Positive Y-axis Research Articles

Extended Fitts' Law for Three-Dimensional Environment

This study explored an extended three-dimensional Fitts' law that is more suited for the pointing task than the conventional Fitts' law. The experiments were conducted under the manipulation of the distance to the target, size of the target, and direction of the target's location that can be described by two angles, ?1 and ?2. Considering the starting point as the center of coordinates, ?1 is the angle between the positive z-axis and the target location and ?2 is the angle between the positive y-axis and the projected target location on the x-y plane. From the experimental results, we confirmed that all four variables significantly affect the movement time. As we extended the index of difficulty of the conventional Fitts' model by incorporating ?1 and ?2, we established an extended Fitts' model that showed better accordance with the empirical data than the conventional Fitts' model and 3D Fitts' law of Murata and Iwase, in terms of the r² and the standard error of the residual between the measured movement time and the predicted value.

Extended Fitts' law in Three-Dimensional Pointing Tasks

This study explored an extended three-dimensional Fitts' law that is more suited for the pointing task than the conventional Fitts' law. The experiments were conducted under the manipulation of the distance to the target, size of the target, and direction of the target's location that can be described by two angles, θ 1 and θ 2. Considering the starting point as the center of coordinates, θ 1 is the angle between the positive z-axis and the target location and θ 2 is the angle between the positive y-axis and the projected target location on the x-y plane. From the experimental results, we confirmed that all four variables significantly affect the movement time. As we extended the index of difficulty of the conventional Fitts' model by incorporating θ 1 and θ 2, we established an extended Fitt's model that showed better accordance with the empirical data than the conventional Fitts' model, in terms of the r2 and the standard error of the residual between the measured movement time and the predicted value.

Second class particles and cube root asymptotics for Hammersley’s process

We show that, for a stationary version of Hammersley’s process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly North–East path L(t,t) from (0,0) to (t,t) is equal to $2\mathbb{E}(t-X(t))_{+}$, where X(t) is the location of a second class particle at time t. This implies that both $\mathbb{E}(t-X(t))_{+}$ and the variance of L(t,t) are of order t2/3. Proofs are based on the relation between the flux and the path of a second class particle, continuing the approach of Cator and Groeneboom [Ann. Probab. 33 (2005) 879–903].

First-principles study of lithium adsorption on Si(1 0 0)2 × 1 and Ge(1 0 0)2 × 1 surface at 1.0 monolayer coverage

First-principles calculations based on density functional theory have been carried out to determine the atomic structure and electronic properties of the Si(1 0 0)2 × 1–Li and Ge(1 0 0)2 × 1–Li adsorption systems at 1.0 monolayer (ML) coverage. For the Si(1 0 0)2 × 1–Li chemisorption system, the lowest energetic configuration is that one Li atom resides at the T3′ (which is displaced along the positive y-axis from the valley bridge (T3) site by 0.90 Å) and the other resides at pedestal (HH) site. For the Ge(1 0 0)2 × 1–Li chemisorption system, the most stable configuration is found to be that one Li atom resides at HH site and the other one will penetrate deeply into the substrate surface. Chemisorption of the lithium atoms is found to result in a minimum energy configuration characterized by symmetric dimers in agreement with the results of high-resolution core-level photoelectron spectroscopy. The adsorption systems show semiconducting surface characterization.

Hammersley’s process with sources and sinks

We show that, for a stationary version of Hammersley’s process, with Poisson “sources” on the positive x-axis, and Poisson “sinks” on the positive y-axis, an isolated second-class particle, located at the origin at time zero, moves asymptotically, with probability 1, along the characteristic of a conservation equation for Hammersley’s process. This allows us to show that Hammersley’s process without sinks or sources, as defined by Aldous and Diaconis [Probab. Theory Related Fields 10 (1995) 199–213] converges locally in distribution to a Poisson process, a result first proved in Aldous and Diaconis (1995) by using the ergodic decomposition theorem and a construction of Hammersley’s process as a one-dimensional point process, developing as a function of (continuous) time on the whole real line. As a corollary we get the result that EL(t,t)/t converges to 2, as t→∞, where L(t,t) is the length of a longest North-East path from (0,0) to (t,t). The proofs of these facts need neither the ergodic decomposition theorem nor the subadditive ergodic theorem. We also prove a version of Burke’s theorem for the stationary process with sources and sinks and briefly discuss the relation of these results with the theory of longest increasing subsequences of random permutations.

