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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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.

Symmetry properties of one- and two- electron molecular integrals

The maximum numbers of distinct one- and two-electron integrals that arise in calculating the electronic energy of a molecule are discussed. It is shown that these may be calculated easily using the character table of the symmetry group of the set of basis functions used to express the wave function. Complications arising from complex group representations and from a conflict of symmetry between the basis set and the nuclear configuration are considered and illustrated by examples.

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.

A Caputo fractional derivative of a function with respect to another function

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

Fractional differential equations with dependence on the Caputo-Katugampola derivative

In this paper we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo–Katugampola derivative, is proven. A decomposition formula for the Caputo–Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation.

Modeling some real phenomena by fractional differential equations

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.