This paper deals with linear fractional bilevel programming problem. The goals of objective functions are determined by optimizing individual objective function subject to the system constraints. Then the fractional objective functions are transformed into equivalent linear functions at the optimal solution point by using first order Taylor polynomial series. Since the objectives of the decisio...

We discuss some results and problems related to the Newton–Puiseux algorithm its generalization for nonzero characteristic obtained by author earlier. A new method is suggested obtaining efficient estimates of roots a polynomial in field fractional power series case arbitrary characteristic.

Exact solutions to conformable time fractional (3+1)dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE. The resultant polynomial equation is solved by using algebrai...

We use the recently established higher-level Bailey lemma and Bose–Fermi polynomial identities for the minimal models M(p, p) to demonstrate the existence of a Bailey flow from M(p, p) to the coset models (A (1) 1 )N ×(A (1) 1 )N ′/(A (1) 1 )N+N ′ where N is a positive integer and N ′ is fractional, and to obtain Bose–Fermi identities for these models. The fermionic side of these identities is ...

In microbial and chemical risk assessments, careful dose-response modeling is emphasized because a target risk level (probability of infection or illness) is often in the low benchmark response range of 1% to 10%. To address model uncertainty at low doses and enhance diversity and flexibility for model-averaging, a set of fractional polynomial dose-response models can be considered. However, el...

As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet ...

Multivariable fractional polynomial (MFP) models are commonly used in medical research. The datasets in which MFP models are applied often contain covariates with missing values. To handle the missing values, we describe methods for combining multiple imputation with MFP modelling, considering in turn three issues: first, how to impute so that the imputation model does not favour certain fracti...

We propose and derive the asymptotic distribution of a tapered narrow-band least squares estimator (NBLSE) of the cointegration parameter in the framework of fractional cointegration. This tapered estimator is invariant to deterministic polynomial trends. In particular, we allow for arbitrary linear time trends that often occur in practice. Our simulations show that, in the case of no determini...

In this paper using a transform defined by the translation operator we introduce concept of spectrum sequences that are bounded given polynomial. We apply spectral theory to study asymptotic behavior solutions fractional linear difference equations. One obtained results is an extension famous Katznelson-Tzafriri Theorem, saying ?-resolvent associated with equation, satisfies estimate type, prov...

This paper presents a new Fuzzy Logic Controller (FLC) having the ability to support fractional polynomial membership functions. These functions are general forms of triangular and trapezoidal membership functions, and also those functions which are used in linguistic hedge FLC (LHFLC). A two-input, single-output Takagi–Sugeno–Kang (TSK) type 0 FLC is designed in 0.35 μm standard CMOS process. ...