The accuracy of estimating proximal tibial translation during natural cadence walking: bone vs. skin mounted targets

Objective. To assess the efficacy of estimating proximal tibial translation using video-based motion capture and an array of surface-mounted targets ideal for tracking motion of the tibia. Design. Superficial and bone-anchored tracking targets were used to create two independent sets of data locating the proximal tibia in a global coordinate system. Background. Knowledge of the effect that soft tissue movement has on estimates of proximal tibial translation has not been reported to date. This basic information is necessary to establish construct validity for any study proposing to document tibial translation using standard video-based motion capture methods. Methods. A six camera motion capture system was used to collect surface-mounted and bone-anchored data for seven healthy adult subjects walking at a self-selected speed. The subjects walked along the positive Y-axis of the global reference system, with the positive Z-axis oriented vertically. Results. Average peak differences in the location of the proximal tibia calculated from the bone and surface-mounted targets were 7.1, 3.7 and 2.1 mm along the X, Y and Z axes of the global coordinate system respectively. Individual subject peak differences were as large as 14.1, 11.8 and 8.3 mm along the X, Y and Z axes. Conclusions. Estimates of tibial translation with a measurement resolution better than 3 mm are not likely using standard motion capture methods and tracking targets attached superficially to the lower leg. Relevance The results of this study clearly depict the considerable effect that soft tissue motion of the lower leg has on estimates of proximal tibial translation. Without consideration for the difficulties in measuring femoral, or patellar motion, we believe it is not feasible to routinely obtain sufficiently accurate estimates of detailed knee joint translations using superficial tracking target attachment methods.

Correlation and quantification of projected 2-dimensional radiographic images with actual 3-dimensional y-axis vertebral rotations

Background: Historically, measurement of 2-dimensional (2-D) radiographic images on the anteroposterior radiograph has been made to assess 3-dimensional (3-D) y-axis vertebral rotations. Objectives: To correlate and quantify measurements of the projected 2-D radiographic image with the degree of 3-D y-axis rotation. Study design: A computer model was positioned in a simulated x-ray beam. Points of model contact with the simulated beam were projected onto a line in the neutral position and the first 7 degrees of both positive and negative y-axis rotation using two different axes of rotation. A larger model, a shape-altered model, and a decreased source-object-distance model were also studied. Results: 3-D y-axis rotation of vertebrae causes an off-center displacement of the 2-D projected lamina junction in relation to the projected vertebral body. The magnitude of displacement increases with increasing degrees of rotation. In our model, no clinically significant difference was found in the amount of the projected off-center displacement of the lamina junction between either of our two chosen axes of rotation. However, significant differences in the projected offset were found between vertebrae with the same degree of rotation as a result of changes in vertebral shape, size, and positioning. The projected lamina junction offcentering at a given rotation is quantified for our model. Conclusion: Use of millimetric measurement of the projected lamina offset on the anteroposterior radiograph is an inaccurate method for the assessment of the degree of 3-D y-axis vertebral rotation. (J Manipulative Physiol Ther 1999;22:21–5)

Kinetics of static strain aging in polycrystalline NiAl-based alloys

The kinetics of yield point return have been studied in two NiAl-based alloys as a function of aging time at temperatures between 300 and 700 K. The results indicate that the upper yield stress increment, Delta sigma(sub u) (i.e., stress difference between the upper yield point and the final flow stress achieved during prestraining), in conventional purity (CP-NiAl) and in high purity carbon-doped (NiAl-C) material first increased with a t(exp 2/3) relationship before reaching a plateau. This behavior suggests that a Cottrell locking mechanism is the cause for yield points in NiAl. In addition, positive y-axis intercepts were observed in plots of Delta sigma(sub u) versus t(exp 2/3) suggesting the operation of a Snoek mechanism. Analysis according to the Cottrell Bilby model of atmosphere formation around dislocations yields an activation energy for yield point return in the range 70 to 76 kJ/mol which is comparable to the activation energy for diffusion of interstitial impurities in bcc metals. It is, thus, concluded that the kinetics of static strain aging in NiAl are controlled by the locking of dislocations by Cottrell atmospheres of carbon atoms around dislocations.

Initiation of folding and boudinage in wrench shear and transpression

A linear stability analysis is performed on a deforming layered three-dimensional linear viscous system. The system consists of a single layer of viscosity μ embedded in a medium of viscosity μ′. The layer is oriented normal to the z-axis and both the layer and medium are subjected to uniform simple shearing parallel to the y-axis (wrench shear) with superposed uniform shortening parallel to x and extension parallel to z (transpression). The stability of cylindrical perturbations of the form ζ = A ( t) cos ( ax − βy) is examined. It is found that fold-type perturbations are unstable and pinch-and-swell disturbances are unstable in some cases. For the case of wrench shear alone the fastest growing buckling disturbances are oriented at 45° to the positive y-axis, while the fastest growing pinch-and-swell disturbances have positive growth rates and are oriented 90° to the fold axes. Additional shortening parallel to the x-axis (transpression) causes the fold axes to initiate at lower angles to the y-axis. Pinch-and-swell disturbances may or may not be unstable in transpression depending on the magnitude of stretching parallel to the z-axis.

