The relation between the working alliance and therapeutic outcome was examined in 21 therapist-client dyads. This relation was analyzed in terms of the level of alliance at the third counseling session, midpoint of treatment, and last session with linear and curvilinear models of the temporal development of the working alliance. Analyses were conducted with hierarchical linear modeling. Results...

BACKGROUND AND PURPOSE The accuracy of preoperative blood oxygen level-dependent fMRI remains controversial. This study assessed the association between the anatomic location of a tumor and the accuracy of fMRI-based motor function mapping in diffuse lower-grade gliomas. MATERIALS AND METHODS Thirty-five patients with lower-grade gliomas involving motor areas underwent preoperative blood oxyg...

One proves that the Mazur-Ulam theorem can be extended in the framework of metric spaces as long as a well behaved concept of midpoint is available. This leads to the new concept of Mazur-Ulam space. Besides the classical case of real normed spaces, other examples such as Sym++(n,R), the space of all n × n dimensional positive definite matrices, appear as cones attached to suitable Euclidean Jo...

We propose an optimal convergence function for achieving fault-tolerant, internal clock synchroniza, tion in the presence of arbitrary process and clock failures. The diflerential fault-tolerant midpoint convergence function guarantees an optimal maximum correction, an optimal maximum drift rate, and an optimal maximum deviation. The proposed convergence function is simple and easy to compute. ...

My G4G8 exchange item is a screw-together cube made of two identically shaped nylon parts, one dyed red and one dyed yellow. It can be seen as a cube sliced by the propeller of an airplane flying through it. Formally, it is cube which has been split along a helicoid surface whose axis is aligned with a two-fold axis of the cube, i.e. passing from one edge midpoint to the opposite edge midpoint....

The constant K has the same meaning as above. 1CAS = Computer Algebra System. 2The interval [0, 2π] is for convenience only. Everything we say can easily be extended to an arbitrary interval [a, b]. 3One notices that the error bound for the midpoint rule is one half that of the trapezoidal rule; compare (2) with (3). For a pretty geometrical explanation of why one can expect the midpoint rule t...

Irregularly and sparsely sampled seismic data that has been shot with a predominant azimuth for long offsets can be completely reconstructed. Our method uses reposting along receiver lines to exact crossline positions, followed by least squares reconstruction in the midpoint-offset domain. This reconstruction scheme has been applied to a 3D marine dataset from the North Sea. Various aspects and...

This paper presents the relationship between the Recursive Arbitrary Topology Splines (RATS) method, derived by the authors, and the Catmull and Clark recursive B-Spline method. Both methods are capable of defining surfaces of any arbitrary topology of control points. They "fill-in" n-sided regions with foursided patches. The Catmull & Clark method is derived from the midpoint subdivision of B-...

Abstract. We study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For n ≥ 2 and 1 < p < ∞, it is shown that l ∞ is representable in a Banach space X if and only if it is representable in the Lebesgue-Bochner Lp(X). New criteria for various convexity properties in Banach spaces are also studied. It is proved that a Banach lattice E is...

One approach to testing and/or proving correctness of a floating-point algorithm computing a function is based on finding input floating-point numbers such that the exact result is very close to a “rounding boundary”, i.e. a floating-point number or a midpoint between them. In the present paper we show how to do this for the reciprocal function by utilizing prime factorizations. We present the ...