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Convexity is discussed for several free boundary value problems in exterior domains that are generally formulated as Δ u = f ( u ) in Ω ∖ D , | ∇ u | = g on ∂ Ω , u ≥ 0 in R n , \begin{equation*} \Delta u = f(u) \ \text {in } \Omega \setminus D, \quad |\nabla u | = g \ \text { on } \ \partial \Omega , \quad u\geq 0 \ \text { in } \ \mathbb {R}^n, \end{equation*} where u u is assumed to be continuous in R n \mathbb {R}^n , Ω = { u > 0 } \Omega = \{u > 0\} (is unknown), u = 1 u=1 on ∂ D \partial D , and D D is a bounded domain in R n \mathbb {R}^n ( n ≥ 2 n\geq 2 ). Here g = g ( x ) g= g(x) is a given smooth function that is either strictly positive (Bernoulli-type) or identically zero (obstacle type). Properties for f f will be spelled out in exact terms in the text. The interest is in the particular case where D D is star-shaped or convex. The focus is on the case where f ( u ) f(u) lacks monotonicity, so that the recently developed tool of quasiconvex rearrangement is not applicable directly. Nevertheless, such quasiconvexity is used in a slightly different manner, and in combination with scaling and asymptotic expansion of solutions at regular points. The latter heavily relies on the regularity theory of free boundaries. Also, convexity for several systems of equations in a general framework is discussed, and some ideas along with several open problems are presented.

We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensional set of pairs of badly approximable numbers on a vertical line. We also prove a uniform assertion of this nature, generalising a strong form of a result by Haynes, Jensen and Kristensen. Finally, we establish a similar result involving inhomogeneously badly approximable numbers, making progress towards a problem posed by Pollington, Velani, Zafeiropoulos and Zorin., This generalises the previous version

Purpose The purpose of this study is to assess the extent to which gender impacts the evaluation of vertical line extensions of luxury brands in a cross-national context. The topic of brand/line extensions has been investigated in the mainstream branding literature. On the other hand, the topic has received less attention in the luxury literature. At the same time, while research has examined brand/line extensions from an international perspective, the impact of gender on consumer purchase intentions of luxury downward line extensions in different countries has remained unexplored. Design/methodology/approach Based on an ANOVA design (2 extension types × 2 genders × 2 countries). The independent variables were ordered as follows: gender (male/female), vertical line extensions (upscale/downward) and country of living (France/USA). The purchase intention of the extension was chosen as the dependent variable. Findings The study results show that key differences exist between men and women regarding vertical luxury line extensions. For instance, women in both countries rate a new downward line extension of a luxury brand more positively than men. In contrast, although women evaluate a new upscale line extension of a luxury brand similarly to men in France, women are more positive than men in the USA. Also, US men rate an upscale extension less positively than their French counterparts. Finally, women in both countries rate luxury downward extensions more positively than men. Originality/value This study contributes to the literature of luxury brand management by examining how gender types process and respond to upscale and downward luxury line extensions versus purchase intentions in two different countries. This paper is unique as gender types are not often compared in previous research while fundamental distinctions exist, leading to significant differences. Practically, this study also provides key insights for marketing strategy development and adjustment for luxury manufacturers in terms of their target market, more specifically men versus women.

Vertical line source irrigation (VLSI) is an underground irrigation method suitable for deep-rooted plants. Understanding the characteristics of the soil wetting body of the VLSI was the key to designing this irrigation system. On the basis of experimental verification of the reliability of the HYDRUS simulation results of VLSI under the conditions of soil texture (ST), initial water content (θi), line source buried depth (B), line source diameter (D) and line source length (L), numerical studies of the migration law of the wetting front of VLSI and the distribution characteristics of soil moisture were performed. The wetting front migration (WFM) was mainly influenced by ST, θi, D and L (P < 0.05), while B had little effect on WFM (P > 0.05). The shape of the soil wetting body changed little under different influencing factors. The water content contour was approximately ‘ellipsoidal’ around the line source. The soil moisture near the line source was close to the saturated moisture content. The moisture content around the line source gradually decreased outward, and the contour lines gradually became dense. According to the simulation results, a prediction model of multiple factors influencing the migration process of the VLSI wetting front was established. The predicted value was in good agreement with the measured value. The results of this research could provide a theoretical basis for further optimizing the combination of VLSI and irrigation elements. HIGHLIGHTS Based on HYDRUS-2D, a multi-factor prediction model was established for the wet front migration process in vertical source irrigation.; The validity of the model was verified by experimental data, and the prediction effect was good.; Numerical studies of the migration law of the wetting front of the vertical line source irrigation and the distribution characteristics of soil moisture were performed.; The wetting front migration was mainly influenced by soil texture, initial water content, line source diameter and line source length (P < 0.05), while line source buried depth had little effect on it (P > 0.05).; The shapes of the contours of soil moisture content were slightly different, and were all approximate 'ellipsoids' with the axis of the line source.

