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J M L Bernard - One of the best experts on this subject based on the ideXlab platform.
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propagation over a Constant impedance plane Arbitrary primary sources and impedance analysis of cut in active case exact series and complete asymptotics
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: J M L BernardAbstract:We analyze and detail here a compact solution for the electromagnetic field scattered by an Arbitrary Constant impedance plane, considering exact potentials for primary current sources composed of dipoles with Arbitrary orientations. The special function involved in our expressions is rewritten with nonsingular integral expression valid for any complex arguments that exhibits a correct cut in active case. We describe efficient exact series for Arbitrary cases and complete asymptotics, which are both expressed in terms of error functions.
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on a novel expression of the field scattered by an Arbitrary Constant impedance plane
Wave Motion, 2011Co-Authors: J M L BernardAbstract:Abstract The electromagnetic field scattered by an impedance plane is generally given by its plane wave expansion (Fourier representation). Here we derive an alternative expression which is more suitable for point source illumination. For this, we consider an original expression of the Hertz potentials for the incident field and express the scattered potentials in a novel form. A special function then involved can be expressed in an integral which is in turn expanded in a convergent series. The expression presented also permits us to express complete asymptotics. Our development considers an Arbitrary impedance, passive or active.
Ryan Williams - One of the best experts on this subject based on the ideXlab platform.
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nonuniform acc circuit lower bounds
Journal of the ACM, 2014Co-Authors: Ryan WilliamsAbstract:The class ACC consists of circuit families with Constant depth over unbounded fan-in AND, OR, NOT, and MODm gates, where m > 1 is an Arbitrary Constant. We prove the following. ---NEXP, the class of languages accepted in nondeterministic exponential time, does not have nonuniform ACC circuits of polynomial size. The size lower bound can be slightly strengthened to quasipolynomials and other less natural functions. ---ENP, the class of languages recognized in 2O(n) time with an NP oracle, doesn’t have nonuniform ACC circuits of 2no(1) size. The lower bound gives an exponential size-depth tradeoff: for every d, m there is a Δ > 0 such that ENP doesn’t have depth-d ACC circuits of size 2nΔ with MODm gates. Previously, it was not known whether EXPNP had depth-3 polynomial-size circuits made out of only MOD6 gates. The high-level strategy is to design faster algorithms for the circuit satisfiability problem over ACC circuits, then prove that such algorithms entail these lower bounds. The algorithms combine known properties of ACC with fast rectangular matrix multiplication and dynamic programming, while the second step requires a strengthening of the author’s prior work.
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non uniform acc circuit lower bounds
Conference on Computational Complexity, 2011Co-Authors: Ryan WilliamsAbstract:The class ACC consists of circuit families with Constant depth over unbounded fan-in AND, OR, NOT, and MOD$m$ gates, where $m > 1$ is an Arbitrary Constant. We prove:- $NTIME[2^n]$ does not have non-uniform ACC circuits of polynomial size. The size lower bound can be strengthened to quasi-polynomials and other less natural functions.- $E^{NP}$, the class of languages recognized in $2^{O(n)}$ time with an $NP$ oracle, doesn't have non-uniform ACC circuits of $2^{n^{o(1)}}$ size. The lower bound gives a size-depth tradeoff: for every $d$, $m$ there is a $\delta > 0$ such that $E^{NP}$ doesn't have depth-$d$ ACC circuits of size $2^{n^{\delta}}$ with MOD$m$ gates.Previously, it was not known whether $EXP^{NP}$ had depth-3 polynomial size circuits made out of only MOD6 gates. The high-level strategy is to design faster algorithms for the circuit satisfiability problem over ACC circuits, then prove that such algorithms can be applied to obtain the above lower bounds.
D S Shirokov - One of the best experts on this subject based on the ideXlab platform.
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on Constant solutions of su 2 yang mills equations with Arbitrary current in euclidean space ℝn
Journal of Nonlinear Mathematical Physics, 2020Co-Authors: D S ShirokovAbstract:In this paper, we present all Constant solutions of the Yang-Mills equations with SU(2) gauge symmetry for an Arbitrary Constant non-Abelian current in Euclidean space ℝn of Arbitrary finite dimens...
