Following James’ approach, we shall define the Banach space J(e) for each vector e = (e1, e2, ..., ed) ∈ R d with e1 6= 0. The construction immediately implies that J(1) coincides with the Hilbert space i2 and that J(1;−1) coincides with the celebrated quasireflexive James space J . The results of this paper show that, up to an isomorphism, there are only the following two possibilities: (i) ei...

Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class (answering a question of Truss) and apply this to show that the homeomorphi...

Tannaka duality describes the relationship between algebraic objects in a given category and functors into that category; an important case is that of Hopf algebras and their categories of representations; these have strong monoidal forgetful “fibre functors” to the category of vector spaces. We simultaneously generalize the theory of Tannaka duality in two ways: first, we replace Hopf algebras...

The concept of Support Vector Machines (SVMs) for classification and regression has been introduced by Vapnik in 1995. The classification algorithm proposed by Vapnik was intended as binary classification for linearly separable input data and the solution was to find an Optimal Separating Hyperplane (OSH). Very often the input data is not linearly separable. SVMs employ a technique commonly kno...

In this work, we use similarly separable vectors in Hilbert spaces to provide generalized integral results related majorization, Niezgoda, and Ćebysév type inequalities. Next, furnish some refinements of these Theorems obtained work extend improve several known the literature. An important aspect our is that inequalities are directly Arithmetic, Geometric, Harmonic, Power means. These means hav...

in this paper, a new circuit is proposed for step-up z-source inverter based on qzsi (quasi-z-source inverter). the proposed topology inherits all advantages of the conventional topology. the proposed topology in comparison with conventional topology reduces the st (shoot-through) duty cycle by over 25% at the same voltage boost factor. theoretical analysis of the proposed qzsi in the st and no...

Generating accurate digital tree models from scanned environments is invaluable for forestry, agriculture, and other outdoor industries in tasks such as identifying fall hazards, estimating trees’ biomass calculating traversability. Existing methods reconstruction rely on sparse feature identification to segment a forest into individual trees generate branch structure graph, limiting their appl...

‎let $pa$ be a commutative banach algebra and $ex$ be a left banach $pa$-module‎. ‎we study the set‎ ‎$dec_{pa}(ex)$ of all elements in $pa$ which induce a decomposable multiplication operator on $ex$‎. ‎in the case $ex=pa$‎, ‎$dec_{pa}(pa)$ is the well-known apostol algebra of $pa$‎. ‎we show that $dec_{pa}(ex)$ is intimately related with the largest spectrally separable subalgebra of $pa$ and...