Curvilinear integral theorem for GG-monogenic mappings in the algebra of complex quaternion

For $G$-monogenic mappings taking values in the algebra of complex quaternion we prove a curvilinear analogue of the Cauchy integral theorem in the case where a curve of integration lies on the boundary of a domain.Comment: submitted to International Journal of Advanced Research in Mathematic

Kramers-Kronig constrained variational analysis of optical spectra

A universal method of extraction of the complex dielectric function $\epsilon(\omega)=\epsilon_{1}(\omega)+i\epsilon_{2}(\omega)$ from experimentally accessible optical quantities is developed. The central idea is that $\epsilon_{2}(\omega)$ is parameterized independently at each node of a properly chosen anchor frequency mesh, while $\epsilon_{1}(\omega)$ is dynamically coupled to $\epsilon_{2}(\omega)$ by the Kramers-Kronig (KK) transformation. This approach can be regarded as a limiting case of the multi-oscillator fitting of spectra, when the number of oscillators is of the order of the number of experimental points. In the case of the normal-incidence reflectivity from a semi-infinite isotropic sample the new method gives essentially the same result as the conventional KK transformation of reflectivity. In contrast to the conventional approaches, the proposed technique is applicable, without readaptation, to virtually all types of linear-response optical measurements, or arbitrary combinations of measurements, such as reflectivity, transmission, ellipsometry {\it etc.}, done on different types of samples, including thin films and anisotropic crystals.Comment: 10 pages, 7 figure

Quaternionic G–Monogenic Mappings in Em

We consider a class of so-called quaternionic G-monogenic mappings associated with m-dimensional (m 2 f2; 3; 4g) partial differential equations and propose a description of all mappings from this class by using four analytic functions of complex variable. For G-monogenic mappings we generalize some analogues of classical integral theorems of the holomorphic function theory of the complex variable (the surface and the curvilinear Cauchy integral theorems, the Cauchy integral formula, the Morera theorem), and Taylor’s and Laurent’s expansions. Moreover, we investigated the relation between G-monogenic and H-monogenic (differentiable in the sense of Hausdorff) quaternionic mappings

Generalized integral theorems for the quaternionic G-monogenic mappings

For G-monogenic mappings taking values in the algebra of complex quaternions we generalize some analogues of classical integral theorems of the holomorphic function theory of a complex variable (the surface and the curvilinear Cauchy integral theorems)

Incentive spirometry as a way to prevent pulmonary atelectasis development

The purpose. The purpose of this study was to evaluate the effectiveness of incentive spirometry (IS) as a method of atelectasis prevention in patients with moderate or high risk of PPCs development after upper abdominal surgery. Materials and methods. The study consisted of two stages. The first retrospective stage was to analyze the medical histories data of 51 inpatients, who were included in the comparison group. The prospective part of the study included 39 patients of the study group, who had sessions of the IS during the first 7 days of the postoperative period. Patients of both groups were operated on the upper abdominal organs by open procedure, operation time was more than 2 hours, all patients had an ARISCAT score ≥26 points. Pulmonary atelectasis development was monitored in the groups in the first week of the postoperative period. The statistical analysis of the data was performed using the Microsoft Excel 2013 and Statistica for Windows 6.0 programs. When comparing the groups according to the clinical outcome, the relative risk (RR) and odds ratio (OR) were determined and then confidence intervals (95 % CI) were calculated. Statistical significance of the results was determined depending on the CI values. Results. During the first 7 days, 34 cases of pulmonary atelectasis (67 %) were recorded in the comparison group. In the study group, 9 patients (23 %) were diagnosed with pulmonary atelectasis. The analysis of clinical results showed that when applying incentive spirometry, there was a statistically significant decrease in the relative risk of atelectasis development within the first week of the postoperative period (RR = 0.346, 95 % CI [0.189; 0.634], P = 0.0006). The odds ratio of atelectasis development in the study group was statistically lower than in the group of retrospective study (OR = 0.150, 95 % CI [0.058, 0.386], P = 0.0001). Conclusions. Incentive spirometry is an effective way to prevent pulmonary atelectasis in patients with a moderate or high risk for developing postoperative pulmonary complications according to the ARISCAT scale after upper abdominal surgery

Infrared Spectroscopy of Quantum Crossbars

Infrared (IR) spectroscopy can be used as an important and effective tool for probing periodic networks of quantum wires or nanotubes (quantum crossbars, QCB) at finite frequencies far from the Luttinger liquid fixed point. Plasmon excitations in QCB may be involved in resonance diffraction of incident electromagnetic waves and in optical absorption in the IR part of the spectrum. Direct absorption of external electric field in QCB strongly depends on the direction of the wave vector ${\bf q}.$ This results in two types of $1D\to 2D$ dimensional crossover with varying angle of an incident wave or its frequency. In the case of QCB interacting with semiconductor substrate, capacitive contact between them does not destroy the Luttinger liquid character of the long wave QCB excitations. However, the dielectric losses on a substrate surface are significantly changed due to appearance of additional Landau damping. The latter is initiated by diffraction processes on QCB superlattice and manifests itself as strong but narrow absorption peaks lying below the damping region of an isolated substrate.SubmiComment: Submitted to Phys. Rev.

Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene

We show that the optical transparency of suspended graphene is defined by the fine structure constant, alpha, the parameter that describes coupling between light and relativistic electrons and is traditionally associated with quantum electrodynamics rather than condensed matter physics. Despite being only one atom thick, graphene is found to absorb a significant (pi times alpha=2.3%) fraction of incident white light, which is a consequence of graphene's unique electronic structure. This value translates into universal dynamic conductivity G =e^2/4h_bar within a few percent accuracy