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Location of centers of rigidity (CR) in a confined masonry building is sensitive to the aspect ratio of constituting walls and wall-piers (in case of wall with openings). These centers, generally, do not lie on one vertical line. In contrast, the mass centers (MC) are nearly vertically aligned for a regular confined masonry building. Assuming an average vertical line for the CRs (elastic axis), this paper first presents a simplified framework to arrive at the design force resultants for the force-based seismic design. The framework uses a set of 2D Finite Element (FE) analyses (that can be performed using any commercial software) and some nominal spread sheet calculations. Case study on a recently constructed confined masonry building at Indian Institute of Technology Gandhinagar (India) campus is considered for the purpose of illustration. This framework leads to the design member force resultants close to that calculated using a detailed 3D FE analysis. Next, the framework is converted into a Back-of-the-Envelope method that does not require any FE analysis and yet leads to the member force resultants acceptable for all practical purposes. This is particularly suitable for routine seismic design, especially at the preliminary stage, provided none of the constituting walls comprises of a squat wall-pier.

Let $G$ be a finite simple graph. For $X \subset V(G)$, the difference of $X$, $d(X) := |X| - |N (X)|$ where $N(X)$ is the neighborhood of $X$ and $\max \, \{d(X):X\subset V(G)\}$ is called the critical difference of $G$. $X$ is called a critical set if $d(X)$ equals the critical difference and ker$(G)$ is the intersection of all critical sets. It is known that ker$(G)$ is an independent (vertex) set of $G$. diadem$(G)$ is the union of all critical independent sets. An independent set $S$ is an inclusion minimal set with $d(S) > 0$ if no proper subset of $S$ has positive difference. A graph $G$ is called K\"onig-Egerv\'ary if the sum of its independence number ($\alpha (G)$) and matching number ($\mu (G)$) equals $|V(G)|$. It is known that bipartite graphs are K\"onig-Egerv\'ary. In this paper, we study independent sets with positive difference for which every proper subset has a smaller difference and prove a result conjectured by Levit and Mandrescu in 2013. The conjecture states that for any graph, the number of inclusion minimal sets $S$ with $d(S) > 0$ is at least the critical difference of the graph. We also give a short proof of the inequality $|$ker$(G)| + |$diadem$(G)| \le 2\alpha (G)$ (proved by Short in 2016). A characterization of unicyclic non-K\"onig-Egerv\'ary graphs is also presented and a conjecture which states that for such a graph $G$, the critical difference equals $\alpha (G) - \mu (G)$, is proved. We also make an observation about ker$G)$ using Edmonds-Gallai Structure Theorem as a concluding remark., Comment: 18 pages, 2 figures

Vertical line extensions are a valuable growth strategy for many retail service sectors. Correctly positioning a new vertical line extension in the price/quality spectrum is an important decision that has considerable implications for bottom line profits. This paper examines the moderating role of extension direction on the effect of perceived consistency on vertical extension evaluations. In two studies, we show that a lack of perceived consistency acts as a reminder to consumers that the brand may be stretching beyond its expertise, increasing perceived performance and financial risks for upscale extensions but not for downscale extensions. As a consequence, higher consistency results in higher upscale extension favourability whereas evaluations of downscale extensions are similar regardless of their perceived consistency with the parent brand.

This study investigates changes in the total factor productivity (TFP) and identifies the main sources of TFP growth following the adoption of an individual fishing quota (IFQ) program in the Gulf of Mexico red snapper commercial fishery. Utilizing an unbalanced panel of 722 vertical line vessels Malmquist indices were derived from an output-oriented stochastic distance frontier. The analysis shows that the IFQ program had a positive impact on the productivity of the fleet and that most of the productivity gains were due to improvements in technical efficiency. The study also finds that changes in technical efficiency were time variant suggesting that the exit of the less efficient vessels and easing of command and control regulations such as trip limits and short fishing seasons were responsible for most of these gains. Changes in the exploitable biomass of red snapper were found to have a moderate impact on productivity growth whereas the impact of technological progress was minimal.

International audience; The evolution of languages shares certain characteristics with that of genes, such as the predominantly vertical line of transmission and the retention of traces of past events such as contact. Thus, studies of language phylogenies and their correlations with genetic phylogenies can enrich our understanding of human prehistory, while insights gained from genetic studies of past population contact can help shed light on the processes underlying language contact and change. As demonstrated by recent research, these evolutionary processes are more complex than simple models of gene-language coevolution predict, with linguistic boundaries only occasionally functioning as barriers to gene flow. More frequently, admixture takes place irrespective of linguistic differences, but with a detectable impact of contact-induced changes in the languages concerned.

