also, by the tight binding approximation.

We examine the validity and scope of Johnston's models for scalar field retarded Green functions on causal sets in 2 and 4 dimensions. As in the continuum, the massive Green function can be obtained from the massless one, and hence the key task in causal set theory is to first identify the massless Green function. We propose that the 2-d model provides a Green function for the massive scalar field on causal sets approximated by any topologically trivial 2 dimensional spacetime. We explicitly demonstrate that this is indeed the case in a Riemann normal neighbourhood. In 4-d the model can again be used to provide a Green function for the massive scalar field in a Riemann normal neighbourhood which we compare to Bunch and Parker's continuum Green function. We find that the same prescription can also be used for deSitter spacetime and the conformally flat patch of anti deSitter spacetime. Our analysis then allows us to suggest a generalisation of Johnston's model for the Green function for a causal set approximated by 3 dimensional flat spacetime., Comment: 23 pages, 5 figures

This paper provides sufficient conditions to guarantee the existence, non-existence and multiplicity of solutions for a third order eigenvalue fully differential equation, coupled with three point boundary value conditions. Although the change of sign, some bounds for the second derivative of the Green's function are obtained, which allow to define a different kind of cone that, as far as we know, has not been previously used in the literature. The main arguments are based on the fixed point index theory for bounded and unbounded sets. Some examples are presented in order to show that the different existence theorems proved are not comparable SI

We will see an alternative proof of the non-Archimedean Montel theorem for rational dynamics by using the non-Archimedean Green functions.

Um problema relacionado ao fenômeno de interferência quântica em um sistema nanoestruturado é investigado através do estudo da segregação de impurezas substitucionais. Tais sistemas são formados pela justaposição de camadas de átomos de metais de transição. A segregação de impurezas substitucionais é tratada a partir do cálculo da variação da energia eletrônica total do sistema, considerando as posições da impureza relativamente à superfície. Empregamos o modelo de ligações fortes, com apenas um orbital por sítio, sendo os potenciais das impurezas determinados de modo a satisfazer a neutralidade de carga através da regra de soma de Friedel. Consideramos uma rede cúbica simples e as direções (100) e (110). A problem related to the quantum interference phenomenon in a nanostructured system is investigated by studying the segregation of substitutional impurities. Such systems are formed by the juxtaposition of transition metals atomic layers. The substitutional impurities segregation is treated calculating the total electronic energy variation of the system considering di←erent positions of the impurity relatively to the surface. A single orbital tight-binding model is employed. The potential impurities are determined imposing local or global charge neutrality and satisfying Friedel sum rule. We consider a simple cubic lattice with (100) and (110) directions.

A numerical study has been carried out by means of the Green's function method to explore possible performance improvements of a simple grated waveguide (GWg) by the variations of its grated structure. It is shown that a GWg featuring symmetric two-sided grated structure of 16 teeth with a 60 nm groove depth and having a symmetric refractive index profile with a relatively large contrast between the grated and ungrated layers is capable of delivering largely improved device performance compared to that achieved previously with a one-sided grating of 40 nm groove depth and asymmetric index profile. The improvement is characterized by a remarkable 8-fold and 15-fold increase in the group index and the maximum field intensity, respectively, at the first resonance wavelength above the upper band edge (shorter wavelength), while relatively less improvement is found at the first resonance wavelength below the lower band edge (longer wavelength). It is shown that more than 20% further improvement can be obtained by an appropriate shifting of the two innermost adjacent grating teeth in the case of the 40 nm groove depth. Apart from that, the result also reveals an interesting and remarkable correlation between the variations of the group index and the confined energy.

We establish a boundary Harnack principle for a large class of subordinate Brownian motion, including mixtures of symmetric stable processes, in bounded $\kappa$-fat open set (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded $\kappa$-fat open sets with respect to these processes with their Euclidean boundary., Comment: 34 pages

We prove the Harnack inequality and boundary Harnack principle for the absolute value of a one-dimensional recurrent subordinate Brownian motion killed upon hitting 0, when 0 is regular for itself and the Laplace exponent of the subordinator satisfies certain global scaling conditions. Using the conditional gauge theorem for symmetric Hunt processes we prove that the Green function of this process killed outside of some interval $(a, b)$ is comparable to the Green function of the corresponding killed subordinate Brownian motion. We also consider several properties of the compensated resolvent kernel $h$, which is harmonic for our process on $(0, \infty)$.

