In this paper we study integral operators of the form \[ Tf(x)=\int | x-a_1y|^{-\alpha _1}\dots | x-a_my|^{-\alpha _m}f(y)\mathrm{d}y,
\] $\alpha _1+\dots +\alpha _m=n$. We obtain the $L^p(w)$ boundedness for them, and a weighted $(1,1)$ inequality for weights $w$ in $A_p$ satisfying that there exists $c\ge 1$ such that $w( a_ix) \le cw( x)$ for a.e. $x\in \mathbb R^n$, $1\le i\le m$. Moreover, we prove $\Vert Tf\Vert _{{\mathrm BMO}}\le c\Vert f\Vert _\infty $ for a wide family of functions $f\in L^\infty ( \mathbb R^n)$.
We present some properties of mixture and generalized mixture operators, with special stress on their monotonicity. We introduce new sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. However, mixture operators, generalized mixture operators neither quasi-arithmetic means weighted by a weighting function need not be non-decreasing operators, in general.
Relations between (proper) Pareto optimality of solutions of multicriteria optimization problems and solutions of the minimization problems obtained by replacing the multiple criteria with Lp-norm related functions (depending on the criteria, goals, and scaling factors) are investigated.
In this paper we study the uniqueness for meromorphic functions sharing one value, and obtain some results which improve and generalize the related results due to M. L. Fang, X. Y. Zhang, W. C. Lin, T. D. Zhang, W. R. Lü and others.
We study sub-Bergman Hilbert spaces in the weighted Bergman space $A^2_\alpha $. We generalize the results already obtained by Kehe Zhu for the standard Bergman space $A^2$.
In this paper we give a new definition of the classical contact elements of a smooth manifold M as ideals of its ring of smooth functions: they are the kernels of Weil’s near points. Ehresmann’s jets of cross-sections of a fibre bundle are obtained as a particular case. The tangent space at a point of a manifold of contact elements of M is shown to be a quotient of a space of derivations from the same ringC∞(M) into certain finite-dimensional local algebras. The prolongation of an ideal of functions from a Weil
bundle to another one is the same ideal, when its functions take values into certain Weil algebras; following the same idea vector fields are prolonged, without any considerations about local one-parameter groups. As a consequence, we give an algebraic definition of Kuranishi’s fundamental identification on Weil bundles, and study their affine structures, as a generalization of the classical results on spaces of jets of cross-sections.
A new genus, Weketrema, is erected in the family Lecithasteridae for the species hitherto known as Lecithophyllum hawaiiense. Weketrema hawaiiense (Yamaguti, 1970) comb. n. is redescribed from Scolopsis bilineatus (Bloch) (Perciformes: Nemipteridae) from Lizard Island and Heron Island, Queensland, Plectorhinchus gibbosus (Lacepède) (Perciformes: Haemulidae) from Heron Island and Cheilodactylus nigripes Richardson (Perciformes: Cheilodactylidae) and Latridopsis forsteri (Castelnau) (Perciformes: Latridae) from Stanley, northern Tasmania. The new genus is distinguished from related members of the family Lecithasteridae by its complete lack of a sinus-sac. Although placed in the subfamily Lecithasterinae pro tem, its true subfamily position is not entirely clear. Comment is made on its unusual distribution, both in terms of zoogeography and hosts.
Correct detection of input and output parameters of a welding process is significant for successful development of an automated welding operation. In welding process literature, we observe that output parameters are predicted according to given input parameters. As a new approach to previous efforts, this paper presents a new modeling approach on prediction and classification of welding parameters. 3 different models are developed on a critical welding process based on Artificial Neural Networks (ANNs) which are (i) Output parameter prediction, (ii) Input parameter prediction (reverse application of output prediction model) and (iii) Classification of products. In this study, firstly we use Pareto Analysis for determining uncontrollable input parameters of the welding process based on expert views. With the help of these analysis, 9 uncontrollable parameters are determined among 22 potential parameters. Then, the welding process of ammunition is modeled as a multi-input multi-output process with 9 input and 3 output parameters. 1st model predicts the values of output parameters according to given input values. 2nd model predicts the values of correct input parameter combination for a defect-free weld operation and 3rd model is used to classify the products whether defected or defect-free. 3rd model is also used for validation of results obtained by 1st and 2nd models. A high level of performance is attained by all the methods tested in this study. In addition, the product is a strategic ammunition in the armed forces inventory which is manufactured in a limited number of countries in the world. Before application of this study, the welding process of the product could not be carried out in a systematic way. The process was conducted by trialand- error approach by changing input parameter values at each operation. This caused a lot of costs. With the help of this study, best parameter combination is found, tested, validated with ANNs and operation costs are minimized by 30%.
In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space $\Bbb R^d$, $d=2$ or $3$. The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known {\it a priori}, so we deal with a free boundary value problem. \endgraf We improve the known results by proving a complete wellposedness result: our main result yields a local in time existence and uniqueness of strong solutions for $d=2$ or $3$. Moreover, we prove that the solution is global in time for $d=2$ and also for $d=3$ if the data are small enough.