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This paper deals with the existence of nontrivial solutions for critical possibly degenerate Kirchhoff fractional (p, q) systems. For clarity, the results are first presented in the scalar case, and then extended into the vectorial framework. The main features and novelty of the paper are the (p, q) growth of the fractional operator, the double lack of compactness as well as the fact that the systems can be degenerate. As far as we know the results are new even in the scalar case and when the Kirchhoff model considered is non-degenerate.

In this paper we study parameter estimation via the Expectation Maximization (EM) algorithm for a continuous-time hidden Markov model with diffusion and point process observation. Inference problems of this type arise for instance in credit risk modelling. A key step in the application of the EM algorithm is the derivation of finite-dimensional filters for the quantities that are needed in the E-Step of the algorithm. In this context we obtain exact, unnormalized and robust filters, and we discuss their numerical implementation. Moreover, we propose several goodness-of-fit tests for hidden Markov models with Gaussian noise and point process observation. We run an extensive simulation study to test speed and accuracy of our methodology. The paper closes with an application to credit risk: we estimate the parameters of a hidden Markov model for credit quality where the observations consist of rating transitions and credit spreads for US corporations.

This paper reports the implementation of slip boundary conditions in the open-source computational library OpenFOAM. The linear and nonlinear Navier slip laws, which are newly implemented in this paper, can be used both for Newtonian and viscoelastic constitutive models. For the former case, the Couette flow assumption near the wall is employed, and for the latter, the cell-centered extra-stress tensor components are linearly extrapolated to the wall. The validation is performed by comparing the numerical results obtained for Newtonian and simplified Phan-Thien-Tanner constitutive model fluids in Couette and Poiseuille flows, with existing analytical solutions. The results obtained using different slip factors were shown to be in agreement with the analytical solutions, even for the most extreme cases where the slip factor is high enough to induce a plug flow pattern for the velocity field. The newly implemented boundary conditions are also used to study the influence of slip in polymer processing, namely in the production of an extruded profile. The results obtained show that the developed slip boundary conditions are able to deal with complex geometrical problems, and are an important tool to support the search of a balanced flow distribution in the design of profile extrusion dies., This work is funded by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT-Portuguese Foundation for Science and Technology under the project UID/CTM/50025/2013 and under the scholarship SFRH/BPD/100353/2014. The authors would also like to acknowledge the Minho University cluster under the project Search-ON2: Revitalization of HPC infrastructure of UMinho (NORTE-07-0162-FEDER-000086), co-funded by the North Portugal Regional Operational Programme (ON.2-0 Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF).

In the present paper, the problem of estimating the contingent cone to the solution set associated with certain set-valued inclusions is addressed by variational analysis methods and tools. As a main result, inner (resp. outer) approximations, which are expressed in terms of outer (resp. inner) prederivatives of the set-valued term appearing in the inclusion problem, are provided. For the analysis of inner approximations, the evidence arises that the metric increase property for set-valued mappings turns out to play a crucial role. Some of the results obtained in this context are then exploited for formulating necessary optimality conditions for constrained problems, whose feasible region is defined by a set-valued inclusion.

Fractional analysis has evolved considerably over the last decades and has become popular in many technical and scientific fields. Many integral operators which ables us to integrate from fractional orders has been generated. Each of them provides different properties such as semigroup property, singularity problems etc. In this paper, firstly, we obtained a new kernel, then some new integral inequalities which are valid for integrals of fractional orders by using Riemann-Liouville fractional integral. To do this, we used some well-known inequalities such as Hölder's inequality or power mean inequality. Our results generalize some inequalities exist in the literature.

In this paper, we give an explicit form of the scalar curvaure for the limiting case of the eigenvalue of the hypersurface Dirac operator which arises in the positive mass theorem for black holes. Then, we show that the hypersurface is an Einstein.