An almost vertical line showing an increase of atmospheric CO2 emissions captures the urgency of a changing climate like no other line. Yet lines are also insufficient for grasping what might come ...

One important reason for offering customized products is to satisfy consumers’ need for product uniqueness. In this paper, we take consumers’ unique preferences into account to examine how firms make decisions on vertical line extensions with introducing a customized product. This study develops the consumer’s utility function, which captures consumers’ behavioural and emotional factors, and the results show that the high-quality firm always introduces an upward extension without uniqueness sensitivity. However, introducing a downward extension may be more profitable especially when consumers have the high unique ness sensitivity. We also find that the upward extension of the high-quality firm does not intensify competition with the low-quality firm, but its downward extension will intensify the competition between two firms, whether with or without unique preferences. We also analyse the low-quality firm’s extension decisions when it faces a high-end competitor and find that the low-quality firm may change from introducing a downward extension to introducing an upward extension when intrafirm quality differentiation is small.

The article is dedicated to analysis of the phenomenon typically referred to as “barbarism,” which remains in social and political practice to this day. The authors focus on so-called “vertical bar...

Purpose The purpose of this paper is to empirically assess the impact of branding strategies on horizontal and downward line extensions of French luxury brands in a cross-national context (France vs USA). Design/methodology/approach This study is based on a two line extensions (horizontal/downward) × three branding strategies (direct brand/sub-brand/standalone brand) x two country (France/USA) between-subjects ANOVA design. Findings The study shows that the subtyping effect created by a sub-branded luxury downward line extension tends to be rated similarly to a direct branded extension which oppose previous beliefs put forward in non-luxury settings. In contrast, a new independent/standalone extension fully uses the subtyping effect which helps attenuate this risk related to luxury downward stretches. The study also found that the effect of gender in cross-national settings must always be taken into consideration as significant variations occur in the process. Research limitations/implications The study covers two countries but should be replicated in other cross-national contexts. Practical implications This study helps marketing managers of luxury brands make a better decision when it comes to launching vertical line extensions (upscale/downward) by carefully using types of branding strategies and relevant communications whether women and/or men are targeted in cross-national contexts. Originality/value This study breaks new ground in the international luxury literature by providing key theoretical and managerial insights in terms of launching new downward line extensions with the proper use of branding strategies when targeting specific genders.

Essential tremor (ET) is a common movement disorder affecting the performance of various daily tasks, including drawing. While spiral-drawing task characteristics have been described among patients with ET, research about the significance of the drawing direction of both spiral and lines tasks on the performance process is scarce. This study mapped inter-group differences between people with ET and controls related to drawing directions and the intra-effect of the drawing directions on the tremor level among people with ET. Twenty participants with ET and eighteen without ET drew spirals and vertical and horizontal lines on a digitizer with an inking pen. Time-based outcome measures were gathered to address the effect of the drawing directions on tremor by analyzing various spiral sections and comparing vertical and horizontal lines. Significant group differences were found in deviation of the spiral radius from a filtered radius curve and in deviation of the distance curve from a filtered curve for both line types. Significant differences were found between defined horizontal and vertical spiral sections within each group and between both line types within the ET group. A significant correlation was found between spiral and vertical line deviations from filtered curve outcome measures. Achieving objective measures about the significance of drawing directions on actual performance may support the clinical evaluation of people with ET toward developing future intervention methods for improving their functional abilities.

The paper discusses the issue of political processes in Kosovo and Metohija in a comparative historical perspective. We consider the historical vertical line of processes that followed the political situation of the Serbian people in this area, as well as political processes and events that have marked the contemporary crisis in Kosovo.

We derive a new Sawyer's type sufficient condition for the fractional order Poincare inequality with weights (integral(Omega) vertical bar f(x) - (f) over bar (v,Omega)vertical bar(q) upsilon(x)dx) ...

