An improved method to determine basic probability assignment based on fuzzy mathematics

In D-S evidence theory, the determination of the basic probability assignment function (BPA) is the first and important step. However, the generation of BPA is still a problem to be solved. Based on the concepts in fuzzy mathematics, this paper proposes an improved BPA generation method. By introducing the value of the intersection point of membership function of different targets under the same index to describe the overlap degree of targets, the assignment of unknown items is optimized on this basis. This article applies it to target recognition of robot hands. The results show that the proposed method is more reliable and more accurate.

Ukrainian book art: ways of formation and development

The purpose of the article is to study the development of the directions of Ukrainian book art, the formation of new creative features in the European cultural space. The research methodology consists in the application of general scientific methods (analysis and synthesis, induction and deduction) and methods of art history (comparative, typological, descriptive). The scientific novelty lies in the study of book art, which has always been important in Ukrainian art. Conclusions. Today, we have a large amount of fine works in the genre of book illustrations. These works reflected both the history of the Ukrainian literature, history of the national graphic art, as well as the history of cultural progress of Ukraine in general. Thus, book art is an extremely fruitful object of study, an intersection point, where the complicated process of interaction of socio-political, spiritual, cultural and artistic and aesthetic factors is underway. Thus, Ukrainian book graphics in different periods reflected all European trends – modernism, symbolism, neo-primitive art, futurism, cubism, expressionism, constructivism, realism, surrealism, Art Deco, neoclassicism. The originality of the artistic language emerged through the use of traditional motifs and vanguard image creation tools. Keywords: research, culture, illustration, book, art, national traditions.

Diversification of Time-Varying Tangency Portfolio under Nonlinear Constraints through Semi-Integer Beetle Antennae Search Algorithm

In finance, the most efficient portfolio is the tangency portfolio, which is formed by the intersection point of the efficient frontier and the capital market line. This paper defines and explores a time-varying tangency portfolio under nonlinear constraints (TV-TPNC) problem as a nonlinear programming (NLP) problem. Because meta-heuristics are commonly used to solve NLP problems, a semi-integer beetle antennae search (SIBAS) algorithm is proposed for solving cardinality constrained NLP problems and, hence, to solve the TV-TPNC problem. The main results of numerical applications in real-world datasets demonstrate that our method is a splendid substitute for other evolutionary methods.

Per-pixel displacement mapping using cone tracing with correct silhouette

Per-pixel displacement mapping is a texture mapping technique that adds the microrelief effect to 3D surfaces without increasing the density of their corresponding meshes. This technique relies on ray tracing algorithms to find the intersection point between the viewing ray and the microrelief stored in a 2D texture called a depth map. This intersection makes it possible to deter- mine the corresponding pixel to produce an illusion of surface displacement instead of a real one. Cone tracing is one of the per-pixel displacement map- ping techniques for real-time rendering that relies on the encoding of the empty space around each pixel of the depth map. During the preprocessing stage, this space is encoded in the form of top-opened cones and then stored in a 2D texture, and during the rendering stage, it is used to converge more quickly to the intersection point. Cone tracing technique produces satisfacto- ry results in the case of flat surfaces, but when it comes to curved surfaces, it does not support the silhouette at the edges of the 3D mesh, that is to say, the relief merges with the surface of the object, and in this case, it will not be rendered correctly. To overcome this limitation, we have presented two new cone tracing algorithms that allow taking into consideration the curvature of the 3D surface to determine the fragments belonging to the silhouette. These two algorithms are based on a quadratic approximation of the object geometry at each vertex of the 3D mesh. The main objective of this paper is to achieve a texture mapping with a realistic appearance and at a low cost so that the rendered objects will have real and complex details that are vis- ible on their entire surface and without modifying their geometry. Based on the ray-tracing algorithm, our contribution can be useful for current graphics card generation, since the programmable units and the frameworks associat- ed with the new graphics cards integrate today the technology of ray tracing.

Effect of Molybdate on the Stability of Pit Growth in Duplex Stainless Steel 2205

In the present study, the criteria of pit stabilization and salt formation have been investigated for DSS 2205 using the lead-in-pencil electrode in order to explore the contribution of molybdate in stable pit growth. Results show that the Epit shifts to positive values by increasing molybdate concentration. It is found that the increase in Epit could not be referred to the changes in DCcrit and DCsat, since these values are slightly reduced by adding Molybdate to the solution. In contrast, the active dissolution rate of the metal assessed by idiss,max is hindered in the presence of molybdate ions. Therefore, it is proposed that the mechanism for the inhibitory influence of molybdate can be attributed to an increment in the intersection point of idiss,max/idiff,crit (which reflects Ecrit), and idiss,max/ilim (which reflects Esat). Therefore, increasing the Ecrit and Esat at the pit growth process is responsible for the observed raising of the Epit in presence of Molybdate.