The minimal degree of a permutation group G is defined as the minimal number of non-fixed points of a non-trivial element of G. In this paper, we show that if G is a transitive permutation group of degree n having no non-trivial normal 2-subgroups such that the stabilizer of a point is a 2-group, then the minimal degree of G is at least 2 3 ⁢ n {\frac{2}{3}n} . The proof depends on the classification of finite simple groups.

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of sequences of real numbers. Strongly ideal lacunary ward continuity is also investigated. Interesting results are obtained.

ARAL, Ali/0000-0002-2024-8607; Gupta, Vijay/0000-0002-5768-5763 WOS:000565809500015 In the present paper we establish a general form of Voronovskaja's theorem for functions defined on an unbounded interval and having exponential growth. The case of approximation by linear combinations is also considered. Applications are given for some Szasz-Mirakyan and Baskakov-type operators.

In this paper, we obtain the existence of a global attractor for the higher-order evolution type equation. Moreover, we discuss the asymptotic behavior of global solution.

EgeUn###, For a locally integrable function f on [ 0, ?), we define F(t) = ? t 0 f(u)du and ? ? (t) = ? t 0 (1 - u t) ? (u)du for t > 0. The improper integral ? ? 0 f(u)du is said to be (C, ?) integrable to L for some ? > - 1 if the limit lim x › ? ? ?(t) = L exists. It is known that lim t › ? F(t) = l implies lim t › ? ? ?(t) = l for ? > - 1, but the converse of this implication is not true in general. In this paper, we introduce the concept of the general control modulo of non-integer order for functions and obtain some Tauberian conditions in terms of this concept for the (C, ?) integrability method in order that the converse implication hold true. Our results extend the main theorems in [Ü. Totur and I. Çanak, Tauberian conditions for the (C, ?) integrability of functions, Positivity 21 2017, 1, 73-83]. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019.

Made available in DSpace on 2020-12-10T16:57:45Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-10-01 In this paper, we introduce a new bivariate Kumaraswamy exponential distribution, whose marginals are univariate Kumaraswamy exponential. Some probabilistic properties of this bivariate distribution are derived, such as joint density function, marginal density functions, conditional density functions, moments and stress-strength reliability. Also, we provide the expected information matrix with its elements in a closed form. Estimation of the parameters is investigated by the maximum likelihood, Bayesian and least squares estimation methods. A simulation study is carried out to compare the performance of the estimators by estimation methods. Further, one data set have been analyzed to show how the proposed distribution works in practice. (C) 2019 Mathematical Institute Slovak Academy of Sciences Tanta Univ, Fac Sci, Dept Math, Tanta, Egypt State Univ Sao Paulo, Dept Stat, Sao Paulo, Brazil Kohat Univ Sci & Technol, Dept Math, Kohat 26000, Pakistan State Univ Sao Paulo, Dept Stat, Sao Paulo, Brazil

The well-posedness and the a priori and a posteriori error analysis of the lowest-order Raviart–Thomas mixed finite element method (MFEM) has been established for non-selfadjoint indefinite second-order linear elliptic problems recently in an article by Carstensen, Dond, Nataraj and Pani (Numer. Math., 2016). The associated adaptive mesh-refinement strategy faces the difficulty of the flux error control in H ⁢ ( div , Ω ) {H({\operatorname{div}},\Omega)} and so involves a data-approximation error ∥ f - Π 0 ⁢ f ∥ {\lVert f-\Pi_{0}f\rVert} in the L 2 {L^{2}} norm of the right-hand side f and its piecewise constant approximation Π 0 ⁢ f {\Pi_{0}f} . The separate marking strategy has recently been suggested with a split of a Dörfler marking for the remaining error estimator and an optimal data approximation strategy for the appropriate treatment of ∥ f - Π 0 ⁢ f ∥ L 2 ⁢ ( Ω ) {\|f-\Pi_{0}f\|_{L^{2}(\Omega)}} . The resulting strategy presented in this paper utilizes the abstract algorithm and convergence analysis of Carstensen and Rabus (SINUM, 2017) and generalizes it to general second-order elliptic linear PDEs. The argument for the treatment of the piecewise constant displacement approximation u RT {u_{{\mathrm{RT}}}} is its supercloseness to the piecewise constant approximation Π 0 ⁢ u {\Pi_{0}u} of the exact displacement u. The overall convergence analysis then indeed follows the axioms of adaptivity for separate marking. Some results on mixed and nonconforming finite element approximations on the multiply connected polygonal 2D Lipschitz domain are of general interest.