PurposeCompanies often extend brands to higher or lower quality tiers to access different market segments. However, the impact of such extensions on the brand and its subsequent offerings is not yet conclusive. While some studies found an “averaging” pattern (all models contribute equally to the overall perception of the brand: a symmetric effect), others found a “best-of-brand” pattern (the positive impact of an upstream extension is much greater than the negative impact of a downstream extension: an asymmetric effect). This paper aims to reconcile these seemingly conflicting findings by assessing the conditions under which each pattern is likely to emerge.Design/methodology/approachThree experimental studies are presented to test the conditions under which a symmetric or asymmetric pattern of brand evaluation would merge. Study 1 examined the impact of judgment focus (quality vs expertise) on the pattern of brand evaluations. Study 2 tested the impact of having a comparative set on the assessment of specific brand dimensions. Study 3 examined the impact of the informativeness of price positioning on product quality expectations.FindingsBrand evaluations and attitudes are determined by the presence of a comparative brand and judgment focus. When brands are evaluated without a comparison, a symmetric pattern emerges, as a low-tier extension hurts a brand as much as a high-tier extension helps it. In contrast, when brands are evaluated with a comparison, focusing the assessment on quality leads to a symmetric pattern, while focusing it on expertise leads to an asymmetric one.Research limitations/implicationsThe present research specifies conditions under which a low-tier model may hurt brand perceptions. We used hypothetical brands to avoid the impact of preexisting attitudes. While we expect our results to generalize to real brands, this may be considered a limitation of the present research.Practical implicationsThe current research delineates the circumstances under which vertical line extensions have positive, neutral or negative impact on brand perceptions and future product expectations. We introduce the presence of a comparison set as a key variable and show how it interacts with assessment focus to affect brand evaluations. When thinking about the impact of extensions on brand perceptions, marketers need to consider which assessment focus is likely to be triggered by environmental cues and whether comparisons are salient.Originality/valueBrand extension is an important area of investigation as evidenced by the vast literature dedicated to the subject. The present paper advances knowledge in this area by identifying key factors affecting the impact of vertical extensions on brand perceptions.

In this paper, a method for the problem of depth estimation of a broadband source via reliable acoustic path propagation is presented for the case using a vertical line array (VLA). The estimates are determined by two kinds of multipath time-delay ratios, namely, the ratio of direct-surface-reflected (D-SR) to direct-direct time-delays and the ratio of D-SR to surface-reflected-surface-reflected time-delays. The innovation of ratio behavior is that it provides a mechanism for obtaining a useful depth interval with the assumption of plane-wave propagation. The estimation accuracy of a depth interval relies on the degree to which the actual acoustic propagation characteristic can be modeled by image theory. Furthermore, the variability of depth interval due to the approximation made in the derivation method allows one to achieve binary discrimination of both the source depth and source range with only a minimal amount of prior environmental knowledge. The methodology of multipath time-delay estimation is first reviewed and improved, followed by an illustration of the source depth estimation and a discussion of the performance analysis using results from numerical simulations. Finally, the proposed method is demonstrated with experimental data collected in the South China Sea in which a short-aperture VLA is deployed near the sea bottom.

We have been developing a communication robot “advice robot” that encourages and suggests actions to an elderly person, such as having a meal, taking a bath, taking medicine, etc. If the robot’s affective expressions are weak, an elderly user may not be able to understand or follow the robot’s suggestions. We focused on the vertical line and shadow techniques used in manga, or Japanese comics, to strengthen the affective expressions of disgust and fear, which can be difficult for the robot to express. The results of our experiment showed that the impression of disgust was strengthened by adding vertical lines. On the other hand, the impression of fear could not be strengthened by using the manga techniques. However, when the vertical lines were added to a happy face, the impression of fear was greater than when the lines were added to a fearful face.

The prevailing account of visually controlled routes is that an ant learns views as it follows a route, while guided by other path-setting mechanisms. Once a set of route views is memorised, the insect follows the route by turning and moving forwards when the view on the retina matches a stored view. We engineered a situation in which this account cannot suffice in order to discover whether there may be additional components to the performance of routes. One-eyed wood ants were trained to navigate a short route in the laboratory, guided by a single black, vertical bar placed in the blinded visual field. Ants thus had to turn away from the route to see the bar. They often turned to look at or beyond the bar and then turned to face in the direction of the goal. Tests in which the bar was shifted to be more peripheral or more frontal than in training produced a corresponding directional change in the ants' paths, demonstrating that they were guided by the bar. Examination of the endpoints of turns towards and away from the bar indicate that ants use the bar for guidance by learning how large a turn-back is needed to face the goal. We suggest that the ants' zigzag paths are, in part, controlled by turns of a learnt amplitude and that these turns are an integral component of visually guided route following.