This paper considers to the equation [\int_{S} \frac{U(Q)}{|P-Q|^{N-1}} dS(Q) = F(P), P \in S,] where the surface S is the graph of a Lipschitz function \phi on R^N, which has a small Lipschitz constant. The integral in the left-hand side is the single layer potential corresponding to the Laplacian in R^{N+1}. Let \Lambda(r) be a Lipschitz constant of \phi on the ball centered at the origin with radius 2r. Our analysis is carried out in local L^p-spaces and local Sobolev spaces, where 1 < p < \infty, and results are presented in terms of \Lambda(r). Estimates of solutions to the equation are provided, which can be used to obtain knowledge about the behaviour of the solutions near a point on the surface. The estimates are given in terms of seminorms. Solutions are also shown to be unique if they are subject to certain growth conditions. Local estimates are provided and some applications are supplied.

The purpose of this study was to examine graph comprehension in college students with developmental dyslexia. We investigated how graph types (line, vertical bar, and horizontal bar graphs), graphic patterns (single and double graphic patterns), and question types (point locating and comparison questions) differentially affect graph comprehension of students with and without dyslexia. Groups were compared for (1) reaction times for answering comprehension questions based on graphed data and (2) eye gaze times for specific graph subregions (x-axis, y-axis, pattern, legend, question, and answer). Dyslexic readers were significantly slower in their graph comprehension than their peers with group differences becoming more robust with the increasing complexity of graphs and tasks. In addition, dyslexic readers' initial eye gaze viewing times for linguistic subregions (question and answer) and total viewing times for both linguistic (question and answer) and nonlinguistic (pattern) subregions were significantly longer than their control peers' times. In spite of using elementary-level paragraphs for comprehension and simple graph forms, young adults with dyslexia needed more time to process linguistic and nonlinguistic stimuli. These findings are discussed relative to theories proposed to address fundamental processing deficits in individuals with dyslexia.

Background Normal adults demonstrate a slight upward bias (vertical pseudoneglect) when attempting vertical line bisection. The mechanism for this bias is unknown. Activation of the allocentric (object-centered) ventral visual system during attempted bisection may induce this bias. This object-centered ventral stream may also mediate focal attention. As compared to bisection, when normal participants perform a vertical line quadrisection task that requires more focal attention, they may have a greater upward bias. Methods Sixteen participants bisected and quadrisected vertical lines. Results The mean upward bias (deviation error) for the quadrisection tasks was significantly higher than the mean error for the line bisections. Conclusions These results are consistent with the hypothesis that activation of the ventral stream by a task that requires focal allocentric attention can induce an upward vertical bias that is greater than the upward bias observed with allocentric line bisection, a task that requires more global attention.

The 3 x 3 Maki-Nakagawa-Sakata-Pontecorvo (MNSP) lepton flavor mixing matrix may be slightly non-unitary if the three active neutrinos are coupled with sterile neutrinos. We show that it is in principle possible to test whether the relation vertical bar V-e1 vertical bar(2) + vertical bar Ve(2)vertical bar(2) + vertical bar Ve(3)vertical bar(2) = 1 holds or not in a precision reactor antineutrino oscillation experiment, such as the recently proposed Daya Bay II experiment. We explore three categories of non-unitary effects on the 3 x 3 MNSP matrix: 1) the indirect effect in the (3 + 3) flavor mixing scenario where the three heavy sterile neutrinos do not take part in neutrino oscillations; 2) the direct effect in the (3 + 1) scenario where the light sterile neutrino can oscillate into the active ones; and 3) the interplay of both of them in the (3 + 1 +2) scenario. We find that both the zero-distance effect and flavor mixing factors of different oscillation modes can be used to determine or constrain the sum of vertical bar Ve(1)vertical bar(2), vertical bar Ve(2)vertical bar(2) and vertical bar Ve(3)vertical bar(2) and its possible deviation from one, and the active neutrino mixing angles theta(12) and theta(13) can be cleanly extracted even in the presence of light or heavy sterile neutrinos. Some useful analytical results are obtained for each of the three scenarios. (C) 2012 Elsevier B.V. All rights reserved.

Let A be any n×n array on the symbols [n]={1,…,n}, with at most m symbols in each cell. An n×n Latin square L on the symbols [n] is said to avoid A if no entry in L is present in the corresponding cell of A, and A is said to be avoidable if such a Latin square L exists. The intricacy of this problem is defined to be the minimum number of arrays into which A must be split in order to ensure that each part is avoidable. We present lower and upper bounds for the intricacy, and conjecture that the lower bound is in fact the correct answer.

In this paper we consider the Cauchy problem for the integrable Novikov equation. By using the Littlewood-Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for the integrable Novikov equation is locally well-posed in the Besov space B-p.r(s), with 1 max{1 + 1/p, 3/2} In particular, when u(0) is an element of B-p.r(s) boolean AND H-l with 1 max{1 + 1/p, 3/2}, for all t is an element of [0, T], we have that vertical bar vertical bar u(t)vertical bar vertical bar H-l = vertical bar vertical bar u(0)vertical bar vertical bar(H)l. We also prove that the local well-posedness of the Cauchy problem for the Novikov equation fails in B-2.(3/2)(infinity). (C) 2012 Elsevier Inc. All rights reserved.

