Dissociative Identity: An Objection to Baker’s Constitution Theory

One of the central problems of personal identity is to determine what we are essentially. In response to this problem, Lynne Rudder Baker espouses a psychological criterion, that is, she claims that persons are essentially psychological. Baker’s theory purports to bypass the problems of other psychological theories such as Dissociative Identity Disorder and the problem of individuating persons synchronically. I argue that the theory’s treatment of Dissociative Identity Disorder leads to untenable results, is invalid, and consequently fails to individuate persons.     

Galerkin’s Method in the Theory of Dipole Antennas

It is proved that an approximate solution of the integro-differential equation for the current at the surface of a dipole antenna obtained by Galerkin’s method converges to the exact solution. A method is proposed for calculating the matrix elements of linear operators that enter the above equation.     

Marchaud’s Inequality for Multiple Modules of Continuity in Metric Spaces

Ukrainian Mathematical Journal - For periodic functions of one variable in the metric spaces LΨ [0, 2π], we establish an analog of Marchaud’s inequality for multiple modules of...     

A finite element approximation of the Griffith’s model in fracture mechanics

Summary. The Griffith model for the mechanics of fractures in brittle materials is consider in the weak formulation of SBD spaces. We suggest an approximation, in the sense of –convergence, by a sequence of discrete functionals defined on finite elements spaces over structured and adaptive triangulations. The quasi-static evolution for boundary value problems is also taken into account and some numerical results are shown. Mathematics Subject Classification (2000):65N30     

An Existence Theorem for an Analytic First Order PDE in the Framework of Colombeau’s Theory

 Abstract. We study the existence of a holomorphic generalized solution u of the PDE

Global Whitney‘s Lemma and its Application in Plasticity Theory

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A Global version of Grozman’s theorem

Let $X$ be a manifold. The classification of all equivariant bilinear maps between tensor density modules over $X$ has been investigated by Grozman (Funct Anal Appl 14(2):58–59, 1980), who has provided a full classification for those which are differential operators. Here we investigate the same question without the hypothesis that the maps are differential operators. In our paper, the geometric context is algebraic geometry and the manifold $X$ is the circle $\text{ Spec}\, \mathbb{C }[z,z^{-1}]$ . Our main motivation comes from the fact that such a classification is required to complete the proof of the main result of Iohara and Mathieu (Proc Lond Math Soc, 2012, in press). Indeed it requires to also include the case of deformations of tensor density modules.     

Application of Dzyadyk’s Polynomial Kernels in the Constructive Function Theory

Ukrainian Mathematical Journal - This is a survey of recent results in the constructive theory of functions of complex variable obtained by the author through the application of the theory of...     

A Novel Interpretation of Plato’s Theory of Forms

In several recent issues of this journal, I argued for an account of property possession as strict, numerical identity. While this account has stuck some as being highly idiosyncratic in nature, it is not entirely something new under the sun, since as I will argue in this paper, it turns out to have a historic precedent in Plato’s theory of forms. Indeed, the purpose of this paper is twofold. The first is to show that my account of property possession can be utilized to provide a novel interpretation of Plato’s theory of forms. And the second is to show that once it has been divorced from a variety of implausible doctrines with which it has historically been wedded, Plato’s central insight that all properties possess themselves, far from being of mere historical interest, is independently plausible, ironically enough, even from an empirical point of view.     

Hume’s Argument for the Ontological Independence of Simple Properties

In this paper, I will reconstruct Hume's argument for the ontological (in the sense of rigid existential) independence of simple properties in A Treatise of Human Nature, Book 1 (1739). According to my reconstruction, the main premises of the argument are the real distinctness of every perception of a simple property, Hume's Separability Principle and his Conceivability Principle. In my view, Hume grounds the real distinctness of every perception of a simple property in his atomistic theory of sense perception and his Copy Principle. I will also show why Hume's argument should be seen as relevant nowadays. David Lewis and his followers in metaphysics continue Hume's line of thinking in this respect, which is opposed by power ontologists (Brian Ellis, Stephen Mumford), for example.     