In the Portuguese inheritance system only kin in vertical line were mandatory heirs, thus creating a pool of heirless testators who could dispose freely of their assets. Not only the institutions of the Catholic Church benefitted from them, but also confraternities such as the Misericórdias received property in exchange for salvific rituals such as masses for their souls or charity to the poor. The analysis of single case studies from the Misericórdia of Porto demonstrates that in case of litigation the court favoured the confraternity, on account of its role as provider of charity to the poor. However, the fact that the Misericórdia was under the king’s protection also meant that the latter could use inheritance money in case of financial crisis. Dans le système portugais de transmission de biens par décès seulement les héritiers en ligne verticale étaient obligatoires, créant par la suite nombreux testateurs sans héritiers qui pouvaient disposer de leurs biens en toute liberté. L’étude du cas portugais démontre que les institutions de l’Église catholique n’étaient pas les seules à recevoir leurs biens ; des confréries comme les Misericórdias pouvaient bénéficier de ces héritages en échange de rituels propitiatoires de salvation éternelle, qui consistaient dans la célébration de masses où dans la pratique d'œuvres de charité. L’analyse de deux cas d’étude provenant de la Misericórdia de Porto démontre qu'en cas de conflit les courts de justice favorisaient la confrérie, le justifiant avec son rôle comme pourvoyeuse de charité envers les pauvres. Cependant, le fait que la confrérie était sous la protection du roi signifiait que la couronne pouvait utiliser l’argent des défunts en cas de crise économique.

The vertical-horizontal illusion is the overestimation of a vertical line compared to a horizontal line of the same length. Jackson and Cormack (2007) proposed that the vertical-horizontal illusion might be a byproduct of the mechanisms that generate the environmental vertical illusion, which is the tendency to overestimate vertical distances (i.e., heights) relative to horizontal distances the same length. In our study, 326 undergraduate participants stood atop an 18.6-meter parking structure and estimated both the height of the structure and the horizontal distance of a target placed 18.6 meters away, using a moveable horizontal target across the length of the structure. Participants also completed a vertical-horizontal illusion task by drawing a horizontal line below a 9.1 cm vertical line. We correlated vertical distance estimates with vertical line estimates to test Jackson and Cormack’s byproduct hypothesis. This hypothesis was very weakly—if at all—supported by the data: Participants’ overestimations in the vertical-horizontal illusion task explained 1% of the variance associated with their overestimations in the environmental vertical illusion task. Additionally, to test whether the environmental vertical illusion is impervious to explicit awareness, a random half of our participants were advised to be mindful that people tend to overestimate heights. The results supported our second hypothesis: Even when participants were made aware of the environmental vertical illusion, they still reliably overestimated heights. Discussion addressed implications for the robustness of the environmental vertical illusion (e.g., treatment of those with acrophobia).

Knowledge of target features can guide attention in many conjunction searches in a top-down manner. For example, in search of a red vertical line among blue vertical and red horizontal lines, observers can guide attention toward all red items and all vertical items. In typical conjunction searches, distractors often form perceptually vivid, categorical groups of identical objects. This could favor the efficient search via guidance of attention to these "segmentable" groups. Can attention be guided if the distractors are not neatly segmentable (e.g., if colors vary continuously from red through purple to blue)? We tested search for conjunctions of color × orientation (Experiments 1, 3, 4, 5) or length × orientation (Experiment 2). In segmentable conditions, distractors could form two clear groups (e.g., blue steep and red flat). In non-segmentable conditions, distractors varied smoothly from red to blue and/or steep to flat; thus, discouraging grouping and increasing overall heterogeneity. We found that the efficiency of conjunction search was reasonably high and unaffected by segmentability. The same lack of segmentability had a detrimental effect on feature search (Experiment 4) and on conjunction search, if target information was limited to one feature (e.g., find the odd item in the red set, "subset search," Experiment 3). Guidance in conjunction search may not require grouping and segmentation cues that are very important in other tasks like texture discrimination. Our results support an idea of simultaneous, parallel top-down guidance by multiple features and argue against models suggesting sequential guidance by each feature in turn.

