To describe icosahedral symmetry **axes** with respect to the orthogonal **coordinate** **axes**, two conventions, z(2)-3-5-x(2) and z(2)-3-5-y(2), are commonly used, where 2, 3, and 5 correspond to the icosahedral 2-fold, 3-fold, and 5-fold symmetry **axes**, respectively, and x, y, and z are the orthogonal **coordinate** **axes**. In the z(2)-3-5-x(2) convention, two icosahedral 2-fold **axes** coincide with the z and x **coordinate** **axes** while a set of icosa- hedral 3-fold and 5-fold **axes** lie, in that order, between the z and x **axes** in the xz plane (Fig. 2). Similarly, in the z(2)-3-5-y(2) orientation, a pair of 2-fold **axes** coincide with the z and y **axes** and a 3-fold and a 5-fold axis lie in between in the zy plane. These two orientations are related to each other by a 90° rotation around the z axis. All of the entries in the VIPER web-base are stored uniformly in the z(2)-3-5-x(2) convention.

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Calibration is used for establishing deviations of measuring instruments. If we want reliable results o f calibration, all m easurem ents used in the calibration procedure must be traceable to the primary res. national standard. At present there exist only two methods for the calibration of CMMs at the moment that fulfil all the criteria o f a real calibration. However, these two methods (especially virtual CMM) are very expensive, because the machine needs to be calibrated before each measurement. Such calibration also increases the dead time of the machine. It is hard to believe that industry will accept such expensive methods. Therefore, performance tests (methods using gauge blocks, step gauges, artefacts, gauge rings, etc.) will still be used at the industry level for a certain time to come. These tests are not real calibration methods, but they do at least give us some information about the accuracy of a machine. This information is usually data about linear measurements in the **coordinate** **axes** and diagonals.

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Often in physics or engineering, such systems are necessary to solve problems. For example, a NASA engineer whom I know was solving fluid dynamic equations for airflow over aircraft compressor blades. He chose to let the blade surfaces themselves represent **coordinate** surfaces and specified **coordinate** **axes** to fit. He wrote tensor equations in this somewhat complicated system and produced beautiful theoretical flow patterns, some of which are still hanging framed in our Administration Building and in other places around the laboratory!

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Model Viewer is a computer program that displays the results of three-dimensional ground- water models. Scalar data (such as hydraulic head or solute concentration) may be displayed as a solid or a set of isosurfaces, using a red-to-blue color spectrum to represent a range of scalar values. Vector data (such as velocity or specific discharge) are represented by lines oriented to the vector direction and scaled to the vector magnitude. Model Viewer can also display pathlines, cells or nodes that represent model features such as streams and wells, and auxiliary graphic objects such as grid lines and **coordinate** **axes**. Users may crop the model grid in different

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In section 2 we summarise the balance model used. We then recall the matrix for- mulation for the QG dynamics in section 3 (the leading-order solution in the balance model). In section 4 we derive balanced ellipsoidal solutions complete to second order in Rossby number. The analysis begins in section 4.1 by examining an approximation to the full equations where the source terms in the Poisson equations of the exterior potentials are set to zero (the “homogeneous solution” hereafter). In section 4.2 we consider two particular cases of steady (shape-invariant) motion and explicitly calculate the vortex rotation rate about the z-axis. For the first case in section 4.2.1, where the ellipsoidal **axes** are aligned with the **coordinate** **axes**, we derive the full analytical solution to the balance equations (including the external source terms) and compare it to the homo- geneous solution as well as to numerical solutions of the nonlinear balance model. The second case considered in section 4.2.2 is that of a tilted spheroid for which we obtain the homogeneous solution and compare it with numerical solutions. In section 5 we draw our conclusions and suggest possible future avenues for exploration.

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If the axis of rotation is not one of the two coordinate-axes, but rather an arbitrary horizontal or vertical line, the volume can be similarly calculated, with some slight adjustments[r]

A translation of **coordinate** **axes** occurs when the new **coordinate** **axes** have the same direction as and are parallel to the original **coordinate** **axes**. To see how coordinates in the original system are changed when moving to the translated sys- tem, and vice versa, refer to Figure 1.

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It is well known that the line of intersection of an ellipsoid and a plane is an ellipse. In this note simple formulas for the semi-**axes** and the center of the ellipse are given, involving only the semi-**axes** of the ellipsoid, the componentes of the unit normal vector of the plane and the distance of the plane from the center of coordinates. This topic is relatively common to study, but, as indicated in [1], a closed form solution to the general problem is actually very difficult to derive. This is attemped here. As applications problems are treated, which were posed in the internet [1,2], pertaining to satellite orbits in space and to planning radio-therapy treatment of eyes.

