Search

We show that the projection of a product of two or three Eisenstein series of level one onto the cuspidal subspace is not an eigenform unless the dimension of the cuspidal subspace is one.

We describe the possibilities of the “Cluster Cartography” tool which was created for detailed study of the 2D distribution of galaxies in the clusters. The main tasks of the “Cluster Cartography” tool were the detailed study of the morphologyof galaxy clusters using the statistically significant numerical criteria as well as to detect their regular peculiarities. The tool allows to create the 2D map with positions of galaxies in the cluster field and show for each cluster member its shape and orientation as a best-fit ellipse using input catalogue data. The size of symbols for galaxies correspond to input data.It may reflect the galaxy image in arcseconds from catalogue in the map 4000×4000arcsec. Another way connects the size of the symbol with the magnitude of the galaxy. Tool is able to build the map in four modes: the symbols are dots; the symbols are circles with diameters reflected the magnitudes of galaxies; the symbols are ellipses with size reflected the magnitudesand both ellipticities and orientation from the input catalogue; the symbols illustrate the shape of galaxies in projection to the celestial sphere. The “Cluster Cartography” algorithms allow to detect the standard cases in galaxy distribution, suchas the degree of concentration to the cluster center and/or to some line on a statistically significant level using the numerical criteria. Also “Cluster Cartography” allows to detect other features, such as crosses, semi-crosses, complex crosses and short compact chains, as well as to export the list of galaxies forming the peculiarities for the futurestudy. The final version of the “Cluster Cartography” allows to realize the modern scheme for detailed morphological classification of galaxy clusters. The “Cluster Cartography” is powerful and perspective tool for study of features of galaxy clusters.

This article provides an overview of Spanish SE, covering the main empirical facts, analyses and theoretical issues that it raises, and exploring the prospects to unify all uses –which are over a dozen in the literature– under one same object that keeps its surface properties invariable. We will show that it is almost inescapable to propose that SE is associated to two types of objects, defective arguments and defective verbal heads; both objects share the property of not introducing referentially independent DPs, which can be argued to be the result of the grammaticalisation of a reflexive element in contemporary Spanish. The chapter proposes that a treatment of SE as a projection introduced high in the clausal structure and acting as an agreement locus can be a fruitful way to unify all uses of SE. Este artículo proporciona una visión general del SE en español, cubriendo los principales hechos empíricos, análisis y cuestiones téoricas que produce, y explorando la posibilidad de unificar todos los usos de SE –que son más de una docena en la bibliografía– bajo un solo elemento que mantenga propiedades superficiales invariables. Mostraremos que es casi inevitable proponer que SE se asocia a dos objetos de distinto tipo: argumentos defectivos ny núcleos verbales defectivos, donde la defectividad se refiere a que ninguno de esos objetos introduce SD referenciales, algo que puede entenderse como el resultado de la gramaticalización del reflexivo latino en español actual. El capítulo propone que un análisis del SE como una proyección introducida en una posición alta de la estructura oracional y que funciona como un núcleo de concordancia puede ser un modo de unificar todos los usos de SE.

Tradycja i praktyka zarówno stricte kartograficznego odwzorowania realiów, jak i opracowa- nych na gruncie nauk humanistycznych i społecznych technik odzwierciedlania topografii sytu- ują mapę w centrum dyskursu. W niniejszych rozważaniach potraktowano mapę jako pojemną optykę interpretacyjną rozciągającą się od obiektywnego rzutowania sytuacji przestrzennej na płaszczyznę wedle określonych reguł do krytycznej narracji humanistycznej, wręcz zakładającej nieobojętność recepcji i dokumentowania. Mapa jako optyka oscyluje między obiektywizującą diagnozą kartometryczną a personalizującą konstatacją intencjonalną. W obydwu scenariuszach chodzi o dotarcie do prawdy (prawdopodobieństwa), do odnotowania zmian gradientu cech, do stwierdzenia różnic i podobieństw. Zarówno w jednym, jak i drugim przypadku ważne staje się wyrażenie regularności oraz idiomatyczności świata. Refleksję nad mapowaniem czysto kartograficznym (zmierzającym ku klasyfikacji) i humanistycznym (zwróconym raczej ku kon- ceptualizacji i problematyzacji) rozpisano jako próbę odpowiedzi na trzy pytania: po co? jak / w jaki sposób? kto / dla kogo? Jednym z wniosków jest stwierdzenie, że mapa stanowi dla człowieka istotne medium epistemologiczne i świadectwo ontologiczne.

In this paper, we are interested in the properties of inner and outer projections with a view toward the Eisenbud-Goto regularity conjecture or the characterization of varieties satisfying certain extremal conditions. For example, if X is a quadratic scheme, the depth and regularity X and those of its inner projection from a smooth point are equal. In general, the above equalities do not hold for non-quadratic schemes. Therefore it is natural to investigate the algebraic invariants (e.g., depth and regularity) of X and its projected image in general. We develop a framework which provides partial answers and explains their relations using the partial elimination ideal theory. Our main theorems recover several preceding results in the literature. We also give some interesting examples and applications to illustrate our results.