Recently, combat robot competition has become one of the most famous engineering competitions among schools and universities. The robots are usually built with a destructive weapon, which can immobilize or disable opponent’s robot and win the match. Despite the variety of robot design and concept, the trend has shown that most of the local contestant tend to design a horizontal axis weapon type. In this project, a wireless vertical axis bar spinner combat robot is designed and developed for the 3rd Malaysia Combat Robot Competition which was held at National Science Centre (PSN) in 2017. The robot is controlled using radio control (RC) and powered by a highly discharge 22.2V Lithium Polymer (LiPo) chemical battery. Furthermore, related analysis has been conducted to meet the design and performance requirement of the competition. With the DC brush motor and thick metal bar rotating in vertical axis, the robot has proven to produce high power, torque and speed during the competition.

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.

Conspicuous consumption of status goods signals consumers' status and grants status value to them. In this article, we examine how firms selling status goods make vertical line extension decisions when they take consumers' status preferences into account. Analyzing an incumbent's vertical line extensions when it faces a threat of entry, we find that status preferences can make unprofitable extensions profitable. Moreover, without status preferences, an incumbent can introduce line extensions to crowd out the competitor's profit and deter entry. However, with status preferences, introducing line extensions can increase the competitor's profit and attract entry. We also find that incumbents should introduce downward extensions when they are monopolists and upward extensions when they face competition from lower-quality entrants. As the cost of entry increases, incumbents should change from introducing upward extensions to introducing downward extensions. As consumers' status preferences increase, incumbents introduce downward extensions under a wider range of situations.

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

This article deals with{L^{p}}-{L^{2}}estimates for solutions of the wave equation associated to the Grushin operator{G:=-\Delta-|x|^{2}\frac{\partial^{2}}{\partial t^{2}}}on{\mathbb{R}^{n+1}}. We make use of the{L^{p}}boundedness of Riesz transforms for the Grushin operator in studying the wave equation.

Purpose Literature in brand extensions has relied greatly on categorization theory and on prototypical models of categorization to explain the affect transfer from a parent brand to its extensions. Drawing on the range theory exemplar models of categorization, this paper aims to show the effects of parent brand endpoint prices on consumer judgments of vertical line extensions. Design/methodology/approach Three experiments have been conducted. Experiment 1 tests the hypothesis that consumers rely on the parent brand price range when making judgments of an upscale extension. Experiment 2 tests the hypothesis that the effect of price range on extension evaluation is mediated by perceived risks for upscale extensions but not downscale extensions. The final experiment shows a boundary condition to the product line range effect on upscale extensions. Findings This research shows that upscale extensions are judged more favorably in the context of a wide versus a narrow product line even when the highest endpoints in both product lines are equally close to the extension and that this effect is mediated by perceived consistency and perceived risk. The range effect disappears, however, when consumers have a broad focus in which attention shifts to category endpoint prices, making parent brand prices less diagnostic of upscale extension judgments. Practical implications Managers may display a wider range of products and/or reduce prices of low-end models to expand product line price width. In consequence, low-end products become more competitive in terms of price and at the same time improve favorability ratings of the new upscale product. Originality/value Vertical line extensions and product line pricing are important topics to both academics and practitioners. Nonetheless, this is the first research to demonstrate how product line price width can influence consumer perceptions of vertical line extensions.

The peculiarities of the formation and functioning of three models of the information direction of policy of the national interests’ protection of the states of the world – the subsidiary (USA, UK, EU and NATO), vertical (Russian Federation) and transitional (Ukraine) models – are revealed. It is determined that the subsidiary model focuses on the horizontal informational and communicative interaction between the structural elements of the political system. Its purpose is to create an extensive network of process participants who can independently counteract threats and ensure the implementation of the policy of national interests’ protection on the ground. The vertical model focuses on creation of the clear vertical line of the development and implementation of the information direction of policy of national interests’ protection. The participation of a wide range of stakeholders in its development and implementation is limited. The basic structural elements of the system are the government, ministries and departments, media-controlled authorities, civil society institutions that execute the agenda developed by the “center”. The transitional model is characterized by a combination of vertical and subsidiary models with the subsequent transition to the latter. The features of access and control over the political discourse of each model are distinguished. It is determined that the subsidiary model is oriented on the achievement of a consensus between the state and society, the plurality of opinions, the inclusion of a large number of interested individuals/groups in the development and implementation of policies, including informational one. The state delegates some of its powers to society, and these allows it to be involved in the development, translation and transformation of discourse within the limits of the allowed parameters. The vertical model relies on tight control and subordination of the periphery to the center and eliminates any alternatives. The administrative-command approach allows to make decisions and to fill the political space with the necessary meanings and images fast enough without coordinating the interests of stakeholders which affect the preferences of target audiences. This testifies to full access and control over the production and distribution of political discourse. In the transitional model, emphasis is made on finding optimal options for the development and dissemination of discourse in transit conditions, changes in the management systems of local territories, delegation of part of the powers to the territorial communities, including powers in the information and communication. The peculiarity of such a state is the lack of a single consolidated discourse that would suit most of the interest groups. This situation creates conditions for the simultaneous existence of several conflicting discourses pretending to dominate, and the risk of capturing political-informational, politicalfigurative and political-semantic spaces by other states.

