The Eigen Functions of the Complex Projective Space

In the complex n-dimensional projective space CP^n. let λ_p(=4p(p+n)) be the eigen vaiue of the Laplace-Beltrami operator and H_p be the space of all eigen functions of eigen value λ_p. The reproducing kernel h_p(z, w) of H_p is constructed explicitly in this paper. and a system of complete orthogohal functions of H_p is construncted from h_p(z, w)(p=1,2…).

Why the Incoherent Paradigm Is for the Future Wireless Networks?

This material is aimed to attract attention to the “incoherent approach for power NOMA-RIS-MIMO transmission in wireless channels”. Such kind of approach might be successfully applied in future dense networks formed by High-Speed Vehicles (HSV networks, etc.). Those scenarios take place in doubly selective communication channels typical for such kind of radio networks. The proposal for the presented hereafter incoherent view (“paradigm”) is based on several basic principles: 1) Shift from the “coherent “ideology”, i.e. rejection of the application of any type of Channel State Information (CSI, CSIT);2) Application of the so-called “invariant” to the communication channel’s features (distortions) modulation technique together with its incoherent demodulation;3) Orthogonal channel decomposition by means of “universal” eigen basis (in the form of Prolate Spheroidal Wave Functions, PSWF) as “artificial trajectories” of wave propagation;4) Chaotic filtering (chaos parameter settings as UE signatures) together with sequential multiuser parallel detection algorithms for users’ identification (classification). It is shown that the proposed approach might provide an effective use of the radio resource and it is relatively simple for implementation.

Restrained Bending of Thin-Walled Box Beam with Honeycomb Core

Restrained bending of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are established and solved. The boundary conditions are satisfied rigorously and the solutions are expressed by means of eigen function expansions. The diagram of shearing force is formulated by trigonometric series and used to determine the coefficients in above expansions. The computational resuits give the chord and span wise distributions of nomal and shear stress in the cover plate and the honeycomb core. At the same time, the attenuation of additional stress from fixed end to free end along the length of beam is shown clearly.

Restrained Torsion of Thin-walled Box Beam with Honeycomb Core

Restrained torsion of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are established and solved. The boundary conditions are satisfied rigorously and the solutions are expressed by means of eigen function expansions. The diagram of torque is formulated by trigonometric series and used to determine the coefficients in above expansions. The results of computation provide the chord-wise and span-wise distributions of normal and shear stress in the face plate along with shear stress in the honeycomb core.

Measurement and validation of tsunami Eigen values for the various water wave conditions

This paper proposes the mathematical model to investigate how to compute and analyze the tsunami wave parameters and the retrieval of its early warning using remote sensing technique to improve the detection rate.The different methods available for the evaluation of the tsunami detection systems are also introduced.This research work is to compute and analyze the tsunami wave parameters such as Eigen functions in deep,intermediate and shallow water regions.The computational and algorithmic analysis of tsunami wave parameters are achieved in three steps:the first step is to calculate the earthquake fault parameters such as length,width,area and displacement from the epicenter,which corresponds to the effect of its variation with respect to the earthquake magnitude.The variation of each fault parameters have been measured and recorded out over the certain moment of magnitudes(M).This shows smaller values as compared to the earthquake magnitude M 9.5 at which all the parameters shows very large response.The second step involves the measurements of water wave angular frequency in deep,intermediate and shallower region of ocean.The values of angular frequencies in deep water shows the lesser response as compared to other two water conditions because,in deep water the angular velocity of water particles travels with the lesser speed as compared to the shallower region as per Airy’s wave theory.The simulation results show the angular velocity in Deep Ocean is very less,moderate in the intermediate water and very high on the coastal region.It indicates the higher impact on coastal region.The third step involves the simulation study of measurement of tsunami Eigen functions such as orbital velocity,acceleration,wave potential in deep,intermediate and shallower water regions.The simulation result shows the resultant orbital velocity and accelerations in deep,intermediate and shallow water regions provides the similar response as angular velocity due to same proportion of the water displacement from deep to coastal regions.Hence the dynamic forces are very high approximately 1 km from the beaches.Once the Tsunami waves approaches to the beach,wave height increases whereas particle acceleration decreases because near the coast,due to geological structure of the earth’s surface,inertia and gravity forces increase to the extreme limits,while particle acceleration and velocity values reach close to zero.The wave potential Eigen function has also been plotted and measured with respect to the water depth condition and the similar response is obtained in the simulation result.The validation of each result has also been presented with the standard simulated data,which shows the results as less than 10%of the accuracy.

Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls

The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant walls.Mathematical modeling is based upon the laws of mass and linear momentum.Analytic solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number approximations.The features of the flow characteristics are analyzed by plotting the graphs of various values of physical parameters of interest.Trapping bolus scheme is also presented through streamlines.