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on Constant solutions of rm su 2 yang mills equations with Arbitrary current in pseudo euclidean space mathbb r p q
arXiv: Mathematical Physics, 2019Co-Authors: D S ShirokovAbstract:We present classification and explicit form of all Constant solutions of the Yang-Mills equations with ${\rm SU}(2)$ gauge symmetry for an Arbitrary Constant non-Abelian current in pseudo-Euclidean space ${\mathbb R}^{p,q}$ of Arbitrary finite dimension $n=p+q$. We use the method of hyperbolic singular value decomposition and the method of two-sheeted covering of orthogonal group by spin group to do this. NonConstant solutions of the Yang-Mills equations can be considered in the form of series of perturbation theory. The results of this paper are new and can be used to solve some problems in particle physics, in particular, to describe physical vacuum and to fully understand a quantum gauge theory. The results of this paper generalize our previous results for the case of Arbitrary Euclidean case ${\mathbb R}^n$.
Abimbola Abolarinwa - One of the best experts on this subject based on the ideXlab platform.
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elliptic gradient estimates and liouville theorems for a weighted nonlinear parabolic equation
Journal of Mathematical Analysis and Applications, 2019Co-Authors: Abimbola AbolarinwaAbstract:Abstract Let ( M N , g , e − f d v ) be a complete smooth metric measure space with ∞-Bakry–Emery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation ( Δ f − ∂ ∂ t ) u ( x , t ) + q ( x , t ) u α ( x , t ) = 0 , where ( x , t ) ∈ M N × ( − ∞ , ∞ ) and α is an Arbitrary Constant. As Applications we prove a Liouville-type theorem for positive ancient solutions and Harnack-type inequalities for positive bounded solutions.
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elliptic gradient estimates and liouville theorems for a weighted nonlinear parabolic equation
arXiv: Differential Geometry, 2018Co-Authors: Abimbola AbolarinwaAbstract:Let $(M^N, g, e^{-f}dv)$ be a complete smooth metric measure space with $\infty$-Bakry-\'Emery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation \begin{align*} \displaystyle \Big(\Delta_f - \frac{\partial}{\partial t}\Big) u(x,t) +q(x,t)u^\alpha(x,t) = 0, \end{align*} where $(x,t) \in M^N \times (-\infty, \infty)$ and $\alpha$ is an Arbitrary Constant. As Applications we prove a Liouville-type theorem for positive ancient solutions and Harnack-type inequalities for positive bounded solutions.
Panayiotis Vafeas - One of the best experts on this subject based on the ideXlab platform.
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The 3D Happel model for complete isotropic Stokes flow
Hindawi Limited, 2004Co-Authors: George Dassios, Panayiotis VafeasAbstract:The creeping flow through a swarm of spherical particles that move with Constant velocity in an Arbitrary direction and rotate with an Arbitrary Constant angular velocity in a quiescent Newtonian fluid is analyzed with a 3D sphere-in-cell model. The mathematical treatment is based on the two-concentric-spheres model. The inner sphere comprises one of the particles in the swarm and the outer sphere consists of a fluid envelope. The appropriate boundary conditions of this non-axisymmetric formulation are similar to those of the 2D sphere-in-cell Happel model, namely, nonslip flow condition on the surface of the solid sphere and nil normal velocity component and shear stress on the external spherical surface. The boundary value problem is solved with the aim of the complete Papkovich-Neuber differential representation of the solutions for Stokes flow, which is valid in non-axisymmetric geometries and provides us with the velocity and total pressure fields in terms of harmonic spherical eigenfunctions. The solution of this 3D model, which is self-sufficient in mechanical energy, is obtained in closed form and analytical expressions for the velocity, the total pressure, the angular velocity, and the stress tensor fields are provided
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© Hindawi Publishing Corp. THE 3D HAPPEL MODEL FOR COMPLETE ISOTROPIC STOKES FLOW
2003Co-Authors: George Dassios, Panayiotis VafeasAbstract:The creeping flow through a swarm of spherical particles that move with Constant velocity in an Arbitrary direction and rotate with an Arbitrary Constant angular velocity in a quiescent Newtonian fluid is analyzed with a 3D sphere-in-cell model. The mathematical treatment is based on the two-concentric-spheres model. The inner sphere comprises one of the particles in the swarm and the outer sphere consists of a fluid envelope. The appropriate boundary conditions of this non-axisymmetric formulation are similar to those of the 2D sphere-in-cell Happel model, namely, nonslip flow condition on the surface of the solid sphere and nil normal velocity component and shear stress on the external spherical surface. The boundary value problem is solved with the aim of the complete Papkovich-Neuber differential repre-sentation of the solutions for Stokes flow, which is valid in non-axisymmetric geometries and provides us with the velocity and total pressure fields in terms of harmonic spherical eigenfunctions. The solution of this 3D model, which is self-sufficient in mechanical energy, is obtained in closed form and analytical expressions for the velocity, the total pressure, the angular velocity, and the stress tensor fields are provided