We investigate the boundary-value problem generated by the Sturm-Liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. With a different approach we introduce an adequate Hilbert spaceformulation, investigate some properties of eigenvalues, Green’s function and resolvent operator, andfind simple conditions on the coefficients which guarantee the self-adjointness of the consideredproblem.

A three-step selective photo-ionization for Gd155 and Gd157 isotopes by pulsed laser wasevaluated numerically. Due to large thermal neutron absorption cross sections, these two isotopes innatural gadolinium are good candidates as burnable poison to control reactivity early in the fuel cycleand allow extended fuel burn up. Rate equations have been used to calculate the dynamics of the isotopepopulations, ionization rate, and selection factor. Doppler broadening, as well as power broadening foratomic energy levels, has been considered in the calculations. The effects of laser intensity, frequencybandwidth, and laser detuning in the ionization process have also been assessed. By applying a variety ofconditions, the sensitivity of different parameters in the ionization process was investigated. The resultsshow that the ionization yield increases with the intensities of lasers, and becomes saturated at somespecific values. Depending on the energy bandwidth of each state, laser bandwidth and the detuning oflasers greater than particular values can affect the ionization yield. Due to small and finite isotope shiftsof energy states, the selection factor can be influenced by detuning and laser bandwidth. From theresults, it can be inferred that for Gd155 and Gd157 isotopes, ionization is more sensitive to the first andsecond laser bandwidth and detuning. From these results, optimum selection factors and ionization byusing appropriate laser intensities, bandwidth, and detuning can be achieved.

Here, we have considered the Husimi and Wigner distribution functions. We have, inparticular, shown how the uncertainty principle works for the two cases of simple and damped harmonicoscillators when either of these two distributions are used. The conclusion shows that the Husimidistribution function remains non-negative through the phase space but it does not always satisfies theuncertainty principle. On the other hand the Wigner distribution function while becoming negative incertain regions of the phase space do not violate the uncertainty principle.

In this paper, design and application of a new digital protective relay based on fuzzy logicand value estimation to a radial power system protection was presented. A novel approach based onvalue estimation was investigated for the proposed fuzzy logic based protective relay. In addition to thetheoretical aspect of fuzzy logic, mathematical definition of value estimation, detection andmeasurement of faulty current, determination of its duration, decision mechanism and detailed systemarchitecture were also introduced. The examined technique based on fuzzy logic and value estimation tocontrol the protection action of the protective relay was intended to improve the performance of aconventional protective relay control for human safety and system reliability with the use of a fuzzylogic controller. The difference between estimated and sampled values was used to form the rule base.Proposed relay architecture was used as a detector and was developed to predict faults and to protectparticular sections of a designed prototype radial power system at an early stage. Performance analysiswas made, and related results and discussion were given.

The elementary reaction of kaon exclusive electroproduction on protons has been studied ina broad kinematical range. Data for the calculation of the form factor of the kaon have been taken atdifferent values of the invariant center of mass energy W in the range W=1.8, 1.85, 1.98, 2.08 (GeV), forone value of the transferred 4-momentum Q2=2.35 (GeV/c)2. In this analysis, we calculated σL and σT byusing the Rosenbluth separation. Then the electromagnetic kaon form factor was calculated by Chew-Low extrapolation.

A generalized Heckman model is used for the joint modeling of longitudinal continuousresponses and dropout in order to see the influence of a small perturbation of the elements of thecovariance structure on displacement of the likelihood. The perturbation from random dropout in thedirection of informative dropout is considered for Mastitis data.

We consider the semilinear elliptic boundary value problem  = ∈∂Ω− Δ = ∈Ωu x xu x f u x x( ) 0;( ) λ ( ( ));where λ > 0 is a parameter, Ω is a bounded region in RN with a smooth boundary, and f is asmooth function. We prove, under some additional conditions, the existence of a positive solution for λlarge. We prove that our solution u for λ large is such that = →∞∈Ω|| u ||: sup| u(x) |xas λ →∞.Also, in the case of N = 1, we use a bifurcation theory to show that the solution is unstable.

The design and application of a fuzzy logic based controller to a leakage current relay waspresented in this paper. A novel approach based on fuzzy logic to form the tripping action of leakagecurrent relay was investigated. In addition to the theoretical aspect of fuzzy logic, detection of a leakagecurrent, measurement of the leakage current, determination of its duration, trip opening of faulty casesand detailed system architecture were also introduced. The inspected fuzzy logic technique to control thetripping action of the leakage current relay was intended to improve the performance of conventionalleakage current relay control for human safety and system reliability. The relationship between thecontrolled output of the fuzzy processor and properties of leakage current for the proposed relay wasexplored by using a graphical output expression. It was observed that the proposed leakage current relaybased on fuzzy logic was more reliable than conventional leakage current relay.

The coherent anomaly method and a cluster mean-field approach combined with finite-sizescaling extrapolation were used to determine the critical temperature and the critical exponents of aS =1 Ising chain with a long-range interaction in the form of 1/ r1+σ . The results of criticaltemperature are in good agreement with the recent results of the finite-range scaling method and aremore accurate in the classical region. The critical exponents are in agreement with the results of spin-21Ising chains and indicate that the critical exponents are independent of the magnitude of spin in Isingmodels with long-range interactions.

For the first time in the Minkowski space, an Rn 1 time-like complementary ruled surface isdescribed and relations are given connected with an asymptotic and tangential bundle of the time-likecomplementary ruled surface. Furthermore, theorems are given related to edge space, central space andcentral ruled surface of this complementary ruled surface.