All-reflective optical system design for extreme ultraviolet lithography

All-reflective optical systems,due to their material absorption and low refractive index,are used to create the most suitable devices in extreme ultraviolet lithography （EUVL）.In this letter,we present a design for an all-reflective lithographic projection lens.We also discuss its design idea and structural system.After analysis of the four-mirror optical system,the initial structural parameters are determined,the optical system is optimized,and the tolerances of the system are analyzed.We also show the implementation of optimal layout and desired imaging performance.     

Cascade-exciton model analysis of level density parameter dependence in proton induced fission cross sections of some sub-actinide nuclei

Fission cross sections strongly depend on the ratio of the level density parameter in fission to neutron emission, a_f/a_n. In this work, a cascade-exciton model implemented in the code CEM95 has been used to observe this effect for proton induced fission cross sections of tungsten, lead and bismuth. The method was employed using different level density parameter ratios for each fission cross section calculation. The calculated fission cross sections are compared with the available experimental data in the literature. It has been observed that a change of the ratio of the level density parameter, a_f/a_n, is necessary with the incident energy of the proton, to best estimate the fission cross sections in CEM95.     

An analytical and numerical study of peristaltic transport of a Johnson-Segalman fluid in an endoscope

In the present study, we discuss the peristaltic flow of a Johnson-Segalman fluid in an endoscope. Perturbation, homotopy, and numerical solutions are found for the non-linear differential equation. The comparative study is also made to check the validity of the solutions. The expressions for pressure rise frictional forces, pressure gradient, and stream lines are presented to interpret the behavior of various physical quantities of the Johnson-Segalman fluid.     

Precision position measurement of single atom

Atom localization in a five-level atomic system under the effect of three driving fields and one standing wave field is suggested. A spontaneously emitted photon from the proposed system is measured in a detector. Precision position measurement of an atom is controlled via phase and vacuum field detuning without considering the parity violation.     

Weighted ebyev-Ostrowski type inequalities

In account of the famous ebyev inequality,a rich theory has appeared in the literature.We establish some new weighted ebyev type integral inequalitíes.Our proofs are of independent interest and provide new estimates on these types of inequalities.     

Novel pressure and displacement sensors based on carbon nanotubes

We report newly designed pressure and displacement capacitive sensors based on a flexible paper–CNT structure.The carbon nanotube(CNT)powder was deposited on a thin paper substrate and was pressed at an elevated temperature.The sheet resistance of the paper–CNT films was in the range of 2–4 kΩ/cm2.The paper–CNT films were used to fabricate pressure and displacement sensors.The sensitivities of the pressure and the displacement sensors were found to be17.3 p F·m2/k N and 0.93 10-3p F/μm,respectively.The experimental results were compared with the simulated data and they found good agreement with each other.     

THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type c D δ 0+ u(t) = f (t, u(t), c D σ 0+ u(t)), t ∈ [0, T ], u(0) = αu(η), u(T ) = βu(η), where 1 < δ < 2, 0 < σ < 1, α, β∈ R, η∈ (0, T ), αη(1 -β) + (1-α)(T βη) = 0 and c D δ 0+ , c D σ 0+ are the Caputo fractional derivatives. We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results. Examples are also included to show the applicability of our results.     

The Kadomtsev-Petviashvili equation for dust ion-acoustic solitons in pair-ion plasmas

Using the reductive perturbation method,we have derived the Kadomtsev-Petviashvili(KP) equation to study the nonlinear properties of electrostatic collisionless dust ion-acoustic solitons in pair-ion(p-i) plasmas.We have chosen the fluid model for the positive ions,the negative ions,and a fraction of static charged(both positively and negatively) dust particles.Numerical solutions of these dust ion-acoustic solitons are plotted and their characteristics are discussed.It is found that only the amplitudes of the electrostatic dust ion-acoustic solitons vary when the dust is introduced in the pair-ion plasma.It is also noticed that the amplitude and the width of these solitons both vary when the thermal energy of the positive or negative ions is varied.It is shown that potential hump structures are formed when the temperature of the negative ions is higher than that of the positive ions,and potential dip structures are observed when the temperature of the positive ions supersedes that of the negative ions.As the pair-ion plasma mimics the electron-positron plasma,thus our results might be helpful in understanding the nonlinear dust ion acoustic solitary waves in super dense astronomical bodies.