The locus of reduced bad zero-schemes, B0⊂X[b0], for a linear system |V| on a non singular, n-dimensional, algebraic variety X is defined. The pairs (X,V) for which B0 has the maximal dimension, nb0−1, are characterized. For n=2, non-reduced bad zero-schemes are also discussed.

By means of the Z(2) index, we study the geometrical property of the global attractor for a class of symmetric p-Laplacian equations u(t) - div(vertical bar del u vertical bar(p-2)del u) + vertical bar u vertical bar(r-2)u - lambda vertical bar u vertical bar(s-2)u + f(x.u) = 0, where lambda > 0, 2

We investigate the problem introduced by Baeza-Yates et al. [R.A. Baeza-Yates, J.C. Culberson, G.J.E. Rawlins, Searching with uncertainty, Research report, University of Waterloo, 1987]: given a plane and a horizontal or a vertical line in unknown location give a strategy to find this line. We use a competitive analysis to measure the performance of this strategy. This problem is one of the first generalisations of the cow search problem.

The quantitative relationship between exposure to physical risk factors and upper extremity work-related musculoskeletal disorders (UE-WMSDs) is virtually unknown. To explore the variation, objective measurements were derived in 43 types of work (686 individuals), using goniometry for the wrists and electromyography (EMG) for the forearm extensor muscles. The variations due to work were great for wrist movements, wrist positions, muscular rest, as well as peak load, ranging 1.4-54 degrees/s (flexion velocity; 50th percentile), -30 degrees-3 degrees (flexion angle; 50th percentile), 0.2-23% of time, and 3.4-41% of maximal EMG (90th percentile), respectively. Even within work categories, e.g. "repetitive industrial", there were large variations for all measures. Hence, classification without measurements has limited value. All movement measures were highly correlated (vertical bar r(s)vertical bar=0.82-0.99), but only weakly so to positions (vertical bar r(s)vertical bar = 0.01-0.43). Muscular rest and "static load" (10th percentile), were highly correlated (r(s) = -0.92), but not associated to peak load (90th percentile; vertical bar r(s)vertical bar= 0.05 and 0.08, respectively). Most low-velocity work was accompanied by much muscular rest; however, the low velocity for mouse-intensive computer-work meant very little rest. Technical measurements are suitable as exposure measures in epidemiological studies, as well as a base for decisions about interventions. The multidimensional character of exposure - wrist movements, wrist postures, muscular recovery, and peak load - has to be considered. Relevance to industry: Direct measurements provide objective and quantitative measures of the main physical risk factors for UE-WMSDs, appropriate for estimating the risk, as well as giving priority to, and evaluating, interventions. (c) 2008 Elsevier B.V. All rights reserved. (Less)

SummaryAnts are so low to the ground that slight undulations in the terrain over which they navigate will cause large and unpredictable changes to their view of the scene around them. We describe here evidence of a form of motor learning that helps ants follow their usual route when guiding landmarks vanish from sight. Wood ants were trained to approach a vertical bar presented at varying positions on a LCD screen. In different experiments, the bar was either stationary, moved smoothly, or jumped between two stationary positions. Ants trained in these three ways followed straight, curved, or two-leg routes, respectively. Once ants were accustomed to approaching the bar from different starting points, the bar was made to disappear during their approach. Ants often continued their straight or curved or two-leg paths, despite the missing landmark, showing that they can perform complex routes with no more than intermittent visual feedback.

Vertical line extensions extend an established brand to products at different price/quality points. In this study, we examine consumer evaluations of vertical service line extensions and the feedback effects of these extensions on the parent brand. Findings of two empirical studies in the hotel industry indicate that consumers perceive higher risks in step-up extensions than in step-down extensions, which consequently influences their evaluations of the extensions. This effect of extension direction is also found to be moderated by risk relievers such as service guarantee and consumers’ prior knowledge in the service category. Furthermore, we found that a parent brand receives more positive evaluations after the introduction of a step-up extension than that of a step-down extension.

We consider a pseudomonotone operator, the model of which is -div(b(x, u)vertical bar del u vertical bar(p-2)del u) with 1 2. Full detailed proofs are given in the present Note. The results continue to hold when Omega is unbounded.

