First, we consider a compact real-analytic irreducible subvariety M in a sphere and its dual variety M. We explain that two matrices of the second fundamental forms for both varieties M and M can be regarded as the inverse matrices of each other. Also generalization in hyperbolic space is explained.

We show that weak (Eulerian) solutions for the Semi-Geostrophic system in physical space exhibiting some mild regularity in time cannot yield point masses in dual space. However, such solutions are physically relevant to the model. Thus, we discuss a natural generalization of weak Lagrangian solutions in the physical space to include the possibility of singular measures in dual space. We prove ...

The complexity (quasi-metric) space was introduced in [23] to study complexity analysis of programs. Recently, it was introduced in [22] the dual complexity (quasi-metric) space, as a subspace of the function space [0,+∞)ω. Several quasi-metric properties of the complexity space were obtained via the analysis of its dual. We here show that the structure of a quasi-normed semilinear space provid...

In trying to improve upon Sims' art-by-choice technique known as "evolving expressions," artists have taken up the challenge of developing second generation implementations incorporating additional features, modifications, and controls. In this paper we provide a context for this movement, and present a model which both simplifies and refines the original technique. Technical considerations inc...

The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar cla...

the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

recent developments in the area of smart structures indicate that variable geometry / stiffness truss network is of fundamental importance in designing smart transformable structures and systems for space applications. this paper presents the conceptual design and dynamic modeling of a cooperative re-configurabel dual-arm robotic structure called dual-arm cam-lock manipulator. the manipulator i...

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.