The Dirichlet problem is considered for the heat equation u t = a u x x , a > 0 a constant, for ( x , t ) ∈ [ 0 , 1 ] × [ 0 , T ] , without assuming any compatibility condition between initial and boundary data at the corner points ( 0 , 0 ) and ( 1 , 0 ) . Under some smoothness restrictions on the data (stricter than those required by the classical maximum principle), weak and strong supremum and infimum principles are established for the higher-order derivatives, u t and u x x , of the bounded classical solutions. When compatibility conditions of zero order are satisfied (i.e., initial and boundary data coincide at the corner points), these principles allow to estimate the higher-order derivatives of classical solutions uniformly from below and above on the entire domain, except that at the two corner points. When compatibility conditions of the second order are satisfied (i.e., classical solutions belong to C x , t 2 , 1 on the closed domain), the results of the paper are a direct consequence of the classical maximum and minimum principles applied to the higher-order derivatives. The classical principles for the solutions to the Dirichlet problem with compatibility conditions are generalized to the case of the same problem without any compatibility condition. The Dirichlet problem without compatibility conditions is then considered for general linear one-dimensional parabolic equations. The previous results as well as some new properties of the corresponding Green functions derived here allow to establish uniform L 1 -estimates for the higher-order derivatives of the bounded classical solutions to the general problem.

The article illustrates a formulation to evaluate the array Green's function (AGF) of large finite planar phased array for observation points on the array plane, possibly close to the array contour. The procedure is based on the AGF representation in terms of a double spectral integral, whose integration paths are properly deformed to have an exponential attenuation of the integrand. The diffraction integral is evaluated numerically for point close to the array edges while an asymptotic treatment is proposed far from the edges. This latter comprises higher order contributions. Thanks to the convergence properties, the final algorithm is numerically accurate, stable and more efficient with respect to the individual element summation for large arrays. It also constitutes the basic step for the efficient evaluation of the AGF of a multilayer environment

Suppose that D is the domain in , d ≥ 3, above the graph of a bounded C1,1 function : and that pD(t, x, y) is the Dirichlet heat kernel in D. In this paper we show that there exist positive constants C1, C2, C3, C4 such that for all t > 0 and x, y D, C1((x)(y) / t 1) t -d/2 e -C|x-y|^2 / t ≤ pD(t, x, y), pD(t, x, y) ≤ C3((x)(y) / t 1) t -d/2 e -C|x-y|^2 / t, where (x) stands for the distance between x and D.

In this paper, we study the existence of solution of the nonlinear second-order difference problem with Neumann boundary conditions. Assuming the existence of a pair of ordered lower and upper solutions γ and β, we obtain optimal existence results for the case γ ≤ β and even for γ ≥ β.To this end, we do an exhaustive study of the values of the real parameters α and μ, for which the associated Green's function to the linear operator L[α,μ] uκ ≡ uκ+2 − 2 α uκ+1 + μ uκ with Neumann boundary conditions has fixed sign.

We consider the Pearcey integral P(x; y) for large values of |x|, x, y ∈ C. We can find in the literature several convergent or asymptotic expansions in terms of elementary and special functions, with different levels of complexity. Most of them are based in analytic, in particular asymptotic, techniques applied to the integral definition of P(x; y). In this paper we consider a different method: the iterative technique used for differential equations in [Lopez, 2012]. Using this technique in a differential equation satisfied by P(x; y) we obtain a new convergent expansion analytically simple that is valid for any complex x and y and has an asymptotic property when |x|→ ∞ uniformly for y in bounded sets. The accuracy of the approximation is illustrated with some numerical experiments and compared with other expansions given in the literature. The Universidad Pública de Navarra is acknowledged by its financial support.