The cut-and-project method may be applied to graphs and complexes, although there are technical difficulties, most notably “collisions,” i.e. when the images (under the projection) of two disjoint edges or cells intersect. Given a particular periodic structure, a particular projection space, an appropriate “window” in the orthogonal complement of that space, the induced substructure within the cartesian product of the window and the projection space is projected to the projection space to produce a “model structure.” We may use an index space of vectors from the orthogonal complement to move the window around and obtain a “model system” of model structures. We adapt the notion of “general position” to higher dimensions: the projection space is in “doubly general position” with respect to a graph or complex when the projection of that structure maps vertices of that structure injectively into the projection space and the edges or polytopes of that structure injectively so that their dimension is not reduced and disjoint edges and polytopes remain disjoint. We find that if the initial structure was a periodic graph, if the projection space and its complement are in general position with respect to the vertices and edges, and the window is also in general position, then the model system has uncountably many isomorphism classes - with distinct coordination sequences.

There are a number of helping verbs in Jordanian Arabic that are confused with light verbs or serial verbs. This paper, first, establishes the criteria on which they have been identified as auxiliary verbs. The paper shows the similarities and differences between the inflection of lexical verbs and aux’s in JA. It also tackles the loss of θ-assigning properties which is the crucial property that differentiates between aux and lexical and serial verbs. Second, given the fact that Arabic has rich verbal morphology which provides enough justification for factoring TP into TP and AspP (and perhaps AgrP), the study adopts an articulated version of the IP, in which inflection is separated into its constituent components, each has a maximal functional projection. The study also builds on Ouhalla's proposal (1990, 2005) that auxiliaries originate outside the VP shell. Based on evidence from the distribution of VP adverbs, negation and floating quantifiers, the paper proposes that auxiliaries in Jordanian Arabic are classified under two lexical auxiliary groups. T-aux are borne in a functional projection under T, but raise to T 0 to carry and reflect tense, while Asp-aux are base-generated under Asp 0 and only raise to T in the absence of a T-Aux.

Projectionists are left aside when the cinema apparatus is discussed. The following text is a rare attempt to put a spotlight on them, and the place they occupy: the projection booths. I will talk about the double split the projectionist went through during the history of cinema – split from the filmmaker and split from the spectator, I will discuss their relationship with the projector, the machine they necessarily need for their work, and will explore the miracles they may achieve by manipulation with it and the film reels. When switching the reels, splicing the frame into the film, or cutting the frame out of it, do the projectionists become a filmmaker? While we may talk about the relationship between a/ a filmmaker and camera and b/ spectator and camera, which is the relationship between spectator and projector? Last but not least I will contemplate how the projectionists are portrayed in the film.

Introduction. A kinematic model of group pursuit of a set of targets on a plane is considered. Pursuers use a technique similar to parallel approach method to achieve goals. Unlike the parallel approach method, the speed vectors of pursuers and targets are directed arbitrarily. In the parallel approach method, the instantaneous directions of movement of the pursuer and the target intersect at a point belonging to the circle of Apollonius. In the group model of pursuing multiple goals, the pursuers try to adhere to a network of predictable trajectories.Materials and Methods. The model sets the task of achieving goals by pursuers at designated points in time. This problem is solved by the methods of multidimensional descriptive geometry using the Radishchev diagram. The predicted trajectory is a composite line that moves parallel to itself when the target moves. On the projection plane “Radius of curvature — speed value”, the permissible speed range of the pursuer is displayed in the form of level lines (these are straight lines parallel to one of the projection planes). Images of speed level lines are displayed on the projection plane “Radius of curvature — time to reach the goal”. The search for points of intersection of the speed line images and the appointed time level line is being conducted. Along the communication lines, the values of the intersection points are lowered to the plane “Radius of curvature — speed value”. Using the obtained points, we construct an approximating curve and look for the intersection point with the line of the assigned speed. As a result, we get values of the radius of the circle at the predicted line of the trajectory of the pursuer.Results. Based on the results of the conducted research, test programs have been created, and animated images have been made in the computer mathematics system.Discussion and Conclusions. This method of constructing trajectories of pursuers to achieve a variety of goals at a given time values can be in demand by developers of autonomous unmanned aerial vehicles.

This paper studies the behavior of the lower and upper multifractal Hewitt–Stromberg functions under slices onto ( n - m ) {(n-m)} -dimensional subspaces. More precisely, we discuss the relationship between the multifractal Hewitt–Stromberg functions of a compactly supported Borel probability measure and those of slices or sections of the measure. In addition, we prove that if μ has a finite m-energy and q lies in a certain somewhat restricted interval, then these functions satisfy the expected adding of co-dimensions formula.

