Let there be given, on a category C, a pair (*, *) of adjoint monoidal closed-category-valued pseudofunctors. Thus, to each object X ∈ C is associated a closed category DX , with unit object OX ; and to each C-map ψ : X → Y , adjoint monoidal functors DX ψ∗ ←−− −→ ψ∗ DY . There are also, as before, compatibilities—expressed by commutative diagrams—among adjunction, pseudofunctoriality, and mono...

In this paper, images of the tempered Ψ-Hilfer fractional integral and Ψ-Caputo derivative under generalized Laplace transform are derived. The results applied to find a solution an initial value problem for nonhomogeneous linear differential equation with order α n− 1 <α<n N. An illustrative example is given 0 <α<1 comparing solutions same but different tempering Ψ.

Let (M‾,〈,〉,eψ) be a Riemannian manifold with density, and let M closed n-dimensional submanifold of M‾ the induced metric density. We give an upper bound on first eigenvalue λ1 problem for Δψ (the Laplacian associated to density) in terms average norm vector H→ψ+∇‾ψ respect volume form by where H→ψ is mean curvature density eψ. When M‾=Rn+k or M‾=Sn+k−1, equality between its implies that eψ Ga...

A new mixed variational–hemivariational problem is introduced, a(u,v−u)+b(v−u,λ)+φ(v)−φ(u)+J0(Tu;Tv−Tu)≥(f,v−u)X, b(u,μ−λ)−ψ(μ)+ψ(λ)−Ψ0(Rλ;Rμ−Rλ)≤0, (v∈X, μ∈Λ⊆Y), focusing on its well-posedness. We are looking for a pair solution (u,λ)∈X×Λ working into Hilbert spaces framework. Some particular cases with applications in mechanics highlighted. special attention payed to case leading penalty term...

For a function Ψ : R>0 → R>0, let Exact(Ψ) be the set of real numbers that are approximable by rational numbers to order Ψ, but to no order cΨ with 0 < c < 1. When Ψ is non-increasing and satisfies Ψ(x) = o(x−2), we establish that Exact(Ψ) has Hausdorff dimension 2/λ, where λ is the lower order at infinity of the function 1/Ψ. Furthermore, we study the set Exact(Ψ) when Ψ is not assumed to be n...

We show the density of smooth Sobolev functions Wk,∞(Ω)∩C∞(Ω) in Orlicz-Sobolev spaces Lk,Ψ(Ω) for bounded simply connected planar domains Ω and doubling Young Ψ.

Symmetrical patterns exist in the nature of inequalities, which play a basic role theoretical and applied mathematics. In several studies, inequalities present accurate approximations functions based on their symmetry properties. paper, we prove completely monotonic (CM) property some involving function Δ(l)=ψ″(l)+ψ′(l)2 hence deduce new double inequality for it. Additionally, study CM degree ψ...

and Applied Analysis 3 Proof. First we show thatN ̸ = 0. From (15) and (16), we rewrite J (φ, ψ) = 1 2 ( 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 E1 − ω 1 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 l 2) + 1 2 ( 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 E2 − ω 2 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 l 2) − 1 4 ∑ n∈Z (a 1 φ 4 n + a 2 ψ 4 n + 2a 3 φ 2 n ψ 2 n ) , (18) I (φ, ψ) = 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 E1 − ω 1 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 l 2 + 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 E2 − ω 2 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 l 2 − ∑ n∈Z (a 1 φ 4 n + a 2 ψ 4 n + 2a 3 φ 2 n ψ 2 n )...

Productions of σ meson in J/ψ and ψ(2s) decays Abstract Productions of scalar meson(σ) in the decays of J/ψ → ω + σ,J/ψ → γ + σ and ψ(2s) → ω + σ, J/ψ + σ, γ + σ and ee + annihilations in the regions of J/ψ and ψ are studied 1

Hence, there is an eigenstate |ψ〉 = A|φ〉 of H with this same energy eigenvalue. We could equally well have begun with the statement that H|ψ〉 = E|ψ〉 and then found a state of H given by |φ〉 = A†|ψ〉 with the same energy. Note that a Hamiltonian of the two given forms will have only non-negative eigenvalues: 〈ψ|A†A|ψ〉 = ∣∣|Aψ〉∣∣2 ≥ 0. Equality holds only if the state is annihilated by A. Analogou...