Date of Conference: 10-17 August 2005 Conference Name: 24th International Conference on Low Temperature Physics, LT24 2005 Motivated by the pionieering experiments of Buks et al. [Nature 391, 871 (1998)] we investigate the visibility of the Fano effect in a single-dot Aharonov-Bohm interferometer which is Coulomb-coupled to a nearby quantum dot. The latter acts as a 'Which Path Detector' and is coupled to two leads on which a finite bias is applied. Using the non-equilibrium Keldysh-Green function formalism we compute the currents through the detector and the interferometer. We take into account the first two contributions to the interaction selfenergy and emphasize the correction to the Landauer formula which appears beyond the single-particle approximation. Particular attention is given to the coherence properties of the interferometer in the presence of the electron-electron interaction between the embedded dot and the detector. We show that when the detector is subjected to a finite bias the amplitude of Aharonov-Bohm oscillations of the current through the interferometer decreases. The Fano line is in turn rather stable under interaction. Our results generalize an earlier work of Silva and Levit [Phys. Rev. B 63, 201309 (2001)] and complement the existing description of the controlled dephasing.

International audience; We will report on a some efforts recently made in order to gain a better understanding of some IR properties of the 3-point gluon Green function by following both lattice and continuum QCD approaches.

Dielektrik kaplamalı yarıklı dalga kılavuzu anten dizileri, düşük prolleri, yüksek güç dayanımları ve kullanılan platform üzerindeki eğik yüzeylere uyumlanabilmeleri sebebiyle askeri ve ticari uygulamalarda tercih edilmektedir. Eğik yüzey uyumluluğu özellikle aerodinamiğin ve radar kesit alanının (RKA) kritik olduğu hava platformlarında gerekli hale gelmektedir. Bir hava platformunda anteni aşırı uçuş şartlarından korumak için bir veya daha fazla dielektrik katman kullanılabilir. Eğik yüzeylere uyumlu yarıklı dalga kılavuzu anten dizilerin isabetli analizi ve tasarımı oldukça ilgi çeken bir konu olmasına rağmen literatürde bulunan analiz yöntemleri genellikle düşük etkinlikleri ve yüksek rastgele erişimli hafıza (RAM) gereksinimleri nedeniyle tercih edilmemektedir. Mevcut analiz yöntemleri içinde en yaygın kullanılanlar, Momentler Metodunu kullanan integral denklem çözümleyicilerdir. Ancak, integral denklem çözümleyiciler özellikle silindirik katmanlı ortamların bulunduğu problemlerde çok uzun matris oluşturma süreleri nedeniyle yaygın olarak kullanılmamaktadır.Bu çalışmada eşeksenel olarak dielektrik katmanlar ile kaplı bir yarıklı sektörel dalga kılavuzu anten, birleşik Momentler Metodu/Green'in fonksiyonu tekniği ile uzamsal uzayda çözümlenmiştir. Sektörel dalga kılavuzu içinde sadece temel modun (TE11) uyarıldığı varsayılmıştır. Sektörel dalga kılavuzunun geniş kenarına boylamasına açılan yarıklar dik yönde oldukça ince olduklarından sadece enine elektrik (TE) modların yayıldığı varsayılabilir. Dalga kılavuzunun metal duvarlarının kalınlıklarının olmadığı varsayılır. Çözümleme yapılan geometri denklik teoremi ve yarıklar üzerinde temsili manyetik akım kaynakları kullanılarak ikiye bölünür. Duvar kalınlığının hesaba katılması istendiğinde geometri üçe bölünerek üçüncü bölge olarak bir sektörel oyuk tanımlanabilir. Yarıklar üzerindeki temsili manyetik kaynaklar sonlu sayıda parçalı sinüzoit fonksiyon ile ifade edildikten sonra manyetik alan integral denklemini oluşturmak için yarıklar üzerinde teğet manyetik alanların devamlılığı uygulanır. Oluşturulan integral denklemi, Galerkin'in yöntemi kullanılarak matris denklemi haline getirilir. Karşılıklı geçiri matrisinin elemanlarının hesaplanması için problemin iki bölgesi için iki farklı Green'in fonksiyonuna ihtiyaç vardır. Sektörel dalga kılavuzunun iç bölgesi için, ikici Green'in