We address the issue of separating two finite sets in Rn by means of a suitable revolution cone Γ(z, y, s) = {x ∈ R : s ∥x− z∥ − y (x− z) = 0}. One has to select the aperture coefficient s, the axis y, and the apex z in such a way as to meet certain optimal separation criteria. The homogeneous case z = 0 has been treated in Part I of this work. We now discuss the more general case in which the ...

C o n d e n s a t i o n o f i s a t i n w i t h 4 a m i n o a c e t o p h e n o n e g a v e a q u a n t i t a t i v e y i e l d o f i s a t y l i d e n e j 9 a c e t y l a n i l i n e ( 1 ) . C o n d e n s a t i o n o f 1 w i t h a r o m a t i c a l d e h y d e s y i e l d e d t h e c o r r e s p o n d i n g i s a t y l i d e n e a z o m e t h i n e c h a l c o n e s ( 2 a f ) . I n t e r a c t...

In order to reduce the cropping force and enhance the cropping cross-section quality, a new type of cropping machine is proposed in this paper. The basic structure and working principle of the cropping machine are introduced. Based on D'Alembert's principle, the vibration equations of the cropping machine along the Y direction, X direction and around X, Y, Z axis are built in detail and the mot...

The notation and terminology used here are introduced in the following papers: [17], [19], [20], [3], [4], [2], [16], [5], [1], [18], [9], [11], [12], [8], [6], [7], [13], [10], [21], [14], and [15]. For simplicity, we use the following convention: X denotes a Banach algebra, p denotes a real number, w, z, z1, z2 denote elements of X, k, l, m, n denote natural numbers, s1, s2, s3, s, s ′ denote...

depth estimation of the top of the bedrock in the sedimentary basins is the main goal in geomagnetic explorations. the depth estimation of this kind of anomalies can be done using different methods, in the cases where the bedrock is magnetized. in this article, we use the standard euler deconvolution method and its results to interpret the magnetic data from the reshm region in semnan province ...

We establish two general identities for Bernoulli and Euler polynomials, which are of a new type and have many consequences. The most striking result in this paper is as follows: If n is a positive integer, r + s + t = n and x + y + z = 1, then we have r s t x y n + s t r y z n + t r s z x n = 0 where s t x y n := n k=0 (−1) k s k t n − k B n−k (x)B k (y). It is interesting to compare this with...

The present study investigates the crystal preferred orientation (CPO) of quartz crystals in psammitic rocks to ascertain the deformationmechanism using electron backscatter diffraction (EBSD) on quartz crystals from north of the Renvyle-Bofin Slide (RBS) nearLetterfrack in western Ireland. Complete crystallographic orientations were determined for several thousand individual quartz crystalsin ...

1.1 The hydrodynamic problem The classical water-wave problem concerns the irrotational flow of a perfect fluid of unit density subject to the forces of gravity and surface tension. The fluid motion is described by the Euler equations in a domain bounded below by a rigid horizontal bottom {y = −h} and above by a free surface which is described as a graph {y = η(x, z, t)}, where the function η d...

We discuss the issue of choosing a finite difference scheme for numerical differentiation in case the smoothness of the underlying function is unknown. If low order finite difference schemes are used for smooth functions, then the best possible accuracy cannot be obtained. This can be circumvented by using higher order finite difference schemes, but there is concern that this may cause bad erro...

In this paper we present the maximum simplicial depth estimator and compare it to the ordinary least square estimator in examples from 2D shape analysis focusing on bivariate and multivariate allometrical problems from zoology. We compare two types of estimators derived under different subsets of parametric space on the basis of the linear regression model, θ = (θ1, θ2) ∈ R2 and θ = (θ1, θ2, θ3...