Gogatishvili, Amiran/0000-0003-3459-0355; Yildiz, Tugce Unver/0000-0003-0414-8400; Gogatishvili, Amiran/0000-0003-3459-0355 WOS: 000503861600008 In this paper the solution of the pointwise multiplier problem between weighted Copson function spaces Cop(p1), (q1) ((u1,) (v1)) and weighted Cesaro function spaces Ces(p2, q2) (u(2), v(2)) is presented, where p(1), p(2), q(1), q(2) is an element of (0,infinity), p(2)

The paper analyzes the sensitivity of boundary crossing probabilities of the Brownian motion to perturbations of the boundary. The first- and second-order sensitivities, i.e. the directional derivatives of the probability, are derived. Except in cases where boundary crossing probabilities for the Brownian bridge are given in closed form, the sensitivities have to be computed numerically. We propose an efficient Monte Carlo procedure.

This paper is motivated by the recent progress on the Hermite–Hadamard inequality for convex functions defined on the bounded closed interval, obtained by Z. Pavić [Z. Pavić, Improvements of the Hermite–Hadamard inequality, J. Inequal. Appl. 2015 2015, Article ID 222]. As a generalization, we obtained a new refinement of the Hermite–Hadamard inequality for co-ordinated convex functions defined on the rectangle.

In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors, the Debye function, and can study their asymptotic decay.

In this paper, we study the Riesz potential (G-Riesz potential) generated by the Gegenbauer differential operator G λ = ( x 2 - 1 ) 1 2 - λ ⁢ d d ⁢ x ⁢ ( x 2 - 1 ) λ + 1 2 ⁢ d d ⁢ x , x ∈ ( 1 , ∞ ) , λ ∈ ( 0 , 1 2 ) . G_{\lambda}=(x^{2}-1)^{\frac{1}{2}-\lambda}\frac{d}{dx}(x^{2}-1)^{\lambda+% \frac{1}{2}}\frac{d}{dx},\quad x\in(1,\infty),\,\lambda\in\Bigl{(}0,\frac{1}{2% }\Bigr{)}. We prove that the G-Riesz potential I G α {I_{G}^{\alpha}} , 0 < α < 2 ⁢ λ + 1 {0 , is bounded from the G-Morrey space L p , λ , γ {L_{p,\lambda,\gamma}} to L q , λ , γ {L_{q,\lambda,\gamma}} if and only if 1 p - 1 q = α 2 ⁢ λ + 1 - γ , 1 < p < 2 ⁢ λ + 1 - γ α . \frac{1}{p}-\frac{1}{q}=\frac{\alpha}{2\lambda+1-\gamma},\quad 1 Also, we prove that the G-Riesz potential I G α {I_{G}^{\alpha}} is bounded from the G-Morrey space L 1 , λ , γ {L_{1,\lambda,\gamma}} to the weak G-Morrey space W ⁢ L q , λ , γ {WL_{q,\lambda,\gamma}} if and only if 1 - 1 q = α 2 ⁢ λ + 1 - γ . 1-\frac{1}{q}=\frac{\alpha}{2\lambda+1-\gamma}.

In this paper, using the concept of ideal convergence, which extends the idea of ordinary convergence and statistical convergence, we are concerned with the I-uniform convergence and the I-pointwise convergence of sequences of functions defined on a set of real numbers D. We present the Arzelà–Ascoli theorem by means of ideal convergence and also the relationship between I-equicontinuity and I-continuity for a family of functions.

