Bio‐Inspired Molecular Events in Poly(Ionic Liquids)
Originating from dipolar and polar inter‐ and intra‐chain interactions of the building blocks, the topologies and morphologies of poly(ionic liquids) (PIL) govern their nano‐ and micro‐processibility. Modulating the interactions of cation‐anion pairs with aliphatic dipolar components enables the tunability of properties, facilitated by “bottom‐up ...
Jiahui Liu, Marek W. Urban
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Artificial Intelligence-Driven Automated Design of Anterior and Posterior Crowns Under Diverse Occlusal Scenarios. [PDF]
Hlaing NHMM +5 more
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Evaluating public health campaigns on health promotion, substance use prevention and physical activity: a systematic review. [PDF]
Zandonai T +6 more
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Responsible AI in student management: preventing misdecision in career choice of university students under inaccurate guidance. [PDF]
Yin S +4 more
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Adaptive image encryption approach using an enhanced swarm intelligence algorithm. [PDF]
Minocha S +3 more
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Utilizing aggregation operators based on q-rung orthopair neutrosophic soft sets and their applications in multi-attributes decision making problems. [PDF]
Ali S +4 more
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Let \(E, F\) be Riesz spaces. \(T: E \to F\) is called an ideal (inverse ideal) operator if \(T (I) (T^{-1} (J))\) is an order ideal in \(E (F)\) for each order ideal \(I (J)\) in \(E (F)\). It is shown that these operators can be characterized by their action on principal order ideals.
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Operator Ideals Generalizing the Ideal of Strictly Singular Operators
Mathematische Nachrichten, 1980AbstractIt is well‐known that an operator T ∈ L(E, F) is strictly singular if ∥Tx∥≧λ∥x∥ on a subspace Z ⊂ E implies dim Z < + ∞. The present paper deals with ideals of operators defined by a condition — ∥Tx∥≧λ∥x∥ on an infinite‐dimensional subspace Z ⊂ E implies Z ∉ F — F being a „quasi‐injective”︁ class of BANACH spaces.
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The notion of two-Lipschitz operator arises as a natural extension of the idea of Lipschitz operator from \(X\) (a metric space) to \(E\) (a Banach space) to operators defined on \(X \times Y\) (\(X\) and \(Y\) being metric spaces) and taking values on \(E\). As usual, it is assumed that \(X\) and \(Y\) have each a distinguished point (both denoted by \
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