This article compares theories and social policies of social democrats and other representatives of the left-wing political spectrum in six European countries to explain why, in certain countries such as Sweden, Norway, and Switzerland, weak social groups became the target of illiberal and negative eugenic policy, especially isolation and sterilization, while elsewhere left-wing politicians and...

Vizing conjectured in 1963 that γ(G2H) > γ(G)γ(H) for any graphs G and H. A graph G is said to satisfy Vizing’s conjecture if the conjectured inequality holds for G and any graph H. Vizing’s conjecture has been proved for γ(G) 6 3, and it is known to hold for other classes of graphs. Clark and Suen in 2000 showed that γ(G2H) > 12γ(G)γ(H) for any graphs G and H. We give a slight improvement of t...

Let L be a finite distributive lattice and μ : L → R a logsupermodular function. For functions k : L → R let Eμ(k; q) def = ∑ x∈L k(x)μ(x)q ∈ R[q]. We prove for any pair g, h : L → R of monotonely increasing functions, that Eμ(g; q) ·Eμ(h; q) ≪ Eμ(1; q) · Eμ(gh; q), where “≪ ” denotes coefficientwise inequality of real polynomials. The FKG inequality of Fortuin, Kasteleyn and Ginibre (1971) is ...

We give a new proof of the arithmetic large sieve inequality based on an amplification argument, and use a similar method to prove a new sieve inequality for classical holomorphic cusp forms. A sample application of the latter is also given. 1. The classical large sieve The classical arithmetic large sieve inequality states that, for any real numbers N , Q > 1, any choice of subsets Ωp ⊂ Z/pZ f...

This paper discusses the robust filtering problems for linear discrete-time systems with polytopic parameter uncertainty under the H2 and H , performance. We aim to derive a less conservative design than existing sufficient Iinear matrix inequality (LMI) based conditions. It is shown that a more efficient evaluation of robust HZ or H , performance can be obtained by a matrix inequality conditio...

Abstract -In this paper, the problem of H∞ filtering design is studied for nonlinear sampled-data systems using the Takagi-Sugeno (T-S) fuzzy model approach. Traditionally, the sufficient conditions for the existence of such H∞ filter are characterized in terms of the solution of a differential Hamilton-Jacobi inequality with jumps, which is equivalent to solving the partial differential inequa...

we show that the variational inequality $vi(c,a)$ has aunique solution for a relaxed $(gamma , r)$-cocoercive,$mu$-lipschitzian mapping $a: cto h$ with $r>gamma mu^2$, where$c$ is a nonempty closed convex subset of a hilbert space $h$. fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming more complicated, are not...

In the paper, we study dynamic h-convexity for interval valued functions. Some generalizations of Jensen’s inequality in analysis h-convex functions on time scales are proved paper. seek applications generalized inequality, Hermite-Hadamard type inequalities established. Further discrete analogues newly results also presented numerical examples provided to check validity results.

Let H be the class of complex-valued harmonic mappings f=h+g¯ defined in unit disk D:={z?C:|z|<1}, where h and g are analytic functions D with normalization h(0)=0=h?(0)?1 g(0)=0. H0={f=h+g¯?H:g?(0)=0}. PH0(M):={f=h+g¯?H0:Re(zh??(z))>?M+|zg??(z)|,z?DandM>0}. univalent [Ghosh N, Allu V. On some subclasses mappings. Bull Aust Math Soc. 2020;101:130–140.]. In this paper, we obtain sharp Bohr–Rogos...

and Applied Analysis 3 For given nonlinear operators T, g, h, we consider the problem of finding u ∈ H : h u ∈ K such that 〈 Tu, g v − h u 〉 ≥ 0, ∀v ∈ H : g v ∈ K, 2.1 which is called the extended general variational inequality. Noor 13–16 has shown that the minimum of a class of differentiable nonconvex functions on hg-convex set K in H can be characterized by extended general variational ineq...