Context. The magnetic field is the underlying cause of solar activities. Spectropolarimetric Stokes inversions have been routinely used to extract the vector magnetic field from observations for about 40 years. In contrast, the photospheric continuum images have an observational history of more than 100 years. Aims. We suggest a new method to quickly estimate the unsigned radial component of the magnetic field, |Br|, and the transverse field, Bt, just from photospheric continuum images (I) using deep convolutional neural networks (CNN). Methods. Two independent models, that is, I versus |Br| and I versus Bt, are trained by the CNN with a residual architecture. A total of 7800 sets of data (I, Br and Bt) covering 17 active region patches from 2011 to 2015 from the Helioseismic and Magnetic Imager are used to train and validate the models. Results. The CNN models can successfully estimate |Br| as well as Bt maps in sunspot umbra, penumbra, pore, and strong network regions based on the evaluation of four active regions (test datasets). From a series of continuum images, we can also detect the emergence of a transverse magnetic field quantitatively with the trained CNN model. The three-day evolution of the averaged value of the estimated |Br| and Bt from continuum images follows that from Stokes inversions well. Furthermore, our models can reproduce the nonlinear relationships between I and |Br| as well as Bt, explaining why we can estimate these relationships just from continuum images. Conclusions. Our method provides an effective way to quickly estimate |Br| and Bt maps from photospheric continuum images. The method can be applied to the reconstruction of the historical magnetic fields and to future observations for providing the quick look data of the magnetic fields.

Commercial fishing fleets play a critical role in the population dynamics of exploited stocks. Understanding the spatial distribution of fleets allows managers to anticipate how fishing pressure on exploited stocks changes in response to fishing regulations or to large-scale perturbations. By anticipating how fishing pressure changes, managers can develop proactive responses to better protect stocks that are vulnerable to overfishing. Modern fisheries monitoring techniques, including vessel monitoring systems (VMS), have advanced this endeavor. This paper presents a framework for using VMS data to develop spatial distributions of catch, fishing effort, and catch per unit of effort (CPUE) as well as associated estimates of uncertainty in a vertical line fishery. VMS data are classified as fishing using a random forest (RF) model. Uncertainty is calculated using a two-step approach to account for uncertainty arising from the RF modeling process and the classification accuracy of the model. This framework is applied to investigate changes in the Gulf of Mexico reef fish fishery during a period of 6 years, including the 2010 Deepwater Horizon oil spill.

In this paper we report the measurement and analysis on vertical correlations of acoustic signals received by a vertical line array deployed near the sea bottom in deep water. The source data were from one calibration experiment of sound exposure level of explosive charges. The source–receiver range is about 17 km. The sound transmission duct is the well-known reliable acoustic path (RAP). The vertical correlation coefficients are estimated at center frequencies of 300, 600, 1000 and 1500 Hz with 1/3 octave bands. Two types of explosive charges are used with nominal source depths of 50 and 300 m, respectively. The variation of vertical correlation coefficients strongly relies on source depth and center frequency. For each scene, ten groups of experiment data exhibit uniform variation of vertical correlation coefficients with fractional differences due to the fluctuation of ocean waveguide. Besides, the noise-free numerical modeling results reach good agreements with the measured ones, which reflect the stability of RAP as a sound transmission duct in the space/frequency domain. Due to the obvious arrival structures of rays, the theoretical solution of vertical correlation coefficient is derived based on the ray theory. At last, the effects of source–receiver geometry on the variability of vertical correlation are discussed.

