This research deals with the dynamical evolutions played by a simple mechanical model. The model is constituted of a parallelepiped standing on a horizontal plane. As the plane performs vibrational displacements the parallelepiped begins to evolve its positions and, this “parallelepiped movements” constitutes the subject of our concern. Plane movement is assumed so, notwithstanding we name it a...

In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions 2 and 3 and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.

In this work we solve a special case of the problem of building an n-dimensional parallelepiped using a given set of n-dimensional parallelepipeds. Consider the identity x = xHx 1L Hx 2L + 3 xHx 1L + x. For sufficiently large x, we associate with x3 a cube with edges of size x, with x Hx 1L Hx 2L a parallelepiped with edges x, x 1, x 2, with 3 x Hx 1L three parallelepipeds of edges x, x 1, 1, a...

In this paper, the design and dynamic balancing of a novel 3DOF parallel mechanism referred to as parallelepiped mechanism are addressed. Two types of actuation schemes of the mechanism are considered. The balancing equations are derived by imposing that the center of mass of the mechanism is fixed and that the total angular momentum is constant with respect to a fixed point. Optimization is pe...

since the ancient times, burial practices have displayed certain characteristics among different iranian ethnic groups and regions were influenced by the local religious orientations, traditions and environments, and are regarded as part of the spiritual culture of any given population. indeed, religious beliefs play the main role in this diversity. because of the empire’s long endurance and va...

The s-lecture hall polytopes Ps are a class of integer polytopes defined by Savage and Schuster which are closely related to the lecture hall partitions of Eriksson and Bousquet-Mélou. We define a half-open parallelopiped Pars associated with Ps and give a simple description of its integer points. We use this description to recover earlier results of Savage et al. on the δ-vector (or h∗-vector)...

In this paper, we consider diffeomorphic mappings of a nondegenerate parallelepiped onto another such parallelepiped. We prove that the image any face first under mapping is certain second Moreover, also obtain several auxiliary results on transformation boundary points action diffeomorphism.

The “shape” of the desired frequency passband is an important consideration in the design of nonseparable multidimensional ( -D) filters in -D multirate systems. For -D th-band filters, the passband shape should be chosen such that the th-band constraint is satisfied. The most commonly used shape of the passband for -D th-band low-pass filters is the so-called symmetric parallelepiped (SPD) . I...

In the past, various virtual Frisch-grid designs have been proposed for cadmium zinc telluride (CZT) and other compound semiconductor detectors. These include three-terminal, semi-spherical, CAPture, Frisch-ring, capacitive Frisch-grid and pixel devices (along with their modifications). Among them, the Frisch-grid design employing a noncontacting ring extended over the entire side surfaces of p...