In this paper, we study the boundedness of the Hardy operators on Musielak–Orlicz spaces.

SET, ERHAN/0000-0003-1364-5396; Akdemir, Ahmet Ocak/0000-0003-2466-0508 WOS: 000426436000011 In this paper, we establish Ostrowski-type inequalities for strongly convex functions, by using some classical inequalities and elementary analysis. We also give some results for the product of two strongly convex functions.

There has been much interest in reconstructing bi-directional regulatory networks linking the circadian clock to metabolism in plants. A variety of reverse engineering methods from machine learning and computational statistics have been proposed and evaluated. The emphasis of the present paper is on combining models in a model ensemble to boost the network reconstruction accuracy, and to explore various model combination strategies to maximize the improvement. Our results demonstrate that a rich ensemble of predictors outperforms the best individual model, even if the ensemble includes poor predictors with inferior individual reconstruction accuracy. For our application to metabolomic and transcriptomic time series from various mutagenesis plants grown in different light-dark cycles we also show how to determine the optimal time lag between interactions, and we identify significant interactions with a randomization test. Our study predicts new statistically significant interactions between circadian clock genes and metabolites in Arabidopsis thaliana, and thus provides independent statistical evidence that the regulation of metabolism by the circadian clock is not uni-directional, but that there is a statistically significant feedback mechanism aiming from metabolism back to the circadian clock.

The aim of the paper is twofold. First, we present a new general approach to the definition of a class of mixed norm spaces of analytic functions A(q;X)(D), 1

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch), The paper is related to a coupled problem describing piezoelectric effects in an elastic body. For this problem, we deduce majorants of the distance between the exact solution and any approximation in the respective energy class of functions satisfying the boundary conditions. The majorants are fully computable and do not contain mesh dependent constants. They vanish if and only if an approximate solution coincides with the exact one and provide guaranteed upper bounds of errors in terms of the natural energy norm associated with the coupled problem studied.

This paper develops a new estimator for cointegrating and spurious regressions by applying a two-stage generalized Cochrane-Orcutt transformation based on an autoregressive approximation framework, even though the exact form of the error term is unknown in practice. We prove that our estimator is consistent for a wide class of regressions. We further show that a convergent usual t-statistic based on our new estimator can be constructed for the spurious regression cases analyzed by (Granger, C. W. J., and P. Newbold. 1974. “Spurious Regressions in Econometrics.” Journal of Econometrics 74: 111–120) and (Granger, C. W. J., N. Hyung, and H. Jeon. 2001. “Spurious Regressions with Stationary Series.” Applied Economics 33: 899–904). The implementation of our estimator is easy since it does not necessitate estimation of the long-run variance. Simulation results indicate the good statistical properties of the new estimator in small and medium samples, and also consider a more general framework including multiple regressors and endogeneity.

In this paper, we consider the problem of tracking a solution of a reference parabolic equation by a solution of another equation. A stable algorithm based on the extremal shift method is proposed for this problem. The algorithm is designed to work on a sufficiently large time interval where both equations operate.

We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.

This paper deals with the asymptotic behavior of the sequence of codimensions c n ⁢ ( A ) ${c_{n}(A)}$ , n = 1 , 2 , … , ${n=1,2,\ldots,}$ of an algebra A over a field of characteristic zero. It is shown that when such sequence is polynomially bounded, then lim sup n → ∞ ⁡ log n ⁡ c n ⁢ ( A ) ${\limsup_{n\to\infty}\log_{n}c_{n}(A)}$ and lim inf n → ∞ ⁡ log n ⁡ c n ⁢ ( A ) ${\liminf_{n\to\infty}\log_{n}c_{n}(A)}$ can be arbitrarily distant. Also, in case the codimensions are exponentially bounded, we can construct an algebra A such that exp ⁡ ( A ) = 2 ${\exp(A)=2}$ and, for any q ≥ 1 ${q\geq 1}$ , there are infinitely many integers n such that c n ⁢ ( A ) > n q ⁢ 2 n ${c_{n}(A)>n^{q}2^{n}}$ . This gives counterexamples to a conjecture of Regev for both cases of polynomial and exponential codimension growth.