In March 2020, several projectionists or vjs (visual djs) projected an image of a flustered Jair Bolsonaro wearing a facemask over his eyes, nose, and mouth onto one of the tallest residential buil...

The article deals with the problem of optimization of the dictionary description of the stereotypes of the Russian linguoculture, reflected by linguistic units, which is relevant for Russian cultural linguistics and lexicography. The possibilities of solving this problem are shown with a thematic vocabulary systematization of proverbs regulating the communicative behavior of Russians. A review of modern linguoculturological and linguoaxiological studies of paremias reflecting communicative behavior in their projection onto lexicographic practice is carried out. The development of the ideas of paremiographers of the 19th century in modern concepts of thematic dictionaries is shown, special attention is paid to the rubrication of sections and methods of commenting on proverbs of speech-behavioral topics. The author’s version of the classification of proverbial material reflecting the communicative behavior of Russians is given, the expediency of the dispersed arrangement of paremias in the headings representing speech genres and features of communication in certain socio-cultural spheres is substantiated. In accordance with this concept, the system of linguoaxiological parameterization of proverbs, developed by the authors earlier, has been modified. Samples of dictionary macrostates representing the axiologems of the speech-behavioral sphere are given; proverbial material of Internet communication that has not been reflected in dictionaries at the moment is used. The possibilities of using the proposed linguoaxiological parameterization of the material in the bilingual thematic dictionary of proverbs are shown.

Cette étude décrit la révolution scientifique qui se produit en cartographie au tournant des années 1960 (et que nous proposons de nommer « révolution méthodologique »). Dans les premières phases de son existence en tant que science indépendante, la cartographie est liée de près au concept de chorologie tel qu’il s’emploie en géographie, et la cartographie économique de Baranskiy est l’une des premières options à concurrencer cette cartographie chorologique. La révolution méthodologique a deux sources. La première est la révolution quantitative en géographie, qui se manifeste par l’intégration des modèles topologiques au domaine de la cartographie, par son influence sur la cartographie d’objets et de phénomènes et sur la généralisation et la théorie des projections cartographiques et, en général, par sa contribution à l’usage actif des méthodes mathématiques en cartographie. La seconde est la formulation et le développement de la théorie sur la méthode de recherche cartographique. La révolution méthodologique provoque un changement de paradigme, entre celui qui s’inspire de la chorologie et celui de la « nouvelle cartographie ». L’établissement de la dualité essentielle des cartes géographiques par Bunge et Kansky (les cartes allient les propriétés du langage et du modèle) contribue à l’émergence de plusieurs concepts qui coexistent au sein de la « nouvelle cartographie ». Ce nouveau paradigme allait préparer la cartographie à son entrée dans le monde des technologies numériques.

Quasi-periodic behavior underlying gravitational three-body dynamics may supply naturally bounded reference trajectories to control spacecraft motion. To insert or maintain a spacecraft into bounded motion that resembles quasi-periodic behavior, guidance algorithms may require target position and velocity values, potentially at a fixed epoch. Within lower fidelity models that are autonomous, Poincare maps are a particularly effective tool to identify target conditions for nearly quasi-periodic motion; however, challenges remain in transitioning the application of Poincare maps to higher fidelity models that are nearly time-periodic. In fact, Poincare maps are often visualized in lower dimensional spaces for inspection; such visualizations do not often supply a static and comprehensive description for the underlying dynamical structures, when dynamics are nearly time-periodic. In this work, we explore a framework to facilitate the interpretation of Poincare map patterns associated with epoch-dependent solutions and states that are projected to lower dimensional position and velocity spaces. The introduction of chaos indicators may reveal regions of the projection that produce bounded motion as a function of the given epoch and/or initial state perturbation. Within precisely time-periodic systems, these regions may be the image, or shadow, of underlying torus manifolds. In the Poisson sense, shadows of quasi-periodic motion may be considered regions of stability within the lower dimensional space. Within the projection space, chaos indicators may capture time variations of a reference shadow or reveal special perturbation patterns. The framework is presented in two case studies: the first study demonstrates application within binary asteroid dynamics that are precisely time-periodic; the second study demonstrates application within nearly time-periodic dynamics (i.e., an ephemeris representation of the Earth-Moon system), when solutions resemble quasi-periodic motion only over finite time intervals.

Glrac semigroups are common generalizations of left GC-lpp semigroups and left inverse semigroups. And, such a semigroup is a left restriction semigroup if and only if the projection set is a semilattice. So, glrac semigroup is also a generalization of left restriction semigroup. Permissible subsets of a glrac semigroup are introduced in this paper. In terms of permissible subsets, we define (uniquely) factorizable glrac semigroups and (uniquely) almost factorizable glrac semigroups. Many characterizations of (uniquely) factorizable glrac semigroups and (uniquely) almost factorizable glrac semigroups are obtained. As their applications, we establish the structures of uniquely factorizable left GC-lpp semigroups (left inverse semigroups, inverse semigroups, ample semigroups, left restriction semigroup, restriction semigroups) and uniquely almost factorizable left GC-lpp semigroups (left inverse semigroups, inverse semigroups, ample semigroups, left restriction semigroup, restriction semigroups). Our results enrich and extend the related results of almost factorizable restriction semigroups.