fonksiyonunun boylamasına manyetik akımları boylamasına manyetik alanlara ilişkilendiren bileşeni detaylı şekilde türetilmiştir. Silindirik katmanlı ortam için ise manyetik akım modlarının kesiştiği veya üst üste olduğu durumlarda dahi kullanılabilen kapalı-form Green'in fonksiyonları türetilmiştir. Bu çalışmada sunulan çözümleme yöntemi silindirik katmanlı ortamlarda gömülü malzemeye entegre dalga kılavuzları, oyuk antenler ve benzeri açıklık tipi antenlerin analizi için de kullanılabilir. Bu çalışmada sunulan çözümleme yöntemi ile, örnek silindirik katmanlı yarıklı sektörel dalga kılavuzu yapıları için eşdeğer yarık akımları ve uzak-alan ışıma örüntüleri hesaplanmış, ve elde edilen sonuçlar tam dalga elektromanyetik çözümleyicilerin sonuçları ile kıyaslanmıştır. Slotted waveguide antenna arrays with dielectric covers are widely used in both military and civil applications due to their low-prole, high power handling capacity, and the ability to conform to the host platform. Conformity is especially required for air platforms where aerodynamics and radar cross section (RCS) of the vehicle are of utmost importance. For an air platform, one or more dielectric layers (monolithic or sandwich radomes) can be used to protect the antenna from the extreme flight conditions. Although accurate and ecient design and analysis of low-prole conformal slotted waveguide arrays is of great interest, available solution methods in the literature usually suffer in terms of efficiency and memory requirements. Among the available solution methods, integral equation (IE)based ones that utilize the Method of Moments (MoM) are widely used. However, the IE solvers suffer from long matrix fill times, especially when cylindrically stratified media are considered.In this study, a slotted sectoral waveguide antenna, coaxially covered by multiple dielectric layers is analyzed with a hybrid MoM/Green's function technique in the space domain. Only the fundamental mode of propagation (TE11) is assumed to be excited inside the sectoral waveguide. The longitudinal slots are on the broadside wall of the sectoral waveguide and are very thin in the transverse direction; therefore, only the TE modes are assumed to propagate. The solution domain is divided into two by using the equivalence theorem and fictitious magnetic current sources on the waveguide slots. Note that for the purposes of this study, the waveguide wall thickness is assumed to be zero. However, it can be incorporated into the problem by adding a third region which would be a sectoral cavity. The magnetic sources on the slots are expanded by piecewise sinusoid basis functions, and the continuity of the tangential magnetic elds across the slots is enforced to construct the integral equation. The integral equation is then converted into a matrix equation using Galerkin's procedure. To compute the elements of the mutual admittance matrix, two Green's function representations for the two solution regions are used. For the sectoral waveguide interior, the dyadic Green's function components for a sectoral waveguide corresponding to longitudinal magnetic currents are rigorously derived. For the cylindrically stratified dielectric region, closed-form Green's function representations for magnetic currents are developed, which are valid for all source and observation points, including the source region, where two magnetic current modes fully or partially overlap with each other. The proposed analysis method can be easily extended to include: slotted substrate integrated waveguides, slotted cavity antennas, and similar aperture type antennas embedded in cylindrically stratied media. Numerical results in the form of equivalent slot currents and far-zone radiation patterns for a generic slotted sectoral waveguide are presented, and compared to the results obtained from the commercially available full-wave electromagnetic solvers. 110