In [Acta Math. Hungar. 66 (1995), 337–343], Bell and Daif proved that if R is a prime ring admitting a nonzero derivation such that d ( x y ) = d ( y x ) ${d(xy)=d(yx)}$ for all x , y ∈ R ${x,y\in R}$ , then R is commutative. The objective of this paper is to examine similar problems when the ring R is equipped with involution. It is shown that if a prime ring R with involution * of a characteristic different from 2 admits a nonzero derivation d such that d ( x x * ) = d ( x * x ) ${d(xx^*)=d(x^*x)}$ for all x ∈ R and S ( R ) ∩ Z ( R ) ≠ ( 0 ) ${S(R)\cap Z(R)\ne (0)}$ , then R is commutative. Moreover, some related results have also been discussed.

WOS: 000398461200003, Let R be a ring and I is a nonzero ideal of R. A mapping F : R -> R is called a multiplicative generalized derivation if there exists a mapping g : R -> R such that F(xy) = F(x)y + xg(y), for all x, y is an element of R. In the present paper, we shall prove that R contains a nonzero central ideal if any one of the following holds: i) F([x, y]) = 0, vii) F([x, y]) = +/-[F(x), y], ii) F(x circle y) = 0, viii) F(x circle y) = +/-(F(x)circle y), iii) F([x, y]) = +/-[x, y], ix) F(xy) +/- xy is an element of Z, iv) F(x circle y) =+/-(x circle y), x) F(xy)+/- yx is an element of Z, v) F([x, y]) = +/-(x circle y), xi) F(xy) +/- [x, y]is an element of Z, vi) F(x circle y) = +/-[x, y], xii) F(xy) +/- (x circle y)is an element of Z, for all x, y is an element of I. (C) 2016 Mathematical Institute Slovak Academy of Sciences

Gene regulatory networks, in which edges between nodes describe interactions between transcription factors (TFs) and their target genes, model regulatory interactions that determine the cell-type and condition-specific expression of genes. Regression methods can be used to identify TF-target gene interactions from gene expression and DNA sequence data. The response variable, i.e. observed gene expression, is modeled as a function of many predictor variables simultaneously. In practice, it is generally not possible to select a single model that clearly achieves the best fit to the observed experimental data and the selected models typically contain overlapping sets of predictor variables. Moreover, parameters that represent the marginal effect of the individual predictors are not always present. In this paper, we use the statistical framework of estimation of variable importance to define variable importance as a parameter of interest and study two different estimators of this parameter in the context of gene regulatory networks. On yeast data we show that the resulting parameter has a biologically appealing interpretation. We apply the proposed methodology on mammalian gene expression data to gain insight into the temporal activity of TFs that underly gene expression changes in F11 cells in response to Forskolin stimulation.

In this paper, we present some abstract results giving a general connection between null-controllability and several inverse problems for a class of parabolic equations. We obtain some conditional stability estimates for the inverse problems consisting of determining the initial condition and the source term, from interior or boundary measurements. We apply this framework for Stokes system with interior and boundary observations, for a coupling of two Stokes system and a linear fluid-structure system.

The decomposition and filtering of time series is an important issue in economics and econometrics and related fields. Even though there are numerous competing methods on the market, in applications one often meets one of the few favorites, like the Hodrick & Prescott filter or the Bandpass filter. In this paper we suggest to employ penalized splines fitting for detrending, extending recent results of Krivobokova & Kauermann (2007). The approach allows to take correlation of the residuals into account and provides a data driven setting of the smoothing parameter, none of which the classical filters allow. We show the simplicity of the penalized spline filter using the open source software R and demonstrate differences and features with numerous data examples taken from Stock & Watson (1999).