The representation of measurable functions by integrals with kernels of unitary transformations of the space 𝐿₂(0,∞,)

1965 ◽  
pp. 241-268
Author(s):  
A. A. Talaljan
Keyword(s):  
Measurable Functions ◽  
Unitary Transformations

scholarly journals Experimental demonstrations of unconditional security in a purely classical regime

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Byoung S. Ham
Keyword(s):  
Quantum Key Distribution ◽  
Key Distribution ◽  
Unconditional Security ◽  
Zehnder Interferometer ◽  
Experimental Demonstration ◽  
Orthogonal Bases ◽  
Unitary Transformations ◽  
Mach Zehnder Interferometer

AbstractSo far, unconditional security in key distribution processes has been confined to quantum key distribution (QKD) protocols based on the no-cloning theorem of nonorthogonal bases. Recently, a completely different approach, the unconditionally secured classical key distribution (USCKD), has been proposed for unconditional security in the purely classical regime. Unlike QKD, both classical channels and orthogonal bases are key ingredients in USCKD, where unconditional security is provided by deterministic randomness via path superposition-based reversible unitary transformations in a coupled Mach–Zehnder interferometer. Here, the first experimental demonstration of the USCKD protocol is presented.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

1997 ◽  
Vol 4 (6) ◽  
pp. 557-566
Author(s):  
B. Půža
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Vector Function ◽  
Unique Solvability ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Deviating Arguments ◽  
Measurable Functions

Abstract Sufficient conditions of solvability and unique solvability of the boundary value problem u (m)(t) = f(t, u(τ 11(t)), . . . , u(τ 1k (t)), . . . , u (m–1)(τ m1(t)), . . . . . . , u (m–1)(τ mk (t))), u(t) = 0, for t ∉ [a, b], u (i–1)(a) = 0 (i = 1, . . . , m – 1), u (m–1)(b) = 0, are established, where τ ij : [a, b] → R (i = 1, . . . , m; j = 1, . . . , k) are measurable functions and the vector function f : ]a, b[×Rkmn → Rn is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.

Lie groups and unitary transformations in ligand field theory

1983 ◽  
Vol 23 (1) ◽  
pp. 169-183 ◽  
Author(s):  
Chia-Chung Sun ◽  
Yan-De Han ◽  
Be-Fu Li ◽  
Qian-Shu Li
Keyword(s):  
Field Theory ◽  
Lie Groups ◽  
Ligand Field ◽  
Ligand Field Theory ◽  
Unitary Transformations

scholarly journals Graphical description of unitary transformations on hypergraph states

2017 ◽  
Vol 50 (19) ◽  
pp. 19LT01 ◽  
Author(s):  
Mariami Gachechiladze ◽  
Nikoloz Tsimakuridze ◽  
Otfried Gühne
Keyword(s):  
Unitary Transformations

Compact embeddings of some weighted Sobolev spaces on ℝN

1995 ◽  
Vol 117 (2) ◽  
pp. 333-338 ◽  
Author(s):  
Raffaele Chiappinelli
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Compact Embeddings ◽  
Measurable Functions ◽  
Image Position

Let ρ,ρ0,ρ1 be positive, measurable functions on ℝN. For 1 ≤ t < ∞, consider the weighted Lebesgue and Sobolev spaces

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