Narrow Results

Let $R$ be a ∗-ring. Then $R$ is called a ∗-symmetric ring if for any $a,b,c\in R,abc=0$ implies $ac{b}^{\ast }=0.$ Obviously, ∗-symmetric ring is certainly symmetric ring, while ∗-ring and symmetric ring does not equal ∗-symmetric ring. Even though reduced rings are symmetric, reduced rings need not be ∗-symmetric ring. In this paper, we further add some conditions for symmetric ring to be ∗-symmetric and reduced. As an application, we discover if $R$ be a ∗-symmetric ring, then $R^{\#}=R^{EP}=R^{+}=R^{\mathrm{\text{reg}}}.$ Also, we expand the definition of ∗-symmetric ring to different combinations of $a,b,c$. The properties of ∗-symmetric ring play a role in generalized inverses of elements in rings.

The use of self-organizing maps to analyze data often depends on finding effective methods to visualize the SOM's structure. In this paper we propose a new way to perform that visualization using a variant of Andrews' Curves. Also we show that the interaction between these two methods allows us to find sub-clusters within identified clusters. Perhaps more importantly, using the SOM to pre-process data by identifying gross features enables us to use Andrews' Curves on data sets which would have previously been too large for the methodology. Finally we show how a three way interaction between the human user and these two methods can be a valuable exploratory data analysis tool.

Let X be an n-dimensional non-degenerated subvariety of ℙ^N with N≥2n+1. We give a rough classification for varieties X having G_n-1,n-defect. In case n=3, we give a fine classification for smooth varieties X having G_2,3-defect.

In this paper, a complete characterization of the B-subdifferential of the projection onto the generalized simplex is given. This work is accomplished with the help of Han–Sun Jacobian, whose full characterization is also given in this case. The characterizations are given with simple and explicit formulae in terms of the active index set of the projection.

The aim of this work is to apply the observable-state model for the quantum field theory of a ϕⁿ self-interaction. We show how to obtain finite values for the two-point and n-point correlation functions without introducing counterterms in the Lagrangian. Also, we show how to obtain the renormalization group equation for the mass and the coupling constant. Finally, we find the dependence of the coupling constant with the energy scale and we discuss the validity of the observable-state model in terms of the projection procedure.

In this paper, we propose a new face detection and tracking algorithm for real-life telecommunication applications, such as video conferencing, cellular phone and PDA. We combine template-based face detection and tracking method with color information to track a face regardless of various lighting conditions and complex backgrounds as well as the race. Based on our experiments, we generate robust face templates from wavelet-transformed lowpass and two highpass subimages at the second level low-resolution. However, since template matching is generally sensitive to the change of illumination conditions, we propose a new type of preprocessing method. Tracking method is applied to reduce the computation time and predict precise face candidate region even though the movement is not uniform. Facial components are also detected using k-means clustering and their geometrical properties. Finally, from the relative distance of two eyes, we verify the real face and estimate the size of facial ellipse. To validate face detection and tracking performance of our algorithm, we test our method using six different video categories of QCIF size which are recorded in dynamic environments.

The contours and segments of objects in digital images have many important applications. Contour extractions of gray images can be converted into contour extractions of binary images. This paper presents a novel contour-extraction algorithm for binary images and provides a deduction theory for this algorithm. First, we discuss the method used to construct convex hulls of regions of objects. The contour of an object evolves from a convex polygon until the exact boundary is obtained. Second, the projection methods from lines to objects are studied, in which, a polygon iteration method is presented using linear projection. The result of the iteration is the contour of the object region. Lastly, addressing the problem that direct projections probably cannot find correct projection points, an effective discrete ray-projection method is presented. Comparisons with other contour deformation algorithms show that the algorithm in the present paper is very robust with respect to the shapes of the object regions. Numerical tests show that time consumption is primarily concentrated on convex hull computation, and the implementation efficiency of the program can satisfy the requirement of interactive operations.

A finite set of nontrivial θ_n-curves is shown to be minimal among those which produce all projections of nontrivial θ_n-curves.

We consider a surface embedded in the 3-space. Such a surface is called unknotted if the closures of the complementary regions in the 3-sphere are both handlebodies. In this paper, we give a sufficient condition for a torus in the 3-space to be unknotted by using a projection onto a plane. We also prove that this condition is not sufficient for surfaces of higher genera.

It is known by few that a trivial knot can be transformed into a lattice knot whose three shadows are all trees (here, three shadows mean the projections of the lattice knot to the directions of ordinary orthogonal axes). Since a knot itself is a loop in the space, this fact may be rather astonishing. It will be interesting to ask whether a non-trivial knot has such a transformation or not. The purpose of this paper is to show that any two-bridge torus knot or link has a transformation into a lattice knot whose three shadows are all trees. The algorithm to construct such a position will be demonstrated.

The singularity set of a generic standard projection to the three space of a closed surface linked in four space, consists of at most three types: double points, triple points or branch points. We say that this generic projection image is p-diagram if it does not contain any triple point. Two p-diagrams of equivalent surface links are called p-equivalent if there exist a finite sequence of local moves, such that each of them is one of the four moves taken from the seven on the well known Roseman list, that connects only p-diagrams. It is natural to ask that whether any of two p-diagrams of equivalent surface links always p-equivalent? We introduce an invariant of p-equivalent diagrams and an example of linked surfaces that answers our question negatively.

We construct various functorial maps (projections) from virtual knots to classical knots. These maps are defined on diagrams of virtual knots; in terms of Gauss diagram each of them can be represented as a deletion of some chords. The construction relies upon the notion of parity. As corollaries, we prove that the minimal classical crossing number for classical knots. Such projections can be useful for lifting invariants from classical knots to virtual knots. Different maps satisfy different properties.

