We consider a perturbed graph consisting of two infinite edges, loop, and glued arbitrary finite γε with small where is obtained by ε−1 times contraction some fixed ε parameter. On the graph, we Schrödinger operator whose potential on edges can singularly depend Kirchhoff condition at internal vertices Dirichlet or Neumann boundary vertices. For eigenvalue corresponding eigenfunction prove holo...

jachymski [ proc. amer. math. soc., 136 (2008), 1359-1373] gave modified version of a banach fixed point theorem on a metric space endowed with a graph. in the present paper, (g, φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. also, hardy-rogers g-contraction have been introduced and some fixed point theorems have been proved. s...

Let G be a locally compact group. We use the canonical operator space structure on the spaces L(G) for p ∈ [1,∞] introduced by G. Pisier to define operator space analoguesOAp(G) of the classical Figà-Talamanca–Herz algebrasAp(G). If p ∈ (1,∞) is arbitrary, then Ap(G) ⊂ OAp(G) such that the inclusion is a contraction; if p = 2, then OA2(G) ∼= A(G) as Banach spaces spaces, but not necessarily as ...

In Reinforcement Learning, the performance of learning agents is highly sensitive to choice time discretization. Agents acting at high frequencies have best control opportunities, along with some drawbacks, such as possible inefficient exploration and vanishing action advantages. The repetition actions, i.e., persistence, comes into help, it allows agent visit wider regions state space improve ...

Let Gn : C → C denote the PGD updates at the n-sample level—that is, as applied to the objective function Ln(θ) = 1 n ∑n i=1 `i(θ;Zi). Similarly, let G denote the projected gradient operator as applied at the population level (to the function L̄ = ELn(θ)). Our goal is to bound the error ‖θ − θ‖2. Last lecture, we showed that if the population loss L̄ : C → R is (γ`, γμ) {strongly convex, smooth},...

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We consider the imaginary time flow of a quadratic hyperbolic Hamiltonian on symplectic plane, apply it to Schrödinger polarization and study corresponding evolution polarized sections. The is periodic in sections has interesting features. On intervals for which real or Kähler, half–form corrected given by unitary operators turn out be equivalent classical Segal-Bargmann transforms (which are u...

A biosignal is used as a control signal for electrical stimulation to restore weakened muscle function due damage the central nervous system. In patients with system damage, sufficient contraction does not occur spontaneously. this case, applying can cause normal contraction. However, it necessary remove artifact caused by stimulation. This paper describes design that removes in real time using...

The curvature KT (w) of a contraction T in the Cowen-Douglas class B1(D) is bounded above by the curvature KS∗(w) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this note, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions o...