The reported militarization of the Horn of Africa by Middle Eastern states has generated great interest among scholars and analysts alike. Their analyses and articles about the projections of power...

The dimension of the visible part of self-affine sets, that satisfy domination and a projection condition, is being studied. The main result is that the assouad dimension of the visible part equals to 1 for all directions outside the set of limit directions of the cylinders of the self-affine set. The result holds regardless of the overlap of the cylinders. The sharpness of the result is also being discussed., Final draft. 13 pages and 1 figure

In the present work, a general and simple approach to determine texture patterns using pole figure was developed. For the rolled materials, the rolling plane can be determined by the ratio of OP/R in the given pole figure. Here, OP is the length from the center to an arbitrary pole in the pole figure, and R is the radius of the projection circle in the pole figure. Rolling direction for the rolled materials or the extrusion direction for the extruded materials can be directly calculated using the coordinate values of the poles in the given pole figure. For cubic and hexagonal materials, the calculated results using the developed approach are in agreement with the standard stereographic projection pole figures. The textures in the rolled and annealed Fe–17Cr ferritic stainless steel and extruded Mg–2Mn alloy were examined by electron backscatter diffraction and X-ray diffraction. The proposed approach was applied to determine texture patterns in the above two materials. It was found that {111} type of γ-fiber texture develops for the as-annealed Fe–17Cr ferritic stainless steel and + double fiber texture develops for the extruded Mg–2Mn alloy.

A novel square equal-area map projection is proposed. The projection combines closed-form forward and inverse solutions with relatively low angular distortion and minimal cusps, a combination of properties not manifested by any previously published square equal-area projection. Thus, the new projection has lower angular distortion than any previously published square equal-area projection with a closed-form solution. Utilizing a quincuncial arrangement, the new projection places the north pole at the center of the square and divides the south pole between its four corners; the projection can be seamlessly tiled. The existence of closed-form solutions makes the projection suitable for real-time visualization applications, both in cartography and in other areas, such as for the display of panoramic images., Comment: 17 pages, 6 figures, 1 table; corrections to Appendix A

This paper is a historical account of the chords theorem, for conic sections from Apollonius to Boscovich. We comment the most significant proofs and applications, focusing on Newton's solution of the Pappus four lines problem. Newton's geometrical achievements drew L'Hospital's attention to the chords theorem as a fundamental one, and led him to search for a simple and direct proof, that he finally obtained by the method of projection. Stirling gave a very elegant algebraic proof; then Boscovich succeeded in finding an almost immediate geometrical proof, and showed how to develop the elements of conic sections starting from this theorem.

In this paper, we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weighted l1 (OWL1) norm ball. In particular, an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem. Global and local quadratic convergence results, as well as the finite termination property, of the algorithm are proved. Numerical comparisons with the two best-known methods demonstrate the efficiency of our method. In addition, we derive the generalized Jacobian of the studied projector which, we believe, is crucial for the future designing of fast second-order nonsmooth methods for solving general OWL1 norm constrained problems.

This paper focuses on efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian. Based on the Lagrangian duality theory, we deal with the projection...

A [Formula: see text]-ring [Formula: see text] is called a nil [Formula: see text]-clean ring if every element of [Formula: see text] is a sum of a projection and a nilpotent. Nil [Formula: see text]-clean rings are the [Formula: see text]-version of nil-clean rings introduced by Diesl. This paper is about the nil [Formula: see text]-clean property of rings with emphasis on matrix rings. We show that a [Formula: see text]-ring [Formula: see text] is nil [Formula: see text]-clean if and only if [Formula: see text] is nil and [Formula: see text] is nil [Formula: see text]-clean. For a 2-primal [Formula: see text]-ring [Formula: see text], with the induced involution given by[Formula: see text], the nil [Formula: see text]-clean property of [Formula: see text] is completely reduced to that of [Formula: see text]. Consequently, [Formula: see text] is not a nil [Formula: see text]-clean ring for [Formula: see text], and [Formula: see text] is a nil [Formula: see text]-clean ring if and only if [Formula: see text] is nil, [Formula: see text]is a Boolean ring and [Formula: see text] for all [Formula: see text].

A point p in projective plane is said to be quasi-Galois for a plane curve if the curve admits a non-trivial birational transformation which preserves the fibers of the projection $$\pi _p$$ from the point p. A number of quasi-Galois points for smooth plane curves of degree d are studied. In this paper, we will study the relationship between dihedral groups and smooth plane curves with many quasi-Galois points.