For a large class of planar simple nested fractals, we prove the existence of the reflected diffusion on a complex of an arbitrary size. Such a process is obtained as a folding projection of the free Brownian motion from the unbounded fractal. We give sharp necessary geometric conditions for the fractal under which this projection can be well defined, and illustrate them by numerous examples. We then construct a proper version of the transition probability densities for the reflected process and we prove that it is a continuous, bounded and symmetric function which satisfies the Chapman–Kolmogorov equations. These provide us with further regularity properties of the reflected process such us Markov, Feller and strong Feller property.

Partial periodic patterns are commonly seen in real-life applications and provide useful prediction with uncertainty. Most previous approaches have set a single minimum support threshold for all events to assume they have similar frequencies which is not practical for real-world applications. Instead of setting a single minimum support threshold for all events, Chen et al. proposed an FP-tree-like algorithm to allow multiple minimum supports for reflecting the natures of the events. However, such a tree-based algorithm encountered an efficiency problem while period length is long or event sequential orders in period segments are varied. Under the circumstance, many tree branches are created and much execution time is spent to find partial periodic patterns. In this paper, we thus propose a projection-based algorithm which examines only prefix subsequences and projects only corresponding postfix subsequences with multiple minimum supports to quickly find the partial periodic patterns in a recursive process. Experiments on both synthetic and real-life datasets show that the proposed algorithm is more efficient than the previous one.

The relationship of Semantic Similarity of an Object as a Function of the Context (SSOFC) being the key factor in data integration is investigated. The SSOFC is a context-based system, which exploits the context of an object by utilizing the semantic similarity involved, in order to reconcile bottleneck conflicts (semantic) standing in the way of interoperability acquisition in heterogeneous systems. SSOFC is further re-enforced with the agents to equip architectural intelligence and facilitate the cooperative tasks, such as the versatility to pass, share, communicate, liaise, and negotiate the information among the architectural components in a human way. The SSOFC operates in semantic and schematic spaces that are linked with a projection facilitated by cooperative agents. In the Semantic Space, the semantic proximity (semPro) through its first component context captures the real world semantics from the local heterogeneous sources. Meanwhile, in Structural Space, the schema correspondences are paramount in order to capture structural similarities in an algebraic or mathematical formalism for reasoning and manipulation on the computer.

An electrically tunable liquid-crystal-on-silicon (LCOS)-based pico projection system based on a liquid crystal lens adopting a liquid crystal and polymer composite film (LCPCF) is demonstrated. The LC lens consists of two built-in sub-lenses: one is an electrically tunable focusing lens controlled by a LC layer and the other is a fixed focused LCPCF lens. The electrically tunable focusing range of the pico projection system is 200 cm to ~7 cm when the voltage is from 0 to 35 V_rms. The image performance is also demonstrated. The related optical analysis is discussed. This study opens a new window for electrically tunable focusing pico projection system.

We consider a two-factor Heath–Jarrow–Morton (HJM) model under the risk neutral measure and show that it may be decoupled into a particular dynamic Nelson–Siegel (NS) model plus a somewhat counter-intuitive adjustment (lying outside the NS family) which keeps it arbitrage-free. We assess the importance of the adjustment for arbitrage-free pricing by comparing the HJM model with a novel NS model which is selected using projection techniques. We analyze forward curves and derivative prices generated by the HJM and projected NS model and consider two real-world case studies. Our analysis shows that the influence of the adjustment term on arbitrage-free evolution is small.

In this paper we investigate the set of correlated equilibria of bimatrix games. These equilibria are interesting, because they can result in outcome profiles that are not feasible as a result of Nash equilibria. After giving an example to illustrate the various concepts, we present a Projection Theorem which relates the two types of equilibria. Some lemmas are provided to clarify and extend this theorem.

In volume rendering, an important issue in acceleration is to reduce the calculations for occluded voxels. Although this issue has been addressed in the ray casting approach, it is difficult to apply the idea to the projection approach due to uncertain termination conditions. In this paper, we propose a new method to effectively address the exclusion problem in the projection approach, so the rendering process can be accelerated without impairing the rendered image quality. In the rendering process, this new method employs the dynamic screen technique to manage the pixels whose accumulated opacity has not reached 1.0. A ray-cast link at each pixel is set up to record the rendered voxels for the corresponding ray cast from the pixel to intersect. According to the rendered voxels covering the pixels whose accumulated opacity value is below 1.0, visible voxels are selected to render from front to back by the neighboring relationship between the rendered voxels and the voxels to be rendered. Thus, the occluded voxels are dynamically excluded from the loading and rendering processes accurately. Our proposed method can be in general applied to both parallel and perspective projections, using regular and irregular volume datasets. Our experimental results showed that the proposed method can significantly accelerate volume rendering if the data volume has a high percentage of occluded voxels. This method can also perform fairly efficiently for the expensive shading calculations if requested in volume rendering.

It is well known that the lattice of subspaces of a vector space over a field is modular. We investigate under which conditions this lattice is orthocomplemented with respect to the orthogonality operation. Using this operation, we define closed subspaces of a vector space and study the lattice of these subspaces. In particular, we investigate when this lattice is modular or orthocomplemented. Finally, we introduce splitting subspaces as special closed subspaces and we prove that the poset of splitting subspaces and the poset of projections are isomorphic orthomodular posets. The vector spaces under consideration are of arbitrary dimension and over arbitrary fields.