We extend Walsh’s theory of martingale measures in order to deal with hyperbolic stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation, and driven by spatially homogeneous Gaussian noise. For such equations, the fundamental solution can be a distribution in the sense of Schwartz, which appears as an integrand in the reformulatio...

The multiplicative and the functional renormalization group methods are applied for four-dimensional scalar theory in Minkowski space–time. It is argued that appropriate choice of subtraction point more important than Euclidean parameters cutoff theory, defined by a quasi-particle domain, complex due to mass-shell contributions flow becomes much involved its counterpart.

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

Qualitative research in political science and sociology commonly explores intersectionality, but practical methodological guides for the quantitative researcher are few. I examine methodological challenges in testing intersectionality theory by comparing and contrasting two most frequently used statistical approaches to the quantitative analysis of intersectional demographics: the unitary, or a...

Multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific-heat critical exponent vanishes. Also, the theory is widened to encompass the correlation function. The new relations are then confronted...