Inclusion of planar layered media Green's Functions (GFs) is a major issue in the computational efficiency of full-wave models derived from integral formulations. These GFs may be decomposed into quasi-dynamic and dynamic terms. In a wide range of practical applications, the quasi-dynamic terms may be given in closed form. This paper proposes two criteria to establish when the complete GFs may be approximated by the quasi-dynamic terms. These criteria are based on simple relations between frequency, line length, dielectric thickness and permittivity. If these criteria are satisfied, the inclusion of the GFs into full-wave integral models is straightforward and the overall computational cost is strongly reduced. The proposed criteria are verified through a benchmark test case. The model is then used to perform a full-wave analysis of the power lost in a microstrip, as a consequence of the excitation of parasitic modes, such as surface and leaky waves.

By the use of a Guo-Krasnoselskii theorem in cones, existence of positive eigenvalues yielding nonnegative/positive solutions to the discrete equation[image omitted]is studied. The results are applied to boundary value problems of various types. Journal of Difference Equations and Applications

Elastic plane wave scattering of electromagnetic waves on three-dimensional structures is a basic physical interaction process which is of great importance in many practical applications. One may think of measurements in technical and medical diagnostics as well as in remote sensing of our Earth’s atmosphere, for example. During the last decades, not at least due to the possibilities of modern computers, there is a growing interest in modelling more and more realistic scattering scenarios which goes beyond the conventional Mie theory for spherical scatterers. A large variety of rigorous numerical methods (i.e., methods which start from the underlying physical equations without any approximations) for solving the problem of plane wave scattering on single but nonspherical particles have been developed in the past. Among those methods Waterman’s T-matrix approach as well as several boundary and volume integral equation approaches have become very popular and widely used in many applications (for an overview see [1], for example, and the literature cited therein). Differing in concept and execution these methods start from the common assumption that the well-known separation of variables method cannot be applied if the scatterer geometry deviates from that of a spherical surface (see [2] chapter 16.11 therein, and [3], for example). A critical discussion of this assumption is one goal of the paper at hand. On the other hand, there is still an ongoing discussion in the literature concerned with conceptual and technical differences as well as advantages and disadvantages of those standard methods mentioned above.

We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of $\rm{Sp}(4)$, which in addition satisfies the following property: for any $n\geq 3$, there is in this family a walk associated with a reflection group of order $2n$. Moreover, the case $n=4$ corresponds to a process which appears naturally by studying quantum random walks on the dual of $\rm{Sp}(4)$. For all the processes belonging to this family, we find the exact asymptotic of the Green functions along all infinite paths of states as well as that of the absorption probabilities along the boundaries., Comment: 20 pages

Some main non-local boundary value problems are studied for elliptic- hyperbolic type equations with non-smooth lines of changing type and with spectral parameter in a quarter circle and a quarter ring domain. The investigated problems equivalently reduced to a system of integral and sometimes integro-differential equations. In solving the obtained systems methods from the theory of partial differential equations, spectral theory of linear operators, theory of singular integral equations, methods of complex analysis, the energy integral, and also the extremal principle are applied. For finding a system of eigenfunctions the method of separation of variables is used. The following new results are obtained: 1\. Conditions are found for the complex parameter λ, ensuring uniqueness of the solution of the considered problems. Further, in the plane of the complex parameter a domain of values λ is given, outside of which the considered non-local problems can have eigenvalues. 2\. Sufficient conditions are found for uniqueness and existence of solutions of the formulated problems. 3\. Eigenvalues and corresponding eigenfunctions are found for one of the most general mixed problem, in which the third boundary condition on the boundary of the elliptic part of the mixed domain is given, and for the hyperbolic part a non-local condition is given by some integral operator. Moreover, the completeness of eigenfunctions are proved in the class L2. 4\. A new method is developed to prove the existence of the solution of the considered problem, by applying eigenfunctions in evident form as solutions of the formulated problem in the case, when the theorem of uniqueness of the solution of the considered problem is given., Wesentliche nichtlokale Randwertprobleme werden für elliptisch-hyperbolische Gleichungen mit Spektralparameter im Viertelkreis und Viertelring untersucht, wobei der Gleichungstyp sich auf einer nicht glatten Kurve ändert. Die Probleme werden auf äquivalente Systeme von Integral- und gelegentlich Integrodifferentialgleichungen überführt. Methoden für partielle Differentialgleichungen, aus der Spektraltheorie linearer Operatoren, der Theorie der singulären Integralgleichungen, der komplexen Analysis, das Energieintegral und auch das Extremalprinzip werden zur Lösung des erhaltenen Systems angewandt. Zum Auffinden eines Systems von Eigenfunktionen wird die Methode der Trennung der Variablen verwandt. Folgende neue Ergebnisse werden erzielt: 1\. Für den komplexen Parameter λ werden Bedingungen angegeben, die die Eindeutigkeit der Lösung sichern. Außerdem wird in der komplexen Ebene ein Gebiet für den Parameter λ angegeben, außerhalb dessen die untersuchten nichtlokalen Probleme Eigenwerte haben können. 2\. Für Eindeutigkeit und Existenz der Lösungen werden hinreichende Bedingungen formuliert. 3\. Eigenwerte und zugehörige Eigenfunktionen werden für eines der allgemeinen gemischten Probleme gefunden, in dem auf dem Rand des elliptischen Teilgebiets die dritte Randbedingung und für den hyperbolischen Teil mittels Integraloperatoren ausgedrückte nichtlokale Bedingungen gegeben sind. Außerdem wird die Vollständigkeit des Systems der Eigenfunktionen im Raum L2 bewiesen. 4\. Eine neue Methode zum Existenzbeweis für die Lösungen des betrachteten Problems wird entwickelt, indem Eigenfunktionen in offensichtlicher Form als Lösungen des formulierten Problems in dem Fall angewandt werden, in dem die Eindeutigkeit der Lösung des Problems gegeben ist.