Taxicab Geometry—A New Slant

As anyone who has played with a bit of screen wire knows, a square is not a rigid geometrical figure. A slight push to the right or left will deform a square into a nonsquare rhombus. If such a transformation is performed on the points of a plane which has been coordinatized by a square grid so that the positive y-axis makes an angle of 600 with the positive x-axis and the shorter diagonals of each rhombus are drawn, an isometric grid results. Points will still be named by ordered pairs of real numbers with respect to the x-axis and the transformed y-axis (FIGURE la). There are only three regular polygons which will tessellate the plane: the equilateral triangle, the square, and the regular hexagon. The first two of these can be subdivided into smaller similar polygons (yielding the isometric grid and the square grid). Work has already been done on taxicab geometry using the square grid; this note considers taxicab geometry using the isometric grid. Square-taxi geometry arises because, for the two points A = (xi, Y1) and B = (x2, Y2), a new distance function is chosen:

Pristane, Phytane, and Lower Molecular Weight Isoprenoid Distributions in Oils

Phytane in oils is assumed to be mainly a diagenetic product of the phytol side-chain of the ubiquitous plant pigment, chlorophyll. Pristane may be derived from several sources in addition to phytol. Isoprenoids containing fewer than 19 carbons are rare in the biomass and consequently are derivatives of pristane, phytane, or higher molecular weight compounds. The interdependence of phytane and isoprenoids containing less than 20 carbons is considered in this study. The relationships of pristane to phytane, and pristane and phytane to lower molecular weight isoprenoids, are linear. The lines of best fit commonly possess a positive intercept on the dependent variable axes (pristane and lower molecular weight isoprenoids). The positive y-axis intercept suggests that a fraction of pristane and a fraction of lower molecular weight isoprenoids cannot be attributed to chlorophyll (phytol) diagenesis. This observation supports the conclusion that some amount of the nonphytane isoprenoid assemblage must be attributed to a higher molecular weight parent compound(s) whose identity can only be suggested. Isoprenoid ratios and distributions have been useful in geochemical correlations (oil-oil). However, the correlation value of these hydrocarbons should be viewed critically because of the partial interdependence of phytane and lower molecular weight isoprenoids.

Effect of dose increments on serum carbamazepine concentration in epileptic patients.

The effect of progressive dose increments on the steady-state serum concentration of carbamazepine has been investigated prospectively in 20 adult institutionalised epileptic patients receiving long term therapy with the drug. In all but 1 subject, a strong positive correlation between the serum carbamazepine concentration and the prescribed daily dose was found. The relationship appeared to be linear over the dosage range examined (600 to 1400mg in most patients). In some patients, a trend was observed for the extrapolated regression lines to yield positive y-axis intercepts. The latter were significantly different from zero in 3 patients. Although these findings suggest that the relationship between serum carbamazepine concentration and dose may be curvilinear over the lower range of doses, further studies are required to clarify this point.

On a forward-backward parabolic equation

Boundary value problems for the equation $$\operatorname{sgn} (x) \cdot u_y - u_{xx} + ku = f(x,y)$$ (where k is a positive constant and † is a given function) are investigated. The domain of the solutions will be the whole upper half-plane y>0, or the half-plane y>0 cut along the positive y-axis. We are interested in square integrable solutions u, with square integrable generalized derivatives uy and uxx. Existence theorems are proved, with an integral equations technique. Thus a theory is developed of Wiener-Hopf integral equations of the first kind with solutions belonging to Sobolev spaces.

On Montel’s Theorem

In this note we shall prove a theorem which is related to Montel’s theorem [1] on bounded regular functions. Let E be a measurable set on the positive y-axis in the z( = x + iy)-plane, E(a, b) be its part contained in 0 ≦ a ≦ y ≦ b, and ∣E(a, b)∣ be its measure. We define the lower density of E at y = 0 byLEMMA, Let E be a set of positive lower density λ at y = 0. Then E contains a subset E1 of the same lower density at y = 0 such that E1 ∪ {0} is a closed set.

Carathéodory measure and a generalization of the Gauss-Green lemma

where s is the arc length of C and fi is the angle made by the external normal to C at a variable point of C, with the positive y-axis. Thus for the line integral to have a meaning it is necessary that C have length and consequently be defined by two functions x =(t), y =4(t) of bounded variation in t. 2. The applications of this lemma, through Green's theorem, are numerous. Consequently many investigations have been concerned with the types of regions and boundaries for which the lemma is valid. In most cases it has been deemed inherent in such a relation that the boundary be a curve, i.e., that an order relation be known among the points of the boundary. However, attacking the problem by radically different methods, J. P. Schauder$ obtained results for a class of boundaries with no order relation prescribed.True, the only boundaries shown by Schauder to be admissible are those represented by two functions each satisfying the Lipschitz conditions, thus indirectly again introducing order and also a condition more restricting than that of bounded variation. Also Schauder assumed that all points of the boundary of the second class? project on the x-axis in a set of Lebesgue measure zero. Thus so simple a region as all points of the unit circle except the points 0 ? x < 1 of the x-axis does not satisfy his conditions.