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Posterior teeth angulations are measured in the maxillary and mandibular arches between the long axes of premolars' (apex- cusp tip) and the molars' long axes (fu[r]

The aim of this study was to propose the concept of different anatomical **axes** in the proximal and distal parts of the femur; compare these **axes** in normally aligned people in reference to the distance from the intercondy- lar notch of the femur; and also propose the application of these **axes** and their normal ranges for surgeries such as total knee arthroplasties and for comminuted prox- imal and distal femoral fractures, which the anatomy and alignment of the femur are completely distorted.

The circular chart A (Figure 3) is summary for all studied area and reflects distribution in Woolf’s grid of points of an exit to the top hemisphere of **axes** of the main normal tension of compression, stretching and intermediate, points of observations received for local volumes. **Axes** of compression have meridional horizontal position, deviating to the northeast and the northwest. The stretching axis has vertical position more, being sometimes interchanged the position from intermediate. This chart confirms dynamic conditions when upthrus, upth- rus-shift types of deformation elements are formed. This field of tension corres- ponds to the regional field of tension of the first rank which was received earlier and characteristic of all Chatkal-Kurama mountain area (Figure 3(C)). The general regional field of tension for western, Central Asian, parts of Tien Shan, received by us earlier according to geological data is characterized by the same type, but has northwest (southeast) orientation of an axis of compression (Figure 3(B)). The received picture of tension allows understanding kinematics and dynamics of the massif of the Almalyk district, in particular Entre Rios Sauk- bulak- Kyzata-Almalyk. They show that in the Central block shifts in southwest and partly in the western direction are noted. On the Burgundin break existence of right-hand moving is supposed. In the southern part of the site, in points located on different wings of the Miskany break confirm manifestation of left-side shift.

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From the above consideration we can see apparent theoretical difficulty in defi- nition of space and objects in it as a physical reality without any connection to the past. Such an approach would necessitate introduction of a fifth independent **coordinate**—**coordinate** time, while according to other considerations this coor- dinate cannot be independent. Thus in terms of presented Euclidean theory of space and time it is necessary to define space as a set of objects that has traveled to their current positions by unknown, but quite specific, trajectories. Existence of such trajectories is necessary for time location of those objects as well as events which the objects are participants. The formulas (9) and (20) allow no more than determination of time increments from some given event in the ob- ject’s history. So for an evaluation of equality of **coordinate** times of two objects which are in the same point of space it is necessary to accept an important as- sumption, —these two objects have met at least once in their past. This assump- tion can be ensured in the only possible way—all the trajectories have a common initial point, i.e. once in the past all the objects simultaneously emerged from one common origin.

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The idea to introduce the Omnia Mobilis assumption -everything is moving- (Ruiz Estrada, Yap and Nagaraj, 2008) is to reduce the dependency and less uses of Ceteris Paribus assumption in the economic modeling. We propose the openness of substantive isolation through the application of the Omnia Mobilis assumption. It is based on generate the relaxation of all variables without restrictions and limitation that the Ceteris Paribus assumption generates into the economic modeling. To generate this relaxation of a large number of variables in any economic modeling, we suggest the application of multi-dimensional **coordinate** spaces that is offer by Econographication (Ruiz Estrada, 2007). The idea is to draw multidimensional graphs can help in the visualization all changes of several numbers of variables in the same graphical space. Additionally, the multidimensional graphs provide an alternative graphical approach to the Marshall view of step-by-step cumulative partial approach to the economic modeling. The main objective to apply multidimensional graphs is to visualize graphically all changes of the endogenous variable in response to the changes of several numbers of exogenous variables simultaneously. The multidimensional graphs can also be used to show the dynamic behavior of different variables in any economic model without any restriction. The application if the Omnia Mobilis assumption is to capture all possible economic actors and different possible scenarios into the same picture. Therefore, this chapter proposes that Ceteris Paribus assumption is not necessary to be used when economists have opportunity to use the Omnia Mobilis assumption and multidimensional graphs.

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Finally, the common **coordinate** system is created by seri- ation of the DAG. The resulting supergenome, i.e. linear order of the vertices of the graphs corresponds to a lin- ear order of all blocks. In particular, vertices resulting from a simplifier may contain more than one block. Those blocks, however, are already sorted and thus are inserted as a single block. Seriation is naturally divided into two steps. First, topological sorting is used to calculate an ini- tial linear ordering from the DAG. Kahn’s algorithm [40] is a classical solution to the topological sorting problem. For our purposes it is desirable that, if possible, two nodes v and w are placed consecutively whenever there is an edge (v, w) in the final DAG. To this end we modify Kahn’s algorithm by sorting the successors of a node in the order of evidence for their adjacency in the original data.