Recent work in the literature has studied rigid Casimir cavities in a weak gravitational field, or in de Sitter spacetime, or yet other spacetime models. The present review paper studies the difficult problem of direct evaluation of scalar Green functions for a Casimir-type apparatus in de Sitter spacetime. Working to first order in the small parameter of the problem, i.e. twice the gravity acceleration times the plates' separation divided by the speed of light in vacuum, suitable coordinates are considered for which the differential equations obeyed by the zeroth- and first-order Green functions can be solved in terms of special functions. This result can be used, in turn, to obtain, via the point-split method, the regularized and renormalized energy-momentum tensor both in the scalar case and in the physically more relevant electromagnetic case., Comment: 13 pages, special issue review article. In the final version, the calculations of Sec. III have been improved, two References have been added and their content has been summarized

Let $(X,d,\mu)$ be a metric measure space with a local regular Dirichlet form. We give necessary and sufficient conditions for a parabolic Harnack inequality with global space-time scaling exponent $\beta\ge 2$ to hold. We show that this parabolic Harnack inequality is stable under rough isometries. As a consequence, once such a Harnack inequality is established on a metric measure space, then it holds for any uniformly elliptic operator in divergence form on a manifold naturally defined from the graph approximation of the space., Comment: Pages 1-35 are the original paper; pages 36-40 are corrections to the results of section 3

We consider random walks in a random environment of the type p_0+\gamma\xi_z, where p_0 denotes the transition probabilities of a stationary random walk on \BbbZ^d, to nearest neighbors, and \xi_z is an i.i.d. random perturbation. We give an explicit expansion, for small \gamma, of the asymptotic speed of the random walk under the annealed law, up to order 2. As an application, we construct, in dimension d\ge2, a walk which goes faster than the stationary walk under the mean environment., Comment: Published at http://dx.doi.org/10.1214/009117904000000739 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We trace here instantons through the analysis of pure Yang-Mills gluon Green functions in the Landau gauge for a window of IR momenta (0.4, Universidad Pablo de Olavide. Departamento de Sistemas Físicos, Químicos y Naturales, Postprint

Recent developments of the application of the Wigner-path (WP) method to nonequilibrium quantum transport in mesoscopic systems are presented. The concept of WP allows the formulation of a Monte Carlo simulation which is quantum mechanically rigorous and yet very similar to the one used in semiclassical transport theory. Scatterings with the potential profile and with phonons are included in the path in a way that takes automatically into account all quantum effects, such as intracollisional field effect and collisional broadening.

This paper describes a new contribution to the analysis of arbitrary shielded circuits and antennas of complex shapes, in the frame of the integral equation (IE) and Method of Moments formulation (MoM). The technique is based on the spatial image approach and a new specially truncated set of images is developed to enhance the convergence behavior of the series involved. Results show that, with the new specially truncated series of images, convergence is achieved very fast. In this paper simulated results obtained with the new approach are compared with measurements. Universidad Politécnica Federal de Lausanne

Thin films and interfaces are particularly interesting because they offer the possibility of studyng a wide range of magnetic phenomena. Thus it is possible that normally nonmagnetic materials such as Pd or Rh may become magnetic if their dimensionality is reduced. At the Fe/M (M=Mo,Tc,V) interfaces, considered in our paper, Fe induces a spin polarization in previously nonmagnetic transition-metals. These phenomena could be explained on the bases of hybridization between Fe 3d states and 3d or 4d states of transition-metals [1].

