Table 1 Core site, fractional abundance of individual isoprenoid GDGTs and TEX86 values

TEXL86 and TEXH86 are organic palaeothermometers based on the lipids of Group 1 Crenarchaeota, recently proposed as a modified version of the original TEX86 index, but with significantly improved geographical coverage. Since few data from the global core top calibration are from the Pacific, this study was carried out to assess whether the global core top calibration is regionally biased or not. The result of principal components analysis of the fractional abundance of GDGTs, an analysis of variance (ANOVA) and the comparison of the residuals of TEXH 86 derived sea surface temperature (SST) estimates of the Pacific subset with that of the global data set suggest that the Pacific subset has a similar TEXH 86-SST relationship with the global data set. However, the regression line through the Pacific data and an ANOVA on the residuals of TEXL 86 derived SST estimates suggest otherwise. The contradictory findings are likely to stem from the large scatter in the Pacific TEXL 86 values in the mid temperature range. While regionality does not seem to exert a strong bias on TEXL 86 and TEXH 86 calibration, it appears that there is a strong need to resolve the large scatter in the global data set, especially in the mid and high latitudes, in order to improve the calibration for a better SST estimation.

The spectra of linear fractional composition operators on weighted Dirichlet spaces

We completely determine the spectra of composition operators induced by linear fractional self-maps of the unit disc acting on weighted Dirichlet spaces; extending earlier results by Higdon [8] and answering the open questions in this context.

Fractional order of poling period for broadly tunable second harmonic generation

We demonstrate the possibility to use a fractional order of poling period of nonlinear crystal waveguides for tunable second harmonic generation. This approach allows one to extend wavelength coverage in the visible spectral range by frequency doubling in a single crystal waveguide.

Fractional abundances of isoprenoid and branched glycerol dialkyl glycerol tetraethers (GDGT) of cores SO201-2-12KL and SO201-2-114KL

It has been proposed that North Pacific sea surface temperature (SST) evolution was intimately linked to North Atlantic climate oscillations during the last glacial-interglacial transition. However, during the early deglaciation and the Last Glacial Maximum, the SST development in the subarctic northwest Pacific and the Bering Sea is poorly constrained as most existing deglacial SST records are based on alkenone paleothermometry, which is limited prior to 15 ka B.P. in the subarctic North Pacific realm. By applying the TEXL86 temperature proxy we obtain glacial-Holocene-SST records for the marginal northwest Pacific and the Western Bering Sea. Our TEXL86-based records and existing alkenone data suggest that during the past 15.5 ka, SSTs in the northwest Pacific and the Western Bering Sea closely followed millennial-scale climate fluctuations known from Greenland ice cores, indicating rapid atmospheric teleconnections with abrupt climate changes in the North Atlantic. Our SST reconstructions indicate that in the Western Bering Sea SSTs drop significantly during Heinrich Stadial 1 (HS1), similar to the known North Atlantic climate history. In contrast, progressively rising SST in the northwest Pacific is different to the North Atlantic climate development during HS1. Similarities between the northwest Pacific SST and climate records from the Gulf of Alaska point to a stronger influence of Alaskan Stream waters connecting the eastern and western basin of the North Pacific during this time. During the Holocene, dissimilar climate trends point to reduced influence of the Alaskan Stream in the northwest Pacific.

Fractional and time-scales differential equations

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Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

A Discretization of the Hadamard fractional derivative

We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the Hadamard fractional derivative.

A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.

Clifford-Hermite polynomials in fractional Clifford analysis

In this paper we generalize radial and standard Clifford-Hermite polynomials to the new framework of fractional Clifford analysis with respect to the Riemann-Liouville derivative in a symbolic way. As main consequence of this approach, one does not require an a priori integration theory. Basic properties such as orthogonality relations, differential equations, and recursion formulas, are proven.

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

Impact of Routine Fractional Flow Reserve Evaluation During Coronary Angiography on Management Strategy and Clinical Outcome: One-Year Results of the POST-IT.

Penetration of fractional flow reserve (FFR) in clinical practice varies extensively, and the applicability of results from randomized trials is understudied. We describe the extent to which the information gained from routine FFR affects patient management strategy and clinical outcome. METHODS AND RESULTS: Nonselected patients undergoing coronary angiography, in which at least 1 lesion was interrogated by FFR, were prospectively enrolled in a multicenter registry. FFR-driven change in management strategy (medical therapy, revascularization, or additional stress imaging) was assessed per-lesion and per-patient, and the agreement between final and initial strategies was recorded. Cardiovascular death, myocardial infarction, or unplanned revascularization (MACE) at 1 year was recorded. A total of 1293 lesions were evaluated in 918 patients (mean FFR, 0.81±0.1). Management plan changed in 406 patients (44.2%) and 584 lesions (45.2%). One-year MACE was 6.9%; patients in whom all lesions were deferred had a lower MACE rate (5.3%) than those with at least 1 lesion revascularized (7.3%) or left untreated despite FFR≤0.80 (13.6%; log-rank P=0.014). At the lesion level, deferral of those with an FFR≤0.80 was associated with a 3.1-fold increase in the hazard of cardiovascular death/myocardial infarction/target lesion revascularization (P=0.012). Independent predictors of target lesion revascularization in the deferred lesions were proximal location of the lesion, B2/C type and FFR. CONCLUSIONS: Routine FFR assessment of coronary lesions safely changes management strategy in almost half of the cases. Also, it accurately identifies patients and lesions with a low likelihood of events, in which revascularization can be safely deferred, as opposed to those at high risk when ischemic lesions are left untreated, thus confirming results from randomized trials.

Spectra and Laplacian spectra of arbitrary powers of lexicographic products of graphs

Consider two graphs G and H. Let H^k[G] be the lexicographic product of H^k and G, where H^k is the lexicographic product of the graph H by itself k times. In this paper, we determine the spectrum of H^k[G]H and H^k when G and H are regular and the Laplacian spectrum of H^k[G] and H^k for G and H arbitrary. Particular emphasis is given to the least eigenvalue of the adjacency matrix in the case of lexicographic powers of regular graphs, and to the algebraic connectivity and the largest Laplacian eigenvalues in the case of lexicographic powers of arbitrary graphs. This approach allows the determination of the spectrum (in case of regular graphs) and Laplacian spectrum (for arbitrary graphs) of huge graphs. As an example, the spectrum of the lexicographic power of the Petersen graph with the googol number (that is, 10^100 ) of vertices is determined. The paper finishes with the extension of some well known spectral and combinatorial invariant properties of graphs to its lexicographic powers.