Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz--Morrey spaces of the third kind

In the present paper, we will characterize the boundedness of the generalized fractional integral operators $I_{\rho}$ and the generalized fractional maximal operators $M_{\rho}$ on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators $M_{\rho}$ and $I_{\rho}$ on generalized Orlicz--Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators $M_{\rho}$ and $I_{\rho}$ on generalized Orlicz--Morrey spaces

Solutions for a class of iterated singular equations

Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.Comment: 7 page

Electronic and Lattice Dynamical Properties of Ti2SiB MAX Phase

The structural, electronic, mechanic, vibrational and thermodynamic properties of Ti2SiB which is a hypothetical MAX phase compound, have been investigated using density functional theory calculations. The structural optimization of Ti2SiB has been performed and the results have been compared with Ti2SiC, Ti2SiN, and Ti2AlB that are studied in the literature. Then the band structure and corresponding partial density of states are computed. In addition, charge density and Bader charge analysis have been performed. The elastic constants have been obtained, then the secondary results such as bulk modulus, shear modulus, Youngs modulus, Poissons ratio, and Vickers Hardness of polycrystalline aggregates have been derived, and the relevant mechanical properties have been discussed. Moreover, the elastic anisotropy has been visualized in detail by plotting the directional dependence of compressibility, Poisson ratio, Youngs and Shear moduli. Furthermore, the phonon dispersion curves as well as corresponding phonon PDOS, and thermodynamical properties such as free energy, entropy and heat capacity have been computed and the obtained results have been discussed in detail. This study provides the first considerations of Ti2SiB that could have a potential application in nuclear industry

On the Riesz potential and its commutators on generalized Orlicz-Morrey spaces

We consider generalized Orlicz-Morrey spaces M_{\Phi,\varphi}(\Rn) including their weak versions WM_{\Phi,\varphi}(\Rn). In these spaces we prove the boundedness of the Riesz potential from M_{\Phi,\varphi_1}(\Rn) to M_{\Psi,\varphi_2}(\Rn) and from M_{\Phi,\varphi_1}(\Rn) to WM_{\Psi,\varphi_2}(\Rn). As applications of those results, the boundedness of the commutators of the Riesz potential on generalized Orlicz-Morrey space is also obtained. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on $(\varphi_{1},\varphi_{2})$, which do not assume any assumption on monotonicity of $\varphi_{1}(x,r)$, $\varphi_{2}(x,r)$ in r.Comment: 23 pages. J. Funct. Spaces Appl.(to appear

Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces

We consider local "complementary" generalized Morrey spaces M-c({x0})p(.).omega (Omega) in which the p-means of function are controlled over Omega \ B(x(0), r) instead of B(x(0), r), where Omega subset of R-n is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function omega(r) defining the "complementary" Morrey-type norm. In the case where omega is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type M-c({x0})p(.).omega (Omega) -> M-c({x0})p(.).omega (Omega)-theorem for the potential operators I-alpha(.), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities-on omega(r), which do not assume any assumption on monotonicity of omega(r).Science Development Foundation under the President of the Republic of Azerbaijan [EIF-2010-1(1)-40/06-1]; Scientific and Technological Research Council of Turkey (TUBITAK) [110T695]info:eu-repo/semantics/publishedVersio

Multiplex Detection of Aspergillus fumigatus Mycoviruses.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).Mycoviruses are viruses that naturally infect and replicate in fungi. They are widespread in all major fungal groups including plant and animal pathogenic fungi. Several dsRNA mycoviruses have been reported in Aspergillus fumigatus. Multiplex polymerase chain reaction (PCR) amplification is a version of PCR that enables amplification of different targets simultaneously. This technique has been widely used for detection and differentiation of viruses especially plant viruses such as those which infect tobacco, potato and garlic. For rapid detection, multiplex RT-PCR was developed to screen new isolates for the presence of A. fumigatus mycoviruses. Aspergillus fumigatus chrysovirus (AfuCV), Aspergillus fumigatus partitivirus (AfuPV-1), and Aspergillus fumigatus tetramycovirus-1 (AfuTmV-1) dsRNAs were amplified in separate reactions using a mixture of multiplex primer pairs. It was demonstrated that in the presence of a single infection, primer pair mixtures only amplify the corresponding single virus infection. Mixed infections using dual or triple combinations of dsRNA viruses were also amplified simultaneously using multiplex RT-PCR. Up until now, methods for the rapid detection of Aspergillus mycoviruses have been restricted to small scale dsRNA extraction approaches which are laborious and for large numbers of samples not as sensitive as RT-PCR. The multiplex RT-PCR assay developed here will be useful for studies on determining the incidence of A. fumigatus mycoviruses. This is the first report on multiplex detection of A. fumigatus mycovirusesPeer reviewe

January 1958

My dear Brother: It does not require a great stretch of the imagination for me to hear you mutter: Didn\u27t I get one of these yellow sheets only a month ago? Why doesn\u27t he get back to work instead of cluttering up my mail? Well, thereby hangs a tale. A few weeks ago I spent an illuminating, and somewhat dismaying, evening with brother Theophilus in the Middle West. He has a good congregation of about five hundred members. It is an average parish, with the usual complement of saints and sinners, with the lines between them shifting back and forth. Theophilus has worked hard and the Lord of the Church has blessed his hands and his voice

Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-morrey spaces

We prove the boundedness of the Hardy-Littlewood maximal operator and their commutators with BMO-coefficients in vanishing generalized Orlicz-Morrey spaces VM Phi,phi(R-n) including weak versions of these spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators involving the Young function Phi(u) and the function phi(x, r) defining the space. No kind of monotonicity condition on phi(x, r) in r is imposed.Ahi Evran University [PYO.FEN.4003.13.003, PYO.FEN.4001.14.017]; Science Development Foundation under Republic of Azerbaijan [EIF-2013-9(15)-46/10/1]; Russian Fund of Basic Research [15-01-02732

Boundedness of fractional maximal operator and its commutators on generalized Orlicz-Morrey spaces

We consider generalized Orlicz-Morrey spaces $M_{\Phi,\varphi}(\mathbb{R}^{n})$ including their weak versions $WM_{\Phi,\varphi}(\mathbb{R}^{n})$. We find the sufficient conditions on the pairs $(\varphi_{1},\varphi_{2})$ and $(\Phi, \Psi)$ which ensures the boundedness of the fractional maximal operator $M_{\alpha}$ from $M_{\Phi,\varphi_1}(\mathbb{R}^{n})$ to $M_{\Psi,\varphi_2}(\mathbb{R}^{n})$ and from $M_{\Phi,\varphi_1}(\mathbb{R}^{n})$ to $WM_{\Psi,\varphi_2}(\mathbb{R}^{n})$. As applications of those results, the boundedness of the commutators of the fractional maximal operator $M_{b,\alpha}$ with $b \in BMO(\mathbb{R}^{n})$ on the spaces $M_{\Phi,\varphi}(\mathbb{R}^{n})$ is also obtained. In all the cases the conditions for the boundedness are given in terms of supremal-type inequalities on weights $\varphi(x,r)$, which do not assume any assumption on monotonicity of $\varphi(x,r)$ on $r$.Comment: 23 pages. Complex Anal. Oper. Theory (to appear). arXiv admin note: substantial text overlap with arXiv:1310.660

Boundedness of intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces

We shall investigate the boundedness of the intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces $M^{\Phi,\varphi}_{w}({\mathbb R}^n)$. In all the cases, the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on weights $\varphi$ without assuming any monotonicity property of $\varphi(x,\cdot)$ with $x$ fixed.Comment: 21pages. arXiv admin note: text overlap with arXiv:1311.612