This paper is about importing the stable homotopy theory of symmetric spectra [4] and more generally presheaves of symmetric spectra [8] into the Morel-Voevodsky stable category [9], [11], [12]. Loosely speaking, the latter is the result of formally inverting the functor X 7→ T∧X on the category of pointed simplicial presheaves on the smooth Nisnevich site of a field within the Morel-Voevodsky ...

The category of symmetric quandles is a Mal’tsev variety whose subvariety of abelian symmetric quandles is the category of abelian algebras. We give an algebraic description of the quandle extensions that are central for the adjunction between the variety of quandles and its subvariety of abelian symmetric quandles.

There are many ways to measure the dispersion of a random variable. One such method uses the concept of peakedness. If the random variable X is symmetric about a point μ, then Birnbaum (1948) defined the function Pμ(x) = P (|X − μ| ≤ x), x ≥ 0, as the peakedness of X. If two random variables, X and Y , are symmetric about the points μ and ν, respectively, then X is said to be less peaked than Y...

The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the ”quasi-parity” on the Dirac particles’ spectra is also studied. A ”quasi-free” Dirac particle with PDM via an inversely linear plus linear model, a Dirac particle...

The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the ”quasi-parity” on the Dirac particles’ spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S (z) = S (x− ib) (an i...

We consider the Dirichlet problem for the semilinear equation ∆u + f(u) = 0 on a bounded domain Ω ⊂ RN . We assume that Ω is convex in a direction e and symmetric about the hyperplane H = {x ∈ RN : x · e = 0}. It is known that if N ≥ 2 and Ω is of class C2, then any nonzero nonnegative solution is necessarily strictly positive and, consequently, it is reflectionally symmetric about H and decrea...

This paper presents the new concept of second-order cone approximations for convex conic programming. Given any open convex cone K, a logarithmically homogeneous self-concordant barrier for K and any positive real number r ≤ 1, we associate, with each direction x ∈ K, a second-order cone K̂r(x) containing K. We show that K is the intersection of the second-order cones K̂r(x), as x ranges through ...

We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type of their (discrete) Fourier transforms. We also provide three independent new proofs of the strong Huygens’ principle for a suitable constant shift of the w...

Let G = (V,E) be a graph and let C be a finite set of colours. An edge C-colouring of G is a function λ : E → C. If G is symmetric and λ(x, y) = λ(y, x), for all (x, y) ∈ E, then we say that λ is a symmetric edge C-colouring. Let n be a natural number and let Cn = {f, ci : i < n} be a set of n+1 colours. Using a probabilistic construction and an application of the Local Lemma we prove that ther...