Herbrand Theorems for Substructural Logics

Herbrand and Skolemization theorems are obtained for a broad family of first-order substructural logics. These logics typically lack equivalent prenex forms, a deduction theorem, and reductions of semantic consequence to satisfiability. The Herbrand and Skolemization theorems therefore take various forms, applying either to the left or right of the consequence relation, and to restricted classes of formulas.

3D Conversion using Vanishing Points and Image Warping

We describe a user assisted technique for 3D stereo conversion from 2D images. Our approach exploits the geometric structure of perspective images including vanishing points. We allow a user to indicate lines, planes, and vanishing points in the input image, and directly employ these as constraints in an image warping framework to produce a stereo pair. By sidestepping explicit construction of a depth map, our approach is applicable to more general scenes and avoids potential artifacts of depth-image-based rendering. Our method is most suitable for scenes with large scale structures such as buildings.

Limit theorems for nondegenerate U-statistics of continuous semimartingales

This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Multifractional Poisson process, multistable subordinator and related limit theorems

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to the multifractional Poisson process.

Vanishing coccolith vital effects with alleviated carbon limitation

By recreating a range of geologically relevant concentrations of dissolved inorganic carbon (DIC) in the laboratory, we demonstrate that the magnitude of the vital effects in both carbon and oxygen isotopes of coccolith calcite of multiple species relates to ambient DIC concentration. Under high DIC levels, all the examined coccoliths exhibit significantly reduced isotopic offsets from inorganic calcite compared to the substantial vital effects expressed at low (preindustrial and present-day) DIC concentrations. The supply of carbon to the cell exerts a primary control on biological fractionation in coccolith calcite via the modulation of coccolithophore growth rate, cell size and carbon utilisation by photosynthesis and calcification, altogether accounting for the observed interspecific differences between coccolith species. These laboratory observations support the recent hypothesis from field observations that the appearance of interspecific vital effect in coccolithophores coincides with the long-term Neogene decline of atmospheric CO2 concentrations and bring further valuable constraints by demonstrating a convergence of all examined species towards inorganic values at high pCO2 regimes. This study provides palaeoceanographers with a biogeochemical framework that can be utilised to further develop the use of calcareous nannofossils in palaeoceanography to derive sea surface temperature and pCO2 levels, especially during periods of relatively elevated pCO2 concentrations, as they prevailed during most of the Meso-Cenozoic.

Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega) the averages [equation, see text] converge for almost every omicron in. Our result implies that sequences like ([ndelta]), where delta > 1 and not an integer, ([n log n]), and ([n2/log n]) are good averaging sequences for L2. In fact, all the sequences we examine will turn out to be good averaging for Lp, p > 1; and even for L log L. We will also establish necessary and sufficient growth conditions on a(x) so that the sequence ([a(n)]) is good averaging for mean convergence. Note that for some a(x) (e.g., a(x) = log2 x), ([a(n)]) may be good for mean convergence without being good for pointwise convergence.

Of the invention of theorems : manuscript, [17--]

Mathematical notes, equations, theorems, and definitions. Probablynot by William Winthrop (Harvard AB 1770) as it is different handwriting and language habits from other of his manuscript.

Vanishing lines in the sand – Why a new map of the Middle East is necessary. CEPS Commentary, 1 October 2013

As the stalemate in Syria drags on, territorial divisions in the country are becoming more entrenched and the civil war is spreading to Syria’s neighbours; aggravating long-standing sectarian divisions in the whole region. In the view of Steven Blockmans, a lasting agreement cannot be reached in the Middle East if world powers stick to infamous 1916 Sykes-Picot Agreement in which France and the UK secretly dealt with what came to be called the ‘Syria Question’. Any way out of the quagmire will require a grand bargain – one that establishes a new order in the whole region and draws borders accordingly.

Existence theorems in partial differential equations.

"Only the material on elliptic equations will appear in these notes."

Some theorems and algorithms on a new form of decomposition for automata,

Bibliography: p. 28.

Two theorems of statistical separability in the perceptron (Project Para).

"Contract no. Nonr-2381(00)."