Determination of coordinates of the earthquake hypocenter by the method of circles

Objective. The aim of the study is to develop a method for determining the coordinates of the earthquake hypocenter using various combinations of second and fourth order figures as a geo-locus of the hypocenter position points.Method. It is known that the line of intersection of figures of the second and fourth orders, in the case of coincidence of focuses, is a circle. To determine the coordinates of the earthquake source, data from seismographs are used, which are used to construct figures of the second and fourth order, the intersection point of which is the hypocenter. When using data from two seismic sensors, there are two figures, the intersection line of which is a circle. A sphere with a radius equal to the radius of the circle is constructed through the center of this circle. For the other two pairs of seismic sensors, two more spheres are also formed, The intersection point of the three spheres obtained is the sought-for hypocenter of the earthquake.Result. A method has been developed for determining the coordinates of an earthquake source using different shapes of the second and fourth orders for different pairs of seismic sensors.Conclusion. The method allows one to select one of the second or fourth order figures for different pairs of seismic sensors, which makes it possible to reduce the error in determining the source coordinates.

Temporal Bone Landmarks of the Transversesigmoid Sinus Junction: An Anatomical Study in Dried Human Skulls

Objective: To investigate the accuracy in localization of the anterosuperior margin of TSSJ by using the intersection point between the squamosal and parietomastoid sutures (A point) and the intersection of the squamosal suture and supramastoid crest (B point) as bony landmarks.Materials and Methods: The A and B points were marked on the inner surface of a skull by using the transillumination technique. The anatomical relationship between the projected A point, B point, and groove of TSSJ was investigated in 60 dried Thai human skulls (120 sides).Results: Of the 120 sides, the projected A points were located exactly on the anterosuperior margin of the TSSJ in 38 (31.7%) instances and adjacent (above and below) the anterosuperior margin in 82 (68.3%) cases. Of the 118 sides with identifiable supramastoid crests, the projected B points were located precisely on the anterosuperior margin of TSSJ in 60 (50.8%) cases and above the anterosuperior margin of the TSSJ in 57 (48.3%) cases. Hence, the projected B point was a more reliable bony landmark for localizing the anterosuperior margin of the TSSJ when compared with the projected A point (p = 0.003, OR 2.2, and 95% CI =1.3-3.8).Conclusion: The B point is a more reliable temporal bone landmark for localization of the TSSJ than the A point. In temporal craniotomy, an initial burr hole at the B point is relatively safe and carries a very low risk of inadvertent venous sinus injury.

Arginase Signalling as a Key Player in Chronic Wound Pathophysiology and Healing

Arginase (ARG) represents an important evolutionarily conserved enzyme that is expressed by multiple cell types in the skin. Arg acts as the mediator of the last step of the urea cycle, thus providing protection against excessive ammonia under homeostatic conditions through the production of L-ornithine and urea. L-ornithine represents the intersection point between the ARG-dependent pathways and the urea cycle, therefore contributing to cell detoxification, proliferation and collagen production. The ARG pathways help balance pro- and anti-inflammatory responses in the context of wound healing. However, local and systemic dysfunctionalities of the ARG pathways have been shown to contribute to the hindrance of the healing process and the occurrence of chronic wounds. This review discusses the functions of ARG in macrophages and fibroblasts while detailing the deleterious implications of a malfunctioning ARG enzyme in chronic skin conditions such as leg ulcers. The review also highlights how ARG links with the microbiota and how this impacts on infected chronic wounds. Lastly, the review depicts chronic wound treatments targeting the ARG pathway, alongside future diagnosis and treatment perspectives.

Analysis of the speed and curvature of the trajectory in the problem of pursuing a set of targets

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.

Rectangles and spirals

Every reader knows about the Golden Rectangle (see [1, pp. 85, 119], [2, 3]), and that it can be subdivided into a square and a smaller copy of itself, and that this process can be continued indefinitely, converging towards the intersection point of diagonals of any two successive rectangles in the sequence. The circumscribed logarithmic spiral passing through the vertices and converging to the same point is also familiar (see [3, 4]), and is analogous to the circumcircle of a regular polygon or a triangle. The approximate logarithmic spiral obtained by drawing a quarter-circle inside each of the squares is equally well known [3, p. 64]. Perhaps slightly less familiar is the inscribed spiral, which is tangential to a side of every rectangle, like the incircle of a triangle or a regular polygon. It does not (quite) coincide with the spiral passing through the point of subdivision of each side, as discussed in [3, pp. 73-77]. The Golden Rectangle, its subdivisions, and the circumscribed and inscribed spirals are illustrated in Figure 1.