Weightlifting technique can be objectively assessed from two-dimensional video recordings. Despite its importance, participants' bar trajectories in research involving the snatch or clean exercises are often not reported, potentially due to the time required to digitize video. The purpose of this investigation was to evaluate the use of a light-emitting diode (LED)-based marker, digital video, and open-source software to automatically track the bar end during weightlifting exercises. A former national-level weightlifter was recorded with a digital video camera performing the snatch, clean and jerk, and squat exercises. An LED-based marker was placed on the right end of the bar. This marker was automatically tracked using 2 open-source software programs to obtain vertical and horizontal position coordinates. The LED-based marker was successfully auto-tracked for all videos over a variety of camera settings. Furthermore, the vertical and horizontal bar displacements and vertical bar velocity were consistent between the 2 software programs. This study demonstrates that an LED-based marker can be automatically tracked using open-source software. This combination of an LED-based marker, consumer camera, and open-source software is an accessible, low-cost method to objectively evaluate weightlifting technique.

Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl–Hermite expansions on R d \mathbb {R}^d . These expansions arise when one considers the Dunkl–Hermite operator (or Dunkl harmonic oscillator) H κ := − Δ κ + | x | 2 H_{\kappa }:=-\Delta _{\kappa }+|x|^2 , where Δ κ \Delta _{\kappa } stands for the Dunkl–Laplacian. It is shown that the desired mixed norm estimates are equivalent to vector-valued inequalities for a sequence of Cesàro means for Laguerre expansions with shifted parameter. In order to obtain such vector-valued inequalities, we develop an argument to extend these Laguerre operators for complex values of the parameters involved and apply a version of the three lines lemma.

The proposed system was designed for tankendo, kendo, or Japanese fencing using bamboo swords that also use a mask. First, a lightweight, miniaturized world-camera that is 3mm square, or smaller than the width of the vertical bar in the mask, is attached to the center of the vertical bar. This keeps the world-camera out of the field of vision of the competitor and protects the camera from damage. Second, a lengthened signal cable is connected to the control computer and compact power supply attached to the competitor's waist. This minimizes any discomfort a competitor might feel when using the system.

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.

A graph is called a bar 1-visibility graph, if its vertices can be represented as horizontal vertex-segments, called bars, and each edge corresponds to a vertical line of sight which can traverse another bar. If all bars are aligned at one side, then the graph is an aligned bar 1-visibility graph, \(AB1V\) graph for short.

We prove that finite sets of real numbers satisfying vertical bar AA vertical bar 0 cannot have small additive bases nor can they be written as a set of sums B + C with vertical bar B vertical bar, vertical bar C vertical bar >= 2. The result can be seen as a real analog of the conjecture of Sarkozy that multiplicative subgroups of finite fields of prime order are additively irreducible.

The plasma response from an external n = 2 magnetic perturbation field in ASDEX Upgrade has been measured using mainly electron cyclotron emission (ECE) diagnostics and a rigid rotating field. To interpret ECE and ECE-imaging (ECE-I) measurements accurately, forward modeling of the radiation transport has been combined with ray tracing. The measured data is compared to synthetic ECE data generated from a 3D ideal magnetohydrodynamics (MHD) equilibrium calculated by VMEC. The measured amplitudes of the helical displacement around the low field side midplane are in reasonable agreement with the one from the synthetic VMEC diagnostics. Both exceed the prediction from the vacuum field calculations and indicate the presence of a kink response at the edge, which amplifies the perturbation. VMEC and MARS-F have been used to calculate the properties of this kink mode. The poloidal mode structure of the magnetic perturbation of this kink mode at the edge peaks at poloidal mode numbers larger than the resonant components |m| > |nq|, whereas the poloidal mode structure of its displacement is almost resonant |m| ~ |nq|. This is expected from ideal MHD in the proximity of rational surfaces. The displacement measured by ECE-I confirms this resonant response., 34 pages, 19 figures. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

Women's poem is a model integrated vertical, Where the woman was able to embody the poet Arab heritage and at the same time, Penetrate and go beyond, And it worked to break down symmetrical system (Symmetric), And break the two parts system and replace it with a vertical line in the poem, This is the right place for our article about several central questions which came: Are women kept the poet on the elements of poetry column? The update winning it? How should a woman poet be able to make Hebron a starting point to build a system and a different variant of the prevailing during demolition? Then we wondered about the difference between the vertical inherited poem (poetry column / model father) The poem vertical women, and how they are working together and differ, How should a woman be able to break free of the two parts, which suggest gender system (male and female), to create a system of poetic vertically makes the basis for the construction of the line system?. All these questions will try to answer this in our situation.