The developed educational projections, levels and prerequisites of the mathematical educational multilingual ontology OntoMathEdu are presented. Educational projection is viewed as the formalization of a certain system of subject training in mathematics. It is a subset of OntoMathEdu ontology concepts, which are structured at this stage of ontology development using two didactic relationships – educational level and prerequisites. Educational levels are allocated on the basis of the teaching standards of the corresponding education system, the relation of prerequisites is determined by the sequence of the studied concepts in a particular education system. The OntoMathEdu ontology defines two projections representing the educational systems of Russia and Great Britain. The algorithm for constructing an ontology through linking various projections allows it to be further replenished with new educational projections, which can later be used in the system of multilingual teaching of mathematics.

This article starts off with the observation that in certain cases, presuppositions triggered by an element inside a question nucleus may fail to project. In fact, in what looks like coordinated structures involving polar questions, presupposition projection patterns are exactly parallel to what is observed when the corresponding assertions are coordinated. The article further shows that these facts do not fall out straightforwardly from existing theories of polar questions, (apparent) coordinations of questions, and presupposition projection. It then proposes a trivalent extension of inquisitive semantics such that the observed pattern can be understood in terms of existing theories of presupposition projection. The proposal has the following properties: (a) apparent coordinations of questions are indeed coordinations of questions, and (b) the semantic denotation of polar questions is asymmetric with respect to the “yes” and “no” answers.

In order to generate the three-dimensional (3D) mesh of draped fabric based on a two-dimensional (2D) fabric projection, the 3D point cloud of draped fabric was scanned via a self-built 3D scanning...

‘America’, bloated with philosophical significance, serves as a meeting grounds for Heidegger and Derrida, flagging theoretical standoffs, identity crashes, a Nietzscean tipoff, and unstoppable poetry wars. Also featuring psychoanalytical stopovers and Rilkean putdowns..

Power projection, security, pragmatic considerations and a disparate mix of national interests and narrower party-political objectives have driven the foreign policy of Turkey's Justice and Development Party (AKP) in the Middle East since it came to power in 2002. Ideological concerns, consisting of a fluid blend of Islamist, neo-Ottoman and ‘civilizationalist’ ideas, mingled with a hefty dose of Turkish nationalism, have played a variable, auxiliary but none the less significant role. The Arab uprisings of 2011 opened up opportunities for the AKP to pursue its ideological objectives and they became more central to its policies, if only in some areas or clusters of relationships. However, they receded after 2015, when a confluence of domestic and regional factors caused the onset of a transactional, ‘post-ideological’ phase. The article places the Middle East in the wider context of Turkish foreign policy, both historically and in comparison with other regions, arguing in the process that categories of ‘East’ and ‘West’ are of limited value for its proper understanding and interpretation. It then divides it into four sub-regions, distinct in geographical and issue terms: Syria and Iraq (the ‘near abroad’), the wider Arab world, Israel–Palestine, and Iran. It analyses Turkish foreign policy towards them in sequence, illustrating the ways in which power-political considerations have predominated in all, albeit in different ways and to varying degrees, over the past five years.

The Frank-Wolfe algorithm is a method for constrained optimization relying on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational advantage of solving linear minimizations instead of projections. However, the discussions supporting this advantage are often incomplete. We review the complexity bounds for both tasks on several sets commonly used in optimization. Projection methods onto the l p -ball, p ∈ ] 1 , 2 [ ∪ ] 2 , + ∞ [ , and the Birkhoff polytope are also proposed.

In this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem (MSSFP for short) and the split equality fixed point problem (SEFPP for short) with firmly quasi-nonexpansive operators or nonexpansive operators in real Hilbert spaces. Under mild conditions, we prove strong convergence theorems for the algorithm by using the projection method and the properties of projection operators. The result improves and extends the corresponding ones announced by some others in the earlier and recent literature.

The Web Mercator projection is a projection of a relatively recent date. There has been a lot of controversy about its application. Some believe that this projection is not a projection of either the sphere or the surface of the ellipsoid. Therefore, in this paper, several projections of the surface of a rotational ellipsoid into a plane are investigated and it is shown that the Web Mercator projection is one of such projections. Namely, although the equations of this projection are identical to the equations for the projection of the sphere, the basic difference is in the choice of the area of definition, i.e., the domain of the projection. Furthermore, we have shown that the Web Mercator projection can also be interpreted as double mapping: mapping an ellipsoid to a sphere according to the normals and then mapping the sphere to the plane according to the formulas of the Mercator projection for the sphere. The Web Mercator projection is not a conformal projection, but it is close in properties to the Mercator projection.