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The autopilot system is integrated in the aircraft as one of the systems to reduce the pilot workload, improve the dynamic stability of the aircraft as it performs its mission. This autopilot operates on longitudinal, lateral or directional axis and possesses autopilot modes such as the altitude hold, heading hold, roll angle hold, pitch angle hold, coordinated turn and it is embedded into the flight management system for trajectory, guidance and path following. Therefore, the dynamic stability for a light aircraft was investigated on the longitudinal and lateral directional **axes** as the main autopilot operating **axes** based on autopilot modes such as the altitude hold, heading hold, roll angle hold, pitch angle hold, coordinated turn with FMS guidance for trajectory and path following. The results showed that the aircraft is laterally and

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For species like Pistacia vera, which produce vo- luminous seeds, cryopreservation of zygotic embry- onic **axes** could be the answer: because they are much smaller than whole seeds, dozens of embryonic **axes** could be preserved in a single cryovial. Some articles have been published on the cryopreservation of iso- lated embryos of various woody species: Castania sativa, Carya sp., Juglans cinerea, J. nigra and J. regia (Pence 1990), Quercus suber and Q. ilex (Gonzalez- Benito et al. 2002). But, to our knowledge, no study has been reported on the cryopreservation of embry- onic **axes** of Pistacia species.

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Particularly, mast cells could orchestrate the inflammatory response inducing the expression of embryonic programs of tissue formation. Mast cells are derivatives of hematopoietic progenitor cells that migrate into virtually all vascularized tissues, where they complete their maturation. Upon activation their “ plasticity ” allows them greater flexibility and diversity in term of responsiveness to meet the requirements of the inflammatory response in which these cells are involved [155]. In this sense, activated mast cells can induce the expression of the proposed neurovascular **axes** of the inflam- mation. Thus, mast cells secrete numerous biogenic monoamines, i.e. histamine, sero- tonin, and nociceptive molecules that can sensitize sensory neurons which further activate mast cells by releasing neurotransmitter or neuropeptides, i.e. acetylcholine, neurotensin, substance P and somatostatin [157,158]. Mast cells are also the source of many biologically active mediators involved in the process of neovascularization [155,159]. Mast cells are topographically associated with microvessels and their number rises in angiogenesis-dependent events such as inflammation [159,160]. The role of mast cells in angiogenesis is mediated by the release of their stored substances to a variety of stimuli [155,160,161]. Mast cell mediators include histamine, chymases, cyto- kine and growth factors like PDGF and VEGF, all of which exhibit pro-angiogenic properties [159-162]. In addition, post-traumatic inflammation is a strong pro-hemato- poietic stimulus. Mast cells are one of the cells that produce pro-inflammatory pleio- tropic mediators that induce hematopoiesis [163]. Hematopoietic stem cells, in turn, give rise to a hierarchically organized set of progenitors for erythroid, myeloid, lym- phoid and megakaryocyte lineages [36]. Particularly, neutrophils, monocyte/macro- phages and T cells from the bone marrow are always present in the interstitial connective tissue during inflammatory response progression [17,21]. Mast cells infil- trating injured tissues, through the release of granulocyte-macrophage colony stimulat- ing factor (GM-CSF), can act on the bone marrow requesting the inflammatory cells needed for repair. A polarized hematopoietic axis from the bone marrow up to the mesenchymal interstitial space of the injured tissue would be established (Figure 10).

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then the contact between meshing sides of teeth is theoretically linear. Fulfilment of condition (1) is not however unconditionally necessary. A pair of hyperboloids created by rotation of axis o 12 gradu- ally around **axes** o 1 and o 2 can have also toothing with angles of declination β 1 ≠ θ 1 and β 2 ≠ θ 2 , but on condition that β 1 + β 2 = ∑ must be valid. In this case the axis o 12 will take a new position and for gear ratio of screw gearing, the equation is valid:

One of the main components that affect the accuracy of the measurement are errors of the ki- nematic system of the machine on which the mea- surement were carried out. First models of kine- matic errors for **coordinate** measuring machines (CMMs) were created and implemented in practice in 1970’s [1], however, first attempts of eliminat- ing the machine tools geometric errors were made at the second half of XIX century [2, 3]. Nowa- days, in the era of costs minimization the majority of measuring and machining devices are equipped with geometric errors software correction sys- tems because it is more profitable to produce parts (which built kinematic system of machine) that are more distant from ideal geometry and then compensate geometric errors influenced by these faults, rather than to produce expensive parts with very narrow shape and dimension tolerances.

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Gravimetric and geometric measurements were carried out at one million cycle intervals. At each measurement interval, the components were removed from the simulators and cleaned in accordance with a standard operating procedure. The gravimetric wear was determined using a microbalance (Mettler Toledo XP205 analytical balance, Greifensee, Switzerland), which had a readability of 0.01 mg. The change in mass was converted to volumetric wear using a density of 4.37 × 10 − 3 g/mm 3 for BIOLOX ® delta. The geometric measurements were carried out using a **coordinate** measurement machine (Legex 322, Mitutoyo, Japan). Redlux software (Southampton, UK) was used to construct a three-dimensional map of the acetabular cup and femoral head surfaces. Mean values and 95% confidence limits were determined, and two way ANOVA was used for statistical analysis of the wear rates (two variables of inclination angle and number of rotation **axes**) with significance levels taken at p < 0.05.

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