Finite

Photon-like objects are real massless time-stable and spatially finite physical objects with an intrinsically compatible translational-rotational dynamical structure. They carry energy- momentum and propagate as a whole in a translational-rotational periodic manner by the speed of light. The corresponding integral action for one period T is given by the Planck-like constant ”h = ET”, where ”E” is the full energy of the photon-like object. They are composite objects, each one consists of two time recognizable and energy-momentum exchanging continuous subsystems carrying the same stress-energy-momentum and being in a state of dynamical equilibrium. The mutually exchanged energy for one period gives the elementary action ”h”. Photon-like objects follow the rule: no translation as a whole is possible without local rotation, and no local rotation is possible without translation as a whole. The adequate mathematics we came to was Extended Lie derivative and Frobenius integrability/noninte...

In this paper, an extended forming limit stress diagram (EFLSD) was applied to predict neck initiation failure in tube hydroforming of metal bellows. The proposed EFLSD was used in conjunction with ABAQUS/ EXPLICIT finite element simulations to predict the onset of necking in tube hydroforming of metal bellows. The amount of calibration pressure and axial feeding required to produce an acceptable part in finite element method (FEM) were compared with the published experimental data and a satisfactory agreement between the FEM and published test results was achieved. Therefore, the present approach can be used as a reliable criterion for designing metal bellows hydroforming processes and reducing the number of costly trials.

This book aims to summarize in a consistent way the authors' results in attempting to build spatially finite and time-stable models of photon-like objects through extending Maxwell vacuum equations to local energy-momentum exchange relations and making use of modern differential geometry. In particular, we interpret dynamically Frobenius integrability theory of distributions on manifolds through an appropriate $\varphi$-extension along $p$-vector fields of the classical Lie derivative, and give interaction interpretation of the nonintegrability of subdistributions of an integrable distribution recognizing physically these subdistributions as time-stable subsystems of the field object considered and formally presented by the integrable distribution. The space-time propagation of our photon-like object is, of course, along appropriate symmetry of the representing distribution.

We prove versions of the fundamentaltheorems about Cuntz- Krieger algebras for the C∗-algebras of row-finite graphs: directed graphs in which each vertex emits at most finitely many edges. Special cases of these results have previously been obtained using various powerful machines; our main point is that direct methods yield sharper results more easily.

Behaviour of soils in the vadose zone is closely linked to water balance between ground and atmosphere. It seems that transpiration is the most uncertain and difficult to evaluate of all the terms in the soil water balance. The key variable to estimate the transpiration rate is the rate of root water uptake, which depends on the hydrological, geological and meteorological conditions. A mathematical model for the rate of root water uptake incorporating the root growth rate, ground conditions, type of vegetation and climatic parameters, has been developed. A conical shape is considered to represent the geometry of the tree root zone. Using this proposed model, the distribution of moisture and the matric suction profile adjacent to the tree are numerically analysed. Field measurements taken from literature published previously are compared with the authors’ numerical model. The predicted results obtained from the numerical analysis, compared favourably with the field measurements, justifying the assumptions upon which the model was developed. The analysis also indicates that soil suction and settlement increase over the time, with the effect being more significant in the first stages of transpiration.