Carta Geographica de Projecçaõ Espherica Orthogonal da Nova Lusitania ou America Portugueza e Estado do Brazil iz 1798. godine, zajedno sa svojim inačicama iz 1795. (?), 1797. i 1803. godine, nesumnjivo je jedan od kartografskih spomenika izrađenih u Portugalu krajem osamnaestog stoljeća. Njezin je organizator bio geograf, astronom i kapetan fregate Antonio Pires da Silva Pontes Leme koji se oslanjao na rad 34 osobe, uključujući astronome, geografe i inženjere, koji su, iako samo spomenuti u inačici iz 1798. godine, pridonijeli izradi svih drugih. Sve su inačice izgledom slične, ali se razlikuju po veličini, sadržaju, detaljima, količini i distribuciji toponima, no to će biti predmet drugoga rada. Međutim, najveća se sličnost odnosi na kartografsku projekciju. Cilj je ovoga rada analizirati i prikazati moguće hipoteze i zaključke o tome koja je kartografska projekcija usvojena za sve inačice Nove Luzitanije identificiranjem karakteristika koje su omogućile zaključivanje i dokazivanje usvojene projekcije. Primijenjena je metodologija potvrdila da su u bibliografskom pretraživanju podatci o strukturi karte nedovoljni. U članku koji je u listopadu 1950. predstavio general Djalma Polli Coelho navodi se da se čini da je projekcija predložena naslovom kao ortogonalna sferna projekcija zapravo ekvivalentna Sanson-Flamsteedova projekcija. Međutim, naslov Carta Geographica de Projecçaõ Espherica Orthogonal omogućuje nam zaključak da je to možda poprečna ortografska projekcija sfere. S pomoću parametara koji definiraju dvije projekcije bit će moguće uspostaviti usporedne elemente za kartografsku analizu, što bi nam omogućilo da zaključimo i dokažemo strukturu usvojenu za kartu Nova Lusitanija – je li ona poprečna ortografska projekcija ili Sanson-Flamsteedova sinusna projekcija sa srednjim meridijanom od 315°, definiranim u smjeru zapad-stok (u smjeru suprotnom od kazaljke na satu) s otoka El Hierro (Ferro). Taj je meridijan smješten približno –62°39ʹ46ʺ u odnosu na grinički meridijan., The map named Carta Geographica de Projecçaõ Espherica Orthogonal da Nova Lusitania ou America Portugueza e Estado do Brazil from 1798, together with its 1795 (?), 1797 and 1803 versions, is undoubtedly one of the cartographic monuments developed by Portuguese cartography from the late eighteenth century. Its organizer was the geographer, astronomer, and frigate captain Antonio Pires da Silva Pontes Leme, who relied on the work of 34 people, including astronomers, geographers, and engineers, who, although only mentioned in the 1798 version, contributed to the creation of all versions. All of them are similar in appearance, but differ in size, content, details, amount, and distribution of toponyms, which will be the subject of another paper. The greatest similarity, however, concerns the defined map projection. The objective of this paper is to analyse and present the possible hypotheses and conclusions about which map projection was adopted for all versions of Nova Lusitania, through the identification of characteristics that allowed to infer and prove the adopted projection. The applied methodology verified that in the bibliographic search, the information about the map structure is insufficient. An article presented by General Djalma Polli Coelho in October 1950 states that the projection suggested by its title, as orthogonal spherical, appeared to be the Sanson-Flamsteed equal-area projection. However, the expression Carta Geographica de Projecçaõ Espherica Orthogonal allows us to infer also the transverse orthographic projection. Through parameters defined for the two projections, it was possible to establish the comparative elements for a cartographic analysis, which would allow us to conclude and prove the structure adopted for the map, allowing to conclude if the adopted projection for the Nova Lusitania was an azimuthal orthographic equatorial projection, or a Sanson-Flamsteed, sinusoidal projection on the meridian 315°, defined west-east, (counterclockwise), from the El Hierro (Ferro) Island. This meridian is referenced approx. –62°39'46" off the Greenwich meridian.

Este texto analiza la pieza Sun & Sea (Marina), que fue premiada con el León de Oro a la mejor participación nacional en la 58a Bienal de Arte de Venecia (2019). Aunque ha sido destacado el mensaje ecológico de la pieza, entendemos que la misma detona otra serie de reflexiones y se conecta con diversos aspectos del pensamiento contemporáneo que merecen ser explorados y revisados en profundidad. Así, observamos sus asociaciones con la actividad creativa previamente desarrollada por sus autoras, el modo en que se entrelaza con piezas de otros artistas lituanos y su vinculación con los desarrollos conceptuales que arrojan una mirada crítica sobre nuestra sociedad y los valores sobre los que se asienta. Asimismo, observamos detenidamente las consecuencias del empleo del formato de ópera-performance y las posibilidades que despliega para propiciar la proyección desde la propia experiencia de espectadores y espectadoras, haciendo uso de la acción en directo guionizada y los diálogos cantados, trazados desde la ironía y el humor como soporte de posicionamientos críticos.