We consider the nonlinear Schrodinger equation associated to a singular potential of the form a vertical bar u vertical bar(-(1-m))u + bu, for some In is an element of (0, 1), on a possible unbounded domain. We use some suitable energy methods to prove that if Re(a) + Im(a) > 0 and if the initial and right hand side data have compact support then any possible solution must also have a compact support for any t > 0. This property contrasts with the behavior of solutions associated to regular potentials (m >= 1). Related results are proved also for the associated stationary problem and for self-similar Solution on the whole space and potential a vertical bar u vertical bar(-(1-m)u). The existence of solutions is obtained by some compactness methods under additional conditions.

We study a class of geometric stabbing/covering problems for sets of line segments, rays and lines in the plane. While we demonstrate that the problems on sets of horizontal/vertical line segments are NP-complete, we show that versions involving (parallel) rays or lines are polynomially solvable.

Thresholds for detecting the angle of rotation of vertical symmetrical patterns containing few or no explicit vertical or horizontal contours were found to be almost as low as those for an actual vertical line extending approximately the same range. This hyperacuity performance, which we refer to as implicit orientation discrimination, shares most of its properties with the orientation discrimination of explicit lines, suggesting a category of orientation processing whose neural mechanisms are related to those involved in the processing of straight contours and those underlying the detection of axes of symmetry. Strong binding effects between the components of the figures were demonstrated and their temporal interactions were also investigated. Our results have implications for possible neural interactions early in the cortical visual stream. © 1997 Elsevier Science Ltd. All rights reserved

We prove that, for two fixed integers m and n , the study of the tileability of a torus with h m (the horizontal bar of length m and width 1) and v n (the vertical bar of length n and width 1) can be limited to study of a finite number of cases.

By analyzing the history of traditional Phillips curves, this paper criticizes that the nonlinear characteristics have been ignored on the Phillips curve studies. Based on the Chinese annual data during 1979-2005, the paper does an empiricl analysis by creating a long-run Phillips curve. The paper leads with four results as follows: First, the long-run Phillips curve can be a special rational function with the characteristics of hyperbola. Second, the model can explain why the long-run Phillips curve may occupy a negative slope, positive slope or be a parele line, vertical line. Third, the paper finds that the China’s long-run Phillips curve fluctuates periodically aroud the coordinate in an anticlockwise direction. Final, the paper achieves that the threshold of China’s economic overheating at the point of the real GDP growth rate is 10.94% and the threshold of serious inflation at the point of cpi is 7.44%.

In MD-Cartesian space (see Ruiz, 2005) consists of five axes ([X1, X2, X3, X4], Y), representing four independent variables "X1", "X2", "X3" and "X4" and one dependent variable "Y" respectively. Each "X" variable (X1, X2, X3, X4) and "Y" variable has its individual axis that is a vertical line with both positive and negative values. The positive and negative values are represented by ([(X1,-X1), (X2,-X2), (X3,-X3) (X4,-X4)], (Y,-Y)] on the MD-Cartesian plane (see Table 1). In the case of 2-D and 3-D Cartesian plane (see Figure 1), the individual variables can be anywhere along the vertical and horizontal axes; but in the case of MD-Cartesian space all variables (Xi) and the "Y" variable are either on the positive side of respective axes together on the negative side of their respective axes together. In other words, the values of all "Xi" (X1, X2, X3, X4) and "Y" can change in different directions. Therefore, any change in some or all "Xi" will affect "Y" directly. Representing the dependent variable, the fifth axis, "Y" is positioned in the center of the Graph (among the other four axes). "Y" has a positive value and negative value. It is the convergent point of all the other four axes X1, X2, X3 and X4. In other words, all "Xi" axes converge at the "Y" axis. The result is a graph represented by a plane that can be reshaped into two cubes or one cube.

I thank Dr. D. F. Rucker for his comment (Rucker, 2012) on our paper (Zhu and Feng, 2011) about how to get Eq. (4) calculating normal potential at point P (xp, yp, zp) in an electric field generated by vertical line current source A. The essential criticism he gives concerning our work is that we started from an incorrect equation in the development of Eq. (4). After I checked it carefully again and again, I have to accept the fact that the starting equation used in our paper is incorrect. Now I made some revisions listed as follows. Eq. (1) in our paper should be replaced by

Two experiments measured line-dot alignment errors to either a long (2 deg 6 min) or short (12.7 min) oblique test line which was presented either in isolation or abutting a vertical inducing line. Alignment PSE's were obtained for a variety of line-dot separations at both the free end and at the intersect end of the test line, using a multiple randomly interleaved staircase technique. A number of aspects of the data were inconsistent with the hypothesis that alignment errors reflect whole-of-line changes in perceived orientation or intercept when the inducing line is present. Rather, the results were consistent with the notion that long lines are processed by integrating the outputs of analysers which respond to short line segments and that alignment errors reflect the differential weighting given to such analysers, depending upon the distance between the dot and the relevant segment of the line. An alternate hypothesis involving “cognitive mistracking” (Tong and Weintraub, 1974) could not be excluded by the results.