We consider contractive homomorphisms of a planar algebra A(Ω) over a finitely connected bounded domain Ω ⊆ C and ask if they are necessarily completely contractive. We show that a homomorphism ρ : A(Ω) → B(H) for which dim(A(Ω)/ ker ρ) = 2 is the direct integral of homomorphisms ρT induced by operators on two dimensional Hilbert spaces via a suitable functional calculus ρT : f 7→ f(T ), f ∈ A(...

Within this manuscript we generalize the two recently obtained results of O. Popescu and G. Stan, regarding F-contractions in complete, ordinary metric space to 0-complete partial metric-like space. As Stan use less conditions than D. Wardovski did his paper from 2012, introduce, with help one our lemmas, a new method proving fixed point theory. Requiring that function F only be strictly increa...

In this paper, we consider the problem of invariant set computation for black-box switched linear systems using merely a finite observations system trajectories. particular, paper focuses on polyhedral sets. We propose data-driven method based one step forward reachable set. For formal verification proposed method, introduce concepts $\lambda$-contractive sets and almost-invariant systems. The ...

We prove that the first positive eigenvalue, normalized by the volume, of the sub-Laplacian associated with a strictly pseudoconvex pseudo-Hermitian structure θ on the CR sphere S ⊂ C, achieves its maximum when θ is the standard contact form.

In this paper we establish new forward and backward versions of Ekeland’s variational principle for the class of strictly-decreasing forward(resp. backward-) lower-semicontinuou functionals in pseudo-quasimetric spaces. We do not require that the space under consideration either is complete or enjoys the limit uniqueness property due to the fact that the collections of forward and backward limi...

In order to circumvent the difficulties in solving numerically discrete optimal transport problem, which one minimizes linear target function $$P\mapsto \left\langle C,P\right\rangle {:}{=}\sum _{i,j}C_{ij}P_{ij}$$ , Cuturi introduced a variant of problem is altered by convex $$\varPhi (P)=\left\langle -\lambda {{\mathcal {H}}}(P)$$ where $${{\mathcal {H}}}$$ Shannon entropy and $$\lambda $$ po...

In this paper, we prove a Stolarsky type inequality for pseudo-integrals. More precisely, we show that: ∫ sup [0,1] f(x 1 a+b )dx ≥ ( ∫ sup [0,1] f(x 1 a )dx ) ̄ ( ∫ sup [0,1] f(x 1 b )dx ) , where a, b > 0, f : [0, 1] → [0, 1] is a continuous and strictly decreasing function ( strictly increasing function ) and μ is the sup-measure the same as Theorem 2.4. Also ̄ is represented by an increasing...

We relate the collected experimental data on the minimum energy for photoactivation (E(a)) to the wavelengths of peak absorbance (lambda(max)) of 12 visual pigments. The E(a) values have been determined from the temperature-dependence of spectral sensitivity in the long-wavelength range. As shown previously, the simple physical idea E(a) =const. x (1/lambda(max)) (here termed the Stiles-Lewis-B...