We prove the existence of solutions to the Kuramoto–Sivashinsky equation with low regularity data in function spaces based on the Wiener algebra and in pseudomeasure spaces. In any spatial dimension, we allow the data to have its antiderivative in the Wiener algebra. In one spatial dimension, we also allow data that are in a pseudomeasure space of negative order. In two spatial dimensions, we also allow data that are in a pseudomeasure space one derivative more regular than in the one-dimensional case. In the course of carrying out the existence arguments, we show a parabolic gain of regularity of the solutions as compared to the data. Subsequently, we show that the solutions are in fact analytic at any positive time in the interval of existence.

Kant refers to analytic cognition in several prominent places. The prevailing wisdom, however, denies the possibility of analytic cognition within his theory of cognition. I shall argue that this is mistaken. I show that we can account for analytic cognition’s possibility by appealing to variants of the more familiar conditions on the cognition of objects. I also highlight analytic cognition’s connection to insight and analytic knowledge. In the process, I provide a fuller account of Kant’s view of our mental lives than has been typically acknowledged.

In this paper, we consider the time decay of the solutions to some problems arising in strain gradient thermoelasticity. We restrict to the two-dimensional case, and we assume that two dissipative mechanisms are introduced, the temperature and the mass dissipation. First, we show that this problem is well-posed proving that the operator defining it generates a contractive semigroup of linear operators. Then, assuming that the function involving the coupling terms is elliptic, the exponential decay of the solutions is concluded as well as the analyticity of the solutions. Finally, we describe how to obtain the exponential stability in the case of hyperbolic dissipation.

I argue for the claim that there are instances of a priori justified belief – in particular, justified belief in moral principles – that are not analytic, i.e., that cannot be explained solely by the understanding we have of their propositions. §1–2 provides the background necessary for understanding this claim: in particular, it distinguishes between two ways a proposition can be analytic, Basis and Constitutive, and provides the general form of a moral principle. §§3–5 consider whether Hume's Law, properly interpreted, can be established by Moore's Open Question Argument, and concludes that it cannot: while Moore's argument – appropriately modified – is effective against the idea that moral judgments are either (i) reductively analyzable or (ii) Constitutive-analytic, a different argument is needed to show that they are not (iii) Basis-analytic. Such an argument is supplied in §6. §§7–8 conclude by considering how these considerations bear on recent discussions of “alternative normative concepts”, on the epistemology of intuitions, and on the differences between disagreement in moral domains and in other a priori domains such as logic and mathematics.

Associated with every $2n\times 2n$ real positive definite matrix $A,$ there exist n positive numbers called the symplectic eigenvalues of $A,$ and a basis of $\mathbb {R}^{2n}$ called the symplectic eigenbasis of A corresponding to these numbers. In this paper, we discuss differentiability and analyticity of the symplectic eigenvalues and corresponding symplectic eigenbasis and compute their derivatives. We then derive an analogue of Lidskii’s theorem for symplectic eigenvalues as an application.

Logicism is Stang’s name for the Leibnizian doctrine that all necessary truths are derivable from identities and definitions. Stang shows that the early Kant opposed this doctrine because he thought the proposition God exists was a counterexample to it; I raise some non-theological counterexamples as well. Formal necessity is the necessity that attaches to a proposition when its truth is grounded in our categories and forms of intuition. Stang treats it as one of several sui generis kinds of necessity in Kant, all of them falling short of logical or metaphysical necessity. I raise several questions for Stang’s account, including the following: Can our having the forms we do really explain the necessity of geometry? Is our possession of those forms self-grounding in an objectionable way? How can our forms ground general truths without grounding particular instances of them?

In the first part of this paper we consider a general stationary subcritical cluster model in ℝd. The associated pair-connectedness function can be defined in terms of two-point Palm probabilities of the underlying point process. Using Palm calculus and Fourier theory we solve the Ornstein–Zernike equation (OZE) under quite general distributional assumptions. In the second part of the paper we discuss the analytic and combinatorial properties of the OZE solution in the special case of a Poisson-driven random connection model.

The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that are inserted in the T-sentences. yet not in the scope of negation, the system with the reflection schema for these T-sentences assumes the strength of the Kripke-Feferman theory KF. and thus of ramified analysis up to ε0.

This paper focuses on the analyticity of the limiting behavior of a class of dynamical systems defined by iteration of non-expansive random operators. The analyticity is understood with respect to the parameters which govern the law of the operators. The proofs are based on contraction with respect to certain projective semi-norms. Several examples are considered, including Lyapunov exponents associated with products of random matrices both in the conventional algebra, and in the (max, +) semi-field, and Lyapunov exponents associated with non-linear dynamical systems arising in stochastic control. For the class of reducible operators (defined in the paper), we also address the issue of analyticity of the expectation of functionals of the limiting behavior, and connect this with contraction properties with respect to the supremum norm. We give several applications to queueing theory.

We analyze the controllability of the wave equation on a cylinder when the control acts on the boundary, that does not satisfy the classical geometric control condition.We obtain precise estimates on the analyticity of reachable functions.As the control time increases, the degree of analyticity that is required for a function to be reachable decreases as an inverse power of time. We conclude that any analytic function can be reached if that control time is large enough. In the C ∞ class, a precise description of all reachable functions is given.

Let N be a stationary Markov-modulated marked point process on ℝ with intensity β∗ and consider a real-valued functional ψ(N). In this paper we study expansions of the form Eψ(N) = a0 + β∗a1 + ·· ·+ (β∗)nan + o((β∗)n) for β∗→ 0. Formulas for the coefficients ai are derived in terms of factorial moment measures of N. We compute a1 and a2 for the probability of ruin φ u with initial capital u for the risk process in the Markov-modulated environment; a0 = 0. Moreover, we give a sufficient condition for ϕu to be an analytic function of β∗. We allow the premium rate function p(x) to depend on the actual risk reserve.