In this study, we investigate the intial value problem (IVP) for a time-fractional fourth-order equation with nonlinear source terms. More specifically, consider biharmonic exponential nonlinearity and Cahn–Hilliard equation. By using Fourier transform concept, generalized formula mild solution as well smoothing effects of resolvent operators are proved. For IVP associated first one, by Orlicz ...

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

conclusions the use of smoothing methods helps us to eliminate non-linear effects but it is more appropriate to use cox proportional hazards model in medical data because of its’ ease of interpretation and capability of modeling both continuous and discrete covariates. also, cox proportional hazards model and smoothing methods analysis identified that age at diagnosis and tumor size were indepe...

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

Transfer operators in multigrid (MG) are generated, as a rule, on the basis of usual central formulas of weighting and linear interpolation to restriction and prolongation, respectively. This is quite naturally to elliptic problems with smooth coeecients, but not so evidently to hyperbolic equations in gasdynamics, where discontinuous solutions with shocks arise often. Nevertheless, beginning f...

A new form of the discrepancy principle for Poisson inverse problems with compact operators is proposed and discussed in relation to various other proposals. It shown that filter-induced spectral regularization a priori chosen smoothing parameter produces estimators are rate-minimax under source conditions on estimated function. With used posteriori choice parameter, solutions consistent (in pr...

This paper presents algorithms for parallelization of inference in hidden Markov models (HMMs). In particular, we propose parallel backward-forward type filtering and smoothing algorithm as well Viterbi-type maximum-a-posteriori (MAP) algorithm. We define associative elements operators to pose these problems parallel-prefix-sum computations sum-product max-product parallelize them using paralle...

We introduce function spaces for the treatment of non-linear parabolic partial differential equations with variable log–Hölder continuous exponents that only incorporate information symmetric part a gradient. As an analogue Korn's inequality these functions is not available, construction appropriate smoothing method proves to be difficult. Using point-wise Poincaré near boundary bounded Lipschi...

Rotational smoothing is a phenomenon consisting in gain of regularity by means averaging over rotations. This present operators that regularize only certain directions, contrast to regularizing all directions. The the result rotating directions where corresponding operator performs effect. In this paper we carry out systematic study rotational for class includes k-vector-space Riesz potentials ...