This paper is concerned with the existence of positive solutions to a class of nonlocal boundary value problem of the p-Kirchhoff type {-M ( x,integral(ohm) vertical bar del u vertical bar(Rho) dx). Delta(Rho)u= f(x,u,vertical bar del u vertical bar(p-2) del)+lambda g(x,u)in(ohm)on(partial derivative ohm)vertical bar wuis a bounded smooth domain andM, f, and g are continuous functions. The existence of a positive solution is stated through an iterative method based onmountain pass theorem. Copyright (C) 2016 JohnWiley & Sons, Ltd.

Country-of-origin research has provided inconsistent findings about how the country of manufacture (COM) affects brand image evaluations. The authors examine how the COM, vertical line extension (VLE) type, and brand concept interactively affect brand image evaluations after brands introduce products in their existing product categories. The authors draw on schema congruity theory to develop a conceptual framework and confirm it using experimental methods. Results from a sample of U.S. consumers demonstrate that the COM's influence on brand image should be considered in conjunction with the type of VLE strategy and the intended conceptual meaning of a brand. Manufacturing in a country with a favorable image does not always improve brand image evaluations. Functional brands can improve their image with an upward VLE regardless of the COM; however, if these brands pursue a downward VLE, the COM has little to no effect. For prestige brands, downward VLEs result in lower postextension brand image regardless of the COM. However, a favorable COM appears to soften the negative effect of downward VLE on postextension brand image evaluations.

Reliable acoustic path (RAP) is a direct path used for sound propagation between a shallow source and a deep receiver in deep water. The RAP environment can provide a high signal-to-noise ratio (SNR) environment for source localization, so it has been widely studied for underwater passive detection. Active detection can be used for source localization during the descent of a vertical line array (VLA). However, the flow noise originating from the pressure fluctuations in the turbulent boundary layer (TBL) during the descent degrades the detection performance of the VLA. This paper presents a calculation of the response of the cylindrical hydrophones to axisymmetric turbulent wall pressure and the physical properties of flow noise. The flow noise was calculated using the wavenumber-frequency spectrum analysis method, which is based on Carpenter’s TBL pressure spectrum. The results show that the energy of the flow noise is concentrated mainly in low frequencies and it increases and spreads toward high frequencies with increasing stream velocity. The conclusions have been verified with experimental data. In addition, the noise correlation between two hydrophones will undergo oscillatory decay as the hydrophone spacing increases. The above findings will be beneficial for signal processing of an active sonar array.

Array gain (AG) is significant in evaluating the detection performance of the vertical line array, which is directly determined by the correlation of signal and noise, respectively. In this paper, we analyze the vertical correlation for a 16-element vertical line array experimented in the deep ocean in 2016. The ray interference theory is utilized to interpret the mechanism of the vertical correlation of the sound field in different zones. In the direct-arrival zone, the direct rays and once-surface-reflected rays are two dominated components, whose arrival time difference for each element are nearly the same, and the vertical correlation is high. In the shadow zone, the sound field is mainly dominated by bottom-reflected rays and the vertical correlation decreases due to different grazing angles and arrival times of each ray. Different from the previous assumption of noise independence, the effect of noise correlation on the AG is analyzed through the measured marine environmental noise. Results indicate that the noise correlation coefficients in two zones are low but not 0. In the direct-arrival zone, AG is about 10 dB, very close to the ideal value of 10 log M . AG even exceeds it when NG is negative. Moreover, AG in the direct-arrival zone is higher than the one in the shadow zone.

For a bounded domain $\Omega\subset \mathbb{R}^n$ and $p>n$, Morrey's inequality implies that there is $c>0$ such that $$ c\|u\|^p_{\infty}\le \int_\Omega|Du|^pdx $$ for each $u$ belonging to the Sobolev space $W^{1,p}_0(\Omega)$. We show that the ratio of any two extremal functions is constant provided that $\Omega$ is convex. We also explain why this property fails to hold in general and verify that convexity is not a necessary condition for a domain to have this property. As a by product, we obtain the uniqueness of an optimization problem involving the Green's function for the $p$-Laplacian., Comment: 23 pages, 7 figures