The response of the system, consisting of two types of opposite-charged fermions and their bound states (hydrogen-like atoms), to the perturbation by the external electromagnetic field in low particle kinetic energies region is studied. Investigations are based on using a new formulation of the second quantization method that includes a capability of forming the particle bound states [1]. Expressions for Green functions that describe the system response to the external electromagnetic field and take into account the presence of particle bound states (atoms) are found. Macroscopic parameters of the system, such as conductivity, permittivity and magnetic permeability in terms of these Green functions are found. As an example, the perturbation of the ideal hydrogen-like plasma by the external electromagnetic field in low temperature region is considered. Expressions for the values are found that describe the ideal gas of hydrogen-like atoms Bose-condensate response to the external electromagnetic field. Дослiджується вiдгук системи, у якiй присутнi два типи фермiонiв з протилежними зарядами та їх зв’язанi стани (атоми водневого типу), на збурення зовнiшнiм електромагнiтним полем у областi малих кiнетичних енергiй частинок. Дослiдження базуються на використаннi нового формулювання методу вторинного квантування, що включає можливiсть утворення зв’язаних станiв частинок [1]. Знайдено вирази для функцiй Грiна, що описують вiдгук системи на зовнiшнє електромагнiтне поле та враховують присутнiсть зв’язаних станiв частинок (атомiв). За допомогою цих функцiй Грiна знайдено макроскопiчнi параметри системи, такi як провiднiсть, дiелектрична та магнiтна проникнiсть. Як приклад розглянуто збурення iдеальної водневоподiбної плазми зовнiшнiм електромагнiтним полем у низькотемпературному дiапазонi. Знайдено вирази для величин, що описують вiдгук бозе-конденсату iдеального газу водневоподiбних атомiв на зовнiшнє електромагнiтне поле.

A general approach for derivation of the spectral relations for the multitime correlation functions is presented. A special attention is paid to the consideration of the non-ergodic (conserving) contributions and it is shown that such contributions can be treated in a rigorous way using multitime temperature Green functions. Representation of the multitime Green functions in terms of the spectral densities and solution of the reverse problem -- finding of the spectral densities from the known Green functions are given for the case of the three-time correlation functions., Comment: 12 pages, submitted to the special issue of the Condensed Matter Physics journal devoted to the Green's functions method

In this communication, original analytical expressions for the quadruple static potential singular integrals on rectangular domains are presented. These integrals can appear when the method of moments is used to solve the mixed potential integral equation but also the electric and the magnetic static integral equations. The analytical expressions have been obtained for both source and test cells integrals when using 3-D rectangular meshes. The reported expressions can be used to solve an extensive range of electrostatic, magnetostatic and full-wave problems.

cote interne IRCAM: Bensoam09a; None / None; National audience; This paper deals with the theoretical and numerical treatment of the unilateral dynamic contact problem between two arbitrary elastic bodies without friction. In addition to the classical variational statement that arises from static problems, a dynamic contact condition is needed and found by adjusting the balance laws of physical quantities to the impenetrability condition. In the context of infinitesimal deformation, a reciprocal formulation is then used to reduce this well-posed problem to one involving Green functions defined only on contact surfaces. It is then often possible to approximate the system using considerably fewer unknowns than with finite difference algorithms. The ability of the method to predict the contact interaction between two elastic bodies, irrespective of the material constitution and geometry, is highlighted by analytical and numerical simulations.

This paper investigates the reliability of an algorithm that implements the Green function method in free vibration analysis of Euler-Bernoulli beams. The investigation is concerned with the robustness of the algorithm with respect to the occurrence of numerical singularities in the calculation procedure of mode shapes. The problem is studied for beams supported with an arbitrary number of intermediate translational springs, which can be understood as a generalization of the cases when the beam is without elastic supports and when the beam rests on intermediate rigid supports. The problem of numerical singularities arises from the fact that the elements of the modal vector have to be expressed in terms of an "arbitrarily" chosen referential element of that vector, whose value can vanish if it coincides closely enough with a node of the sought mode shape. The problem is generally tackled here with the introduction of a fictitious spring of a vanishingly small stiffness, and the robustness of the algorithm depends crucially on the appropriate placement of that spring. This paper presents several useful guidelines for the implementation of computer code based on these principles and its reliability is demonstrated through examples.

We aim here at determining the Green function for general Schrödinger operators on product networks. The first step consists in expressing Schrödinger operators on a product network as sum of appropriate Schrödinger operators on each factor network. Hence, we apply the philosophy of the separation of variables method in PDE, to express the Green function for the Schrödinger operator on a product network using Green functions on one of the factors and the eigenvalues and eigenfunctions of some Schrödinger operator on the other factor network. We emphasize that our method only needs the knowledge of eigenvalues and eigenfunctions of one of the factors, whereas other previous works need the spectral information of both factors. We apply our results to compute the Green function of Pm×Sh , where Pm is a Path with m vertices and Sh is a Star network with h+1 vertices.