$$ \mathcal{I}_g $$-normal and $$ \mathcal{I}_g $$-regular spaces

$ \mathcal{I}_g $ \mathcal{I}_g -normal and $ \mathcal{I}_g $ \mathcal{I}_g -regular spaces are introduced and various characterizations and properties are given. Characterizations of normal, mildly normal, g-normal, regular and almost regular spaces are also given.     

Pro-\mathcal {C} completions of orientable \text{ PD }^3-pairs

Let \({\mathcal {C}}\) be a class of finite groups. We study some sufficient conditions for the pro- \({\mathcal {C}}\) completion of an orientable \(\text{ PD }^3\) -pair over \(\mathbb {Z}\) to be an orientable profinite \(\text{ PD }^3\) -pair over \(\mathbb {F}_p\) . More results are proven for the pro- \(p\) completion of \(\text{ PD }^3\) -pairs.     

Yangians and $$\mathcal{W} $$ -Algebras

We present a connection between -algebras and Yangians in the case of gl(N) algebras, as well as for twisted Yangians and super-Yangians. We illustrate this connection, which allows constructing an R-matrix for the -algebras and classifying their finite-dimensional irreducible representations, in the framework of the nonlinear Schrödinger equation in 1+1 dimensions.     

A class of multipliers for $$\mathcal{W}^ \bot $$

Let denote the class of ergodic probability preserving transformations which are disjoint from every weakly mixing system. Let be the class of multipliers for , i.e. ergodic transformations whose all ergodic joinings with any element of are also in . Fix an ergodic rotationT, a mildly mixing actionS of a locally compact second countable groupG and an ergodic cocycle ϕ forT with values inG. The main result of the paper is a sufficient (and also necessary by [LeP] whenG is countable Abelian andS is Bernoullian) condition for the skew product build fromT, ϕ andS to be an element of . Moreover, the self-joinings of such extensions ofT are described with an application to study semisimple extensions of rotations. Dedicated to Hillel Furstenberg on the occasion of his retirement The first-named author was supported in part by CRDF, grant UM1-2546-KH-03. The second-named author was supported in part by KBN grant 1P03A 03826.     

Note on $$ \mathcal{I}R $$-closed and $$ A_{\mathcal{I}R} $$-sets

We characterize and discuss the properties of $ \mathcal{I}R $ \mathcal{I}R -closed sets and $ A_{\mathcal{I}R} $ A_{\mathcal{I}R} -sets. Also, we give characterizations of weakly $ \mathcal{I} $ \mathcal{I} -locally closed sets and $ \mathcal{I} $ \mathcal{I} -submaximal spaces. A characterization of codense ideals in terms of $ \mathcal{I}R $ \mathcal{I}R -closed sets is also given.     

On the Intersection of $$$$-Complete Open Subsets with $$\mathcal {C}^2$$C2 Boundary in $$\mathbb {C}^n$$Cn

We prove that in \(\mathbb {C}^n\), the intersection of finitely many open, relatively compact, \((n-1)\)-complete subsets with \(\mathcal {C}^2\) boundary for which every two boundaries intersect transversally, is cohomologically \((n-1)\)-complete.     

Three-dimensional $$ \mathcal{N} $$=4 superconformal superfield theories

We consider the map of three-dimensional N=4 superfields to the N=3 harmonic superspace. The left and right representations of the N=4 superconformal group are constructed on N=3 analytic superfields. These representations are convenient for describing N=4 superconformal couplings of Abelian gauge superfields to hypermultiplets. We investigate the N=4 invariance in the non-Abelian N=3 Yang-Mills theory.     

The completeness characterization of $$C(\mathcal {L})$$ C ( L ) , $$\mathcal {L}$$ L a locale

Positivity - The result of the title is: an archimedean $$\ell $$ -group with weak unit A is (isomorphic to) $$C(\mathcal {L})$$ for some (identifiable) locale $$\mathcal {L}$$ (or, $$\mathbb...     

A Korovkin type approximation theorems via $$\mathcal{I}$$ -convergence

Using the concept of -convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.     

Beckman-Quarles type theorems for mappings from $$ \mathbb{R}^n $$ to $$ \mathbb{C}^n $$

Summary. Let We say that preserves the distance d 0 if for each implies Let A _n denote the set of all positive numbers d such that any map that preserves unit distance preserves also distance d. Let D _n denote the set of all positive numbers d with the property: if and then there exists a finite set S _xy with such that any map that preserves unit distance preserves also the distance between x and y. Obviously, We prove: (1) (2) for n 2 D _n is a dense subset of (2) implies that each mapping f from to (n 2) preserving unit distance preserves all distances, if f is continuous with respect to the product topologies on and      

Lattices of topologies of unary algebras of the variety $$ \mathcal{A}_{1,1} $$

We consider the variety of unary algebras 〈A, f, g〉 defined by the identities f(g(x)) = g(f(x)) = x. We describe algebras of this variety, whose topology lattices are modular, distributive, linearly ordered, complemented, or pseudocomplemented.     

Strong\mathcal{P}-Congruences on\mathcal{P}-Regular semigroupssemigroups

In this paper we describe the strong -congruences on -regular semigroups in terms of their characteristic kernels and characteristic traces. This paper formed a part of the author's doctoral dissertation, written under the direction of Professor Yuqi Guo at Lanzhou University. The author wishes to give many thanks to the supervisor for his encouragement and help.     

Every finite lattice in $$ \mathcal{V} (M_3) $$

We prove that every finite lattice in the variety generated by M₃ is isomorphic to the congruence lattice of a finite algebra.     

The Abelian category of quotients of $$\mathcal{L}\mathfrak{F}$$ -spaces

We construct the category of quotients of -spaces and we show that it is Abelian. This answers a question of L. Waelbroeck from 1990.     

Unirationality of the Hurwitz space $$\varvec{\mathcal {H}_{9,8}}$$

In this paper we prove that the Hurwitz space \(\mathcal {H}_{9,8}\), which parameterizes 8-sheeted covers of \({\mathbb P }^1\) by curves of genus 9, is unirational. Our construction leads to an explicit Macaulay2 code, which will randomly produce a nodal curve of degree 8 of geometric genus 9 with 12 double points and together with a pencil of degree 8.     

On the reflexivity of $$\mathcal {P}_{w}(^{n}E;F)$$

In this paper we prove that if E and F are reflexive Banach spaces and G is a closed linear subspace of the space \(\mathcal {L}_{K}(E;F)\) of all compact linear operators from E into F, then G is either reflexive or non-isomorphic to a dual space. This result generalizes (Israel J Math 21:38-49, 1975, Theorem 2) and gives the solution to a problem posed by Feder (Ill J Math 24:196-205, 1980, Problem 1). We also prove that if E and F are reflexive Banach spaces, then the space \(\mathcal {P}_{w}(^{n}E;F)\) of all n-homogeneous polynomials from E into F which are weakly continuous on bounded sets is either reflexive or non-isomorphic to a dual space.     

Some new integral inequalities for conjugate A-harmonic tensors

A new kind of weight-Ar^λ3 （λ1, λ2, Ω）-weight is used to prove the local and global integral inequalities for conjugate A-harmonic tensors, which can be regarded as generalizations of the classical results. Some applications of the above results to quasiregular mappings are given.     

Fundamentals for symplectic $$ \mathcal{A} $$-modules. Affine Darboux theorem

In his [9–11], the first author shows that the sheaf-theoreti-cally based Abstract Differential Geometry incorporates and generalizes classical differential geometry. Here, we undertake to explore the implications of Abstract Differential Geometry to classical symplectic geometry. The full investigation will be presented elsewhere.