The classical convex feasibility problem in a finite dimensional Euclidean space consists of finding a point in the intersection of two convex sets. In the present paper we are interested in two particular instances of this problem. First, we assume to know how to compute an exact projection onto one of the sets involved and the other set is compact such that the conditional gradient (CondG) method can be used for computing efficiently an inexact projection on it. Second, we assume that both sets involved are compact such that the CondG method can be used for computing efficiently inexact projections on them. We combine alternating projection method with CondG method to design a new method, which can be seen as an inexact feasible version of alternate projection method. The proposed method generates two different sequences belonging to each involved set, which converge to a point in the intersection of them whenever it is not empty. If the intersection is empty, then the sequences converge to points in the respective sets whose distance between them is equal to the distance between the sets in consideration. Numerical experiments are provided to illustrate the practical behavior of the method.

Conics typically include ellipses, hyperbolas, and parabolas with equal eccentricities that intersect infinite line at absolute points. According to the imaging characteristics of conics under a pi...

Although projecting one’s own characteristics onto another person is pervasive, “counter-projection,” or seeing the opposite of oneself in others is also sometimes found, with implications for intergroup conflict. After a focused review of previous studies finding counter-projection (often unexpectedly), we map conditions for counter-projection to an individual out-group member. Counter-projection requires identified antagonistic groups, is moderated by in-group identity, and is moderated by which information is assessed in the target person. Using political groups defined by support for former U.S. President Trump, across our Initial Experiment ( N = 725) and Confirmatory Experiment ( N = 618), we found counter-projection to individual political out-group targets for moral beliefs, personality traits, and everyday likes (e.g., preference for dogs vs. cats). Counter-projection was increased by in-group identification and overlapped considerably with “oppositional” out-group stereotypes, but we also found counter-projection independent of out-group stereotypes (degree of overlap with stereotyping depended on the information being projected).

This article proposes that the temporality of Jonathan Edwards’s aesthetic projection of himself as simultaneously godly and depraved provides an alternative model of early American selfhood from the secular capitalist paradigm of Benjamin Franklin, championed by Max Weber and perpetuated by Charles Taylor’s account of secular time-consciousness in A Secular Age.

The paper shows that the moment invariants proposed recently in this journal by Hjouji et al. (J Math Imaging Vis 62:606–624, 2020) are incomplete, which leads to a limited discriminability. We prove this by means of circular projection of the image. In a broader context, we demonstrate that completeness of the invariants leads to a better recognition power.

The paper presents a method for geometric modelling of a four-dimensional ball. For this, the regularities of the change in the shape of the projections of simple geometric images of two-dimensional and three-dimensional spaces during rotation are considered. Rotations of a segment and a circle around an axis are considered; it is shown that during rotation the shape of their projections changes from the maximum value to the degenerate projection. It was found that the set of points of the degenerate projection belongs to the axis of rotation, and each n-dimensional geometric image during rotation forms a body of a higher dimension, that is, one that belongs to (n + 1) -dimensional space. Identified regularities are extended to the four-dimensional space in which the ball is placed. It is shown that the axis of rotation of the ball will be a degenerate projection in the form of a circle, and the ball, when rotating, changes its size from a volumetric object to a flat circle, then increases again, but in the other direction (that is, it turns out), and then in reverse order to its original position. This rotation is more like a deformation, and such a ball of four-dimensional space is a hypersphere. For geometric modelling of the hypersphere and the possibility of its projection image, the article uses the vector model proposed by P.V. Filippov. The coordinate system 0xyzt is defined. The algebraic equation of the hypersphere is given by analogy with the three-dimensional space along certain coordinates of the center a, b, c, d. A variant of hypersection at t = 0 is considered, which confirms by equations obtaining a two-dimensional ball of three-dimensional space, a point (a ball of zero radius), which coincides with the center of the ball, or an imaginary ball. For the variant t = d, the equation of a two-dimensional ball is obtained, in which the radius is equal to R and the coordinates of all points along the 0t axis are equal to d. The variant of hypersection t = k turned out to be interesting, in which the equation of a two-dimensional sphere was obtained, in which the coordinates of all points along the 0t axis are equal to k, and the radius is . Horizontal vector projections of hypersection are constructed for different values of k. It is concluded that the set of horizontal vector projections of hypersections at t = k defines an ellipse.

Approximately 150 map projections are known, but the inverse forms have been published for only two-thirds of them. This paper focuses on finding the inverse forms of van der Grinten projections I-IV, both by non-linear partial differential equations and by the straightforward inverse of their projection equations. Taking into account the particular cases, new derivations of coordinate functions are also presented. Both the direct and inverse equations have the analytic form, are easy to implement and are applicable to the coordinate transformations.

The method of tomographic reconstruction of inhomogeneities in case of an arbitrary directional diagram and scanning along one coordinate is described. It is shown that in this case registered data (projections) are represented as the sum of the line-by-line convolutions of the lines of the directional diagram and the corresponding line of the reconstructed distribution. The features of projection data, backprojections are analyzed. It is proposed to construct a cumulative image as an additive or conjunctive combination of the backprojection results for different orientation diagrams. An iterative procedure for constructing sequential approximations to the desired solution is proposed.

