It is well known that Landau's phenomenological description' of a continuous phase transition is very useful in classifying syminetry changes which can take place during such a transition. A good illustrative example is given by Lyubarskii. The procedure can be summarized as follows: (1) Find the space group 6 of the high-symmetry phase of a physical system (crystal, alloy, etc.) and the irredu...

Low weight and high load capacity are remarkable advantages of sandwich panels with corrugated core, which make them more considerable by engineering structure designers. It’s important to consider the limitations such as yielding and buckling as design constraints for optimal design of these panels. In this paper, multi-objective optimization of sandwich panels with corrugated core is carried ...

Property (T) for groups means a dichotomy: a representation either has an invariant vector or all vectors are far from being invariant. We show that, under a stronger condition of Żuk, a similar dichotomy holds for almost representations as well.

For a separable rearrangement invariant space X on $$(0,\infty )$$ of fundamental type we identify the set all $$p\in [1,\infty ]$$ such that $$\ell ^p$$ is finitely represented in way unit basis vectors ( $$c_0$$ if $$p=\infty $$ ) correspond to pairwise disjoint and equimeasurable functions. This characterization hinges upon description approximate eigenvalues doubling operator $$x(t)\mapsto ...

All known approaches for the design of increasing translation-invariant binary window "lters involve combinatoric searches. This paper proposes a new switching algorithm having the advantage that the search is over a smaller set than other algorithms. Beginning with an estimate from image realizations of the optimal generic (nonincreasing) window function, the algorithm switches (exchanges) a s...

We study the class of $$ \mathfrak{o} _{2n+1}$$ -invariant quantum integrable models in framework algebraic Bethe ansatz and propose a construction vector terms Drinfeld currents for Yangian double \mathcal{D}Y ( _{2n+1})$$ . calculate action monodromy matrix elements on off-shell vectors these obtain recurrence relations vectors. The formulas can be used to investigate scalar products models.

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

We investigate representations of the Z22-graded extension osp(1|2), which is spectrum generating algebra recently introduced version superconformal mechanics. The main result a classification irreducible lowest weight modules osp(1|2). This done via introduction Verma and its maximal invariant submodule generated by singular vectors. Explicit formulas all vectors are also presented.