There are 24 feasible parameter sets for a primitive non-symmetric association schemes with 3 classes and at most 100 vertices. Using computer search, we prove non-existence for three feasible parameter sets. Eleven cases are still open. In the imprimitive case, we survey the known results including some constructions of infinite families of schemes. In the smallest case that has been open up t...

Pre-symmetric complex Banach spaces have been proposed as models for state spaces of physical systems. A structural projection on a pre-symmetric space A∗ represents an operation on the corresponding system, and has as its range a further pre-symmetric space which represents the state space of the resulting system and symmetries of the system are represented by elements of the group Aut(A∗) of ...

We examine two isomorphisms between affine Hecke algebras of type A associated with parameters q−1, t−1 and q, t. One of them maps the non-symmetric Macdonald polynomials Eη(x; q−1, t−1) onto Eη(x; q, t), while the other maps them onto non-symmetric analogues of the multivariable Al-Salam & Carlitz polynomials. Using the properties of Eη(x; q−1, t−1), the corresponding properties of these latte...

A new constantWD(X) is introduced into any real 2n-dimensional symmetric normed space X . By virtue of this constant, an upper bound of the geometric constant D(X), which is used to measure the difference between Birkhoff orthogonality and isosceles orthogonality, is obtained and further extended to an arbitrarym-dimensional symmetric normed linear space (m≥ 2). As an application, the result is...

This paper is concerned with ground state solutions for the Hénon type equation −∆u(x) = |y|αup−1(x) in Ω, where Ω = B(0, 1) × Bn−k(0, 1) ⊂ R and x = (y, z) ∈ R × Rn−k. We study the existence of cylindrically symmetric and non-cylindrically symmetric ground state solutions for the problem. We also investigate asymptotic behavior of the ground state solution when p tends to the critical exponent...

Local available quantum correlations (LAQC), as defined by Mundarain et al., are analyzed for nonsymmetric 2-qubit X states, that is, states not invariant under the exchange of subsystems and therefore have local Bloch vectors whose norms different. A simple analytic expression their LAQC quantifier is obtained. As an example, we analyze application amplitude damping channel Werner general stat...

Let P be a probability measure on the real line R such that each of the product measures P n assigns the value 1=2 to every half space in R n having the origin as a boundary point. Then P is symmetric. Example: A strictly stable law on R is symmetric ii it has median zero. The treated symmetry problem is related to the problem of characterizing the distribution of X 1 by the distribution of (X ...

Chen and Ruan’s orbifold cohomology of the symmetric product of a complex manifold is calculated. An isomorphism of rings (up to a change of signs) H∗ orb (Xn/Sn; C) ∼= H∗(X ; C) between the orbifold cohomology of the symmetric product of a smooth projective surface with trivial canonical class X and the cohomology of its Hilbert scheme X [n] is obtained, yielding a positive answer to a conject...

This paper proposes fuzzy regression analysis with non-symmetric fuzzy coefficients. By assuming non-symmetric triangular fuzzy coefficients and applying the quadratic programming formulation, the center of the obtained fuzzy regression model attains more central tendency compared to the one with symmetric triangular fuzzy coefficients. For a data set composed of crisp inputs-fuzzy outputs, two...

By a symmetric residuated lattice we understand an algebra A = (A,∨,∧, ∗,→,∼, 1, 0) such that (A,∨,∧, ∗,→, 1, 0) is a commutative integral bounded residuated lattice and the equations ∼∼ x = x and ∼ (x ∨ y) =∼ x∧ ∼ y are satisfied. The aim of the paper is to investigate properties of the unary operation ε defined by the prescription εx :=∼ x → 0. We give necessary and sufficient conditions for ...