Some Theorems on Piecewise Linear Embedding by v. K. A. M. Gugenheim

Combinatorial Embeddings of Manifolds

The following results on embedding manifolds resemble in their form Dehn's Lemma, the Sphere Theorem, and, especially, embedding theorems obtained for differentiable manifolds by A. Haefliger [i]. Let M, Q be finite combinatorial manifolds of dimensions m and q, respectively. Let M, Q be their boundaries (possibly empty), and let ƒ : M—>Q be a piecewise linear map. We define sing (ƒ) to be the ...

Close interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program

  The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We pro...

Piecewise Constant Controlled Linear Fuzzy Systems

Embedding normed linear spaces into $C(X)$

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

Image Steganalysis Based on Co-Occurrences of Integer Wavelet Coefficients

We present a steganalysis scheme for LSB matching steganography based on feature vectors extracted from integer wavelet transform (IWT). In integer wavelet decomposition of an image, the coefficients will be integer, so we can calculate co-occurrence matrix of them without rounding the coefficients. Before calculation of co-occurrence matrices, we clip some of the most significant bitplanes of ...