whereΩ is a bounded smooth domain ofRN ,N ≥ 1, with boundary ∂Ω,ai(u,v) are J-elliptic bilinear forms continuous on H1(Ω)×H1(Ω), (·,·) is the inner product in L2(Ω), and f i are J-regular functions. This system, introduced by Bensoussan and Lions (see [3]), arises in the management of energy production problems where J-units are involved (see [4] and the references therein). In the case studied...

In attribute-based signatures, each signer receives a signing key from the authority, which is associated with the signer’s attribute, and using the signing key, the signer can issue a signature on any message under a predicate, if his attribute satisfies the predicate. One of the ultimate goals in this area is to support a wide class of predicates, such as the class of arbitrary circuits, with...

Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As jω in the analog s-d...

as an application of hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. we have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear backlund transformations and construction of ...

Here, Ω is a bounded smooth domain of RN , N ≥ 1, with boundary ∂Ω, (·,·) is the inner product in L2(Ω), for i= 1, . . . , J , ai(u,v) is a continuous bilinear form on H1(Ω)× H1(Ω), and f i is a regular function. Problem (1.1) arises in themanagement of energy production problems where J power generation machines are involved (see [2] and the references therein). In the case studied here, (MU)i...

This paper considers the globally asymptotic stabilization problem of multi-input multi-output bilinear systems with undamped natural response. Under the conditions for asymptotic stabilization by static state feedback control and system detectability, two output dynamic feedback controllers with saturation bounded control are constructed. The global asymptotic stability of the closed-loop syst...

We prove a super-linear lower bound on the size of a bounded depth bilinear arithmetical circuit computing cyclic convolution. Our proof uses the strengthening of the Donoho-Stark uncertainty principle [DS89] given by Tao [Tao05], and a combinatorial lemma by Raz and Shpilka [RS03]. This combination and an observation on ranks of circulant matrices, which we use to give a much shorter proof of ...

Ω ∇u · v, where u is harmonic in the domain Ω ≡ {(x, t) ∈ Rn+1 : t > φ(x)}, with φ Lipschitz, and where v ∈ W loc is vector valued. He showed that the bilinear form (1.1) is bounded by the L2 norm of the square function plus the non-tangential maximal function of u, times the same expression for v. In the present note, we generalize Dahlberg’s Theorem to variable coefficient divergence form ell...

In this paper, we consider the class of infinite-dimensional discrete-time linear systems with multiplicative random disturbances (i.e. with the state multiplied by a random sequence), also known as stochastic bilinear systems. We formulate and solve the quadratic optimal-control problem for this class of systems subject to an arbitrary additive stochastic £2 input disturbance. Under assumption...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...