An extension of Jung’s theorem

Theorem. Let a set X?Rⁿ have unit circumradius and let B be the unit ball containing X. Put C =conv \(\bar X\) D =diam C (=diam X), k =dim C,d _i = √(2i + 2)/i. Then: (i) D∈[d_n, 2]; (ii) k≧m where m∈{2,3,...,n} satisfies D∈[d_m, d_m?1) (d_i decreases by i); (iii) In case k=m (by (ii), this is always the case when m=n), C contains a k-simplex Δ such that: (α) its vertices are on δB; (β) the centre of B belongs toint Δ; (γ) the inequalitiesλ _k (D) ≦l ≦D with $$\lambda _k (D) = D\sqrt {\frac{{4k - 2D^2 (k - 1)}}{{2 - (k - 2)(D^2 - 2)}}, D \in (d_k ,d_{k - 1} )} $$ are unimprovable estimates for length l of any edge of Δ.     

An extension of one direction in Marty’s normality criterion

We prove the following extension of one direction in Marty’s theorem: If $k$ is a natural number, $\alpha >1$ and $\mathcal{F }$ is a family of functions meromorphic on a domain $D$ all of whose poles have multiplicity at least $\frac{k}{\alpha -1}$ , then the normality of $\mathcal{F }$ implies that the family $$\begin{aligned} \left\{ \frac{|f^{(k)}|}{1+|f|^\alpha }\,:\, f\in \mathcal{F }\right\} \end{aligned}$$ is locally uniformly bounded.     

An Extension of Polyak’s Theorem in a Hilbert Space

Let H be an infinite-dimensional real Hilbert space equipped with the scalar product (⋅,⋅) _H . Let us consider three linear bounded operators,

Global Asymptotics of the Second Painlevé Equation in Okamoto’s Space

We study the solutions of the second Painlevé equation (P II) in the space of initial conditions first constructed by Okamoto, in the limit as the independent variable, x, goes to infinity. Simultaneously, we study solutions of the related equation known as the thirty-fourth Painlevé equation (P 34). By considering degenerate cases of the autonomous flow, we recover the known special solutions, which are either rational functions or expressible in terms of Airy functions. We show that the solutions that do not vanish at infinity possess an infinite number of poles. An essential element of our construction is the proof that the union of exceptional lines is a repeller for the dynamics in Okamoto’s space. Moreover, we show that the limit set of the solutions exists and is compact and connected.     

Bolzano’s Argument for the Existence of Substances: a Formalization with Two Types of Predication

The topic of our analysis is the argument for the existence of substances given by Bernard Bolzano in Athanasia (1827), where he essentially employs two ontological categories: substance and adherence. Bolzano considers the real and conditioned Inbegriff of all adherences, which are wirklich and nicht selbst bestehen. He claims that the formed collection is dependent on something external and non-adherential, which therefore is a substance. Bolzano’s argumentation turns out to be structurally similar to his argument for the existence of God from Lehrbuch der Religionswissenschaft (1834), but in each of these reasonings, we find different plausible interpretations of the key concept “Inbegriff”. The latter argumentation refers to the mereological totality of existentially conditioned objects. We propose the explication of the Bolzanian Inbegriff of all adherences using two types of predication: we consider its extension as composed of certain intensional counterparts of adherences. In our approach, we use a fragment of the theory of abstract objects formulated by E. Zalta (1983), describing two different relations between individuals and properties: extensional exemplification and intensional encoding. We put our reconstruction in a wider context of Bolzano’s ontology, formulating the needed axioms with two primitive predicates of second order ... is an adherence, ... is conditioned by something real as well as the conditionally introduced first order predicate constant \(\mathfrak {In}\) for Inbegriff of all adherential ideas. Finally, we sketch a model for our theory.