Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential

We consider a parametric nonlinear Robin problem driven by the negative p-Laplacian plus an indefinite potential. The equation can be thought as a perturbation of the usual eigenvalue problem. We consider the case where the perturbation $$f(z,\cdot )$$ f ( z , · ) is $$(p-1)$$ ( p - 1 ) -sublinear and then the case where it is $$(p-1)$$ ( p - 1 ) -superlinear but without satisfying the Ambrosetti–Rabinowitz condition. We establish existence and uniqueness or multiplicity of positive solutions for certain admissible range for the parameter $$\lambda \in {\mathbb {R}}$$ λ ∈ R which we specify exactly in terms of principal eigenvalue of the differential operator.

MULTIPLIER OPTIMIZATION FOR CONSTANT PROPORTION PORTFOLIO INSURANCE (CPPI) STRATEGY

Constant proportion portfolio insurance (CPPI) strategy is a very popular investment solution which provides an investor with a capital protection as well as allows for an equity market participation. In this paper, we propose a two-step approach to the numerical optimization of the CPPI main parameter, multiplier. First, we identify an admissible range of the multiplier values by controlling the shortfall probability (chosen as a measure of the gap risk). Second, within the admissible range, we choose the optimal multiplier value with respect to the omega ratio (chosen as a performance measure). We illustrate the performance of our optimization algorithm on simulated CPPI paths in the Black–Scholes environment with discrete trading as well as on the historical S&P500 data using the block-bootstrap simulations.

Дифференциальные характеристики поля течения перерасширенной газовой струи в окрестности кромки сопла

A parametric study of the features of the flow field of a plane and axisymmetric overexpanded ideal gas jet in the vicinity of the nozzle edge has been conducted over the entire theoretically admissible range of determining parameters (nozzle divergence angles, exhaust Mach numbers, jet incalculabilities, and gas adiabat indicators). The exhaust parameters that correspond to the extremes of the differential characteristics of a shockwave falling (descending) from the edge and the flow field behind it have been revealed. A significant difference in the character of changes in the characteristics of the shockwave and the flow field behind it depending on the type of symmetry of the gas jet has been found and studied.

A suggestion on how to include calendar dates in Bloom Filters

ABSTRACT ObjectiveBloom Filters have been used in a number of studies conducted for the Ministry of Health. They are usually recommended because of the possibility that they may participate in secure protocols for the exchange of data. In our case the speed of the program, once the filters have been prepared, is so high that that itself is sufficient motive for their adoption. Nevertheless if two calendar dates differ by one character this may merit more attention than a similar difference in personal names. This became evident in a large linkage between mortality records and hospital separations where the patient had died. Higher scores were obtained when the date fields differed by only one character, but when that character represented a year there would no reason to notice the pair. When the character difference was compatible with a difference of a few days this would be more interesting because in studies like the one just cited it would be reasonable to admit differences of a few days or even, perhaps, weeks between the events ( recording of the death of the patient ).ApproachHow then to represent the difference between dates in a Bloom Filter? A date can be represented as a Boolean vector where the day (or week) is set to '1'. It may be represented by several contiguous '1's to admit admissible uncertainty in comparisons. The similarity between two dates can then just be the Dice Coefficient of the corresponding vectors. ResultBut a vector representing a date may then be very large. It could be as much as 365 bits per year, far more than is usually used for the other fields. The number of logical word comparisons would go up and the program would become slower. Knowing that the admissible range is presented by contiguous '1's means that we can obtain the effect of constructing the Bloom Filter and calculating the Dice Coefficient more directly. Starting with the two dates we can obtain the number of bits that are shared, which will depend on the admissible range. The Dice Coefficient can then be calculated directly without the need to construct the Filter. ConclusionWe are then left with the decision on how to add the result to the value obtained from the other variables, and this will depend on what importance it is felt the date should have.

Uniform strain fields inside multiple inclusions in an elastic infinite plane under anti-plane shear

This paper constructs multiple elastic inclusions with prescribed uniform internal strain fields embedded in an infinite matrix under given uniform remote anti-plane shear. The method used is based on the sufficient and necessary conditions imposed on the boundary values of a holomorphic function, which guarantee the existence of the holomorphic function in a multiply connected region. The unknown shape of each of the multiple inclusions is characterized by a polynomial conformal mapping with a finite number of unknown coefficients. With the aid of Cauchy’s integral formula and Faber series, these unknown coefficients are determined by a system of nonlinear equations. Detailed numerical examples are shown for multiple inclusions with various prescribed uniform internal strain fields, for symmetrical inclusions and for inclusions whose shapes are independent of the remote loading, respectively. It is found that the admissible range of uniform internal strain fields for multiple inclusions is moderately larger than the admissible range of the uniform internal strain field for a single elliptical inclusion under the same remote loading. In particular, specific conditions on the prescribed uniform internal strain fields and elastic constants of the multiple inclusions are derived for the existence of symmetric inclusions and rotationally symmetrical inclusions. Moreover, for any two inclusions among multiple inclusions of shapes independent of the remote loading, it is shown that the ratio between the uniform internal strain fields inside the two inclusions equals a specific ratio determined by the shear moduli of the two inclusions and the matrix.

Admissible Range of Proportional Gain in Stabilizing PID Region

This paper considers the problem of stabilizing linear time-invariant plants by a PID controller. If the proportional gain reaches the extreme value, the closed-loop system contains a double pole on the imaginary axis. Using this property, the admissible range of the proportional gain is derived, also the corresponding integral gain and derivative gain are obtained. If the proportional gain is fixed, the stability region in the plane with respect to the integral gain and the derivative gain is determined by plotting the stability boundary locus. The effectiveness of the method presented is illustrated by several examples.