In this paper, the mixed L p -surface area measures are defined and the mixed L p Minkowski inequality is obtained consequently. Furthermore, the mixed L p projection inequality for mixed projection bodies is established.

We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the `apparent contour' of a single projection to the projective plane. We deal with the case of tangent developables and of general projections to $\mathbb{p}^3$ of rational normal scrolls. In the first case, we use the fact that every such surface is the projection of the tangent developable of a rational normal curve, while in the second we start by reconstructing the rational normal scroll. In both instances we then reconstruct the correct projection to $\mathbb{p}^3$ of these surfaces by exploiting the information contained in the singularities of the apparent contour., 17 pages

The projections for the sacrum are axial anteroposterior with the beam 15 degrees toward the cephalad, and axial posteroanterior in the direction of the beam 15 degrees caudally. Some practitioners take steps to examine the sacrum with AP projections in a perpendicular beam direction. Around the sacrum are reproductive organs that are sensitive to radiation, so it is necessary to select the right projection to reduce the radiation dose and show clear anatomical information. This study aims to determine the projection of an examination that produces clear anatomical information at a minimal dose. This is an experimental study with one shot post-test only. Samples in the form of radiographs were obtained from perpendicular AP and axial AP projections assessed by radiologists regarding the clarity of anatomical information. The radiation dose was measured using TLD on the ovaries and gonads. Data were analyzed by t-test and Wilcoxon test with an error level of 5%. The AP axial projection shows better anatomical information than the perpendicular AP projection. The axial AP projection shows a smaller dose of the ovaries and gonads. There is a difference in anatomical information between AP and axial AP projections with a p-value = 0.017. There was a difference in radiation dose between AP and axial AP projections on the right ovary (p-value = 0.002), left ovary (p-value 0.001) and gonads (p-value = 0.008).

Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions may be defined in terms of capacities with respect to certain kernels. Then, relying on this, we show that the intermediate dimensions of the projection of a set $E \subset \mathbb{R}^n$ onto almost all $m$-dimensional subspaces depend only on $m$ and $E$, that is, they are almost surely independent of the choice of subspace. Our approach is based on `intermediate dimension profiles' that are expressed in terms of capacities. We discuss several applications at the end of the paper, including a surprising result that relates the box dimensions of the projections of a set to the Hausdorff dimension of the set., Comment: 17 pages, 0 figures

Given a triangulation of a closed surface, we consider a cross ratio system that assigns a complex number to every edge satisfying certain polynomial equations per vertex. Every cross ratio system induces a complex projective structure together with a circle pattern on the closed surface. In particular, there is an associated conformal structure. We show that for any triangulated torus, the projection from the space of cross ratio systems with prescribed Delaunay angles to the Teichm\"{u}ller space is a covering map with at most one branch point. Our approach is based on a notion of discrete holomorphic quadratic differentials., Comment: 23 pages, 4 figures. Typos corrected

Coordination of skilled movements and motor planning relies on the formation of regionally restricted brain circuits that connect cortex with subcortical areas during embryonic development. Layer 5 neurons that are distributed across most cortical areas innervate the pontine nuclei (basilar pons) by protrusion and extension of collateral branches interstitially along their corticospinal extending axons. Pons-derived chemotropic cues are known to attract extending axons, but molecules that regulate collateral extension to create regionally segregated targeting patterns have not been identified. Here, we discovered thatEphA7andEfnA5are expressed in the cortex and the basilar pons in a region-specific and mutually exclusive manner, and that their repulsive activities are essential for segregating collateral extensions from corticospinal axonal tracts in mice. Specifically,EphA7andEfnA5forward and reverse inhibitory signals direct collateral extension such thatEphA7-positive frontal and occipital cortical areas extend their axon collaterals into theEfnA5-negative rostral part of the basilar pons, whereasEfnA5-positive parietal cortical areas extend their collaterals into theEphA7-negative caudal part of the basilar pons. Together, our results provide a molecular basis that explains how the corticopontine projection connects multimodal cortical outputs to their subcortical targets.SIGNIFICANCE STATEMENTOur findings put forward a model in which region-to-region connections between cortex and subcortical areas are shaped by mutually exclusive molecules to ensure the fidelity of regionally restricted circuitry. This model is distinct from earlier work showing that neuronal circuits within individual cortical modalities form in a topographical manner controlled by a gradient of axon guidance molecules. The principle that a shared molecular program of mutually repulsive signaling instructs regional organization—both within each brain region and between connected brain regions—may well be applicable to other contexts in which information is sorted by converging and diverging neuronal circuits.

The unicorn of map projections is the one that preserves all the spatial relationships from the globe. Topologically, we know this projection doesn’t exist, as it is impossible to preserve both are...