In this paper, we study and characterize some properties of a given binary operation on a lattice. More specifically, we show necessary and sufficient conditions under which a binary operation on a lattice coincides with its meet (resp. its join) operation. Importantly, we construct two new posets based on a given binary operation on a lattice and investigate some cases that these two posets have a lattice structure. Moreover, we provide some representations of a given lattice based on these new constructed lattices.
One crucial step in the construction of the human representation of the world is found at the boundary between two basic stimuli: visual experience and the sounds of language. In the developmental stage when the ability of recognizing objects consolidates, and that of segmenting streams of sounds into familiar chunks emerges, the mind gradually grasps the idea that utterances are related to the visible entities of the world. The model presented here is an attempt to reproduce this process, in its basic form, simulating the visual and auditory pathways, and a portion of the prefrontal cortex putatively responsible for more abstract representations of object classes. Simulations have been performed with the model, using a set of images of 100 real world objects seen from many different viewpoints and waveforms of labels of various classes of objects. Subsequently, categorization processes with and without language are also compared.
Elevated levels of eukaryotic initiation factor 4E (eIF4E) are implicated in neoplasia, with cumulative evidence pointing to its role in the etiopathogenesis of hematological diseases. As a node of convergence for several oncogenic signaling pathways, eIF4E has attracted a great deal of interest from biologists and clinicians whose efforts have been targeting this translation factor and its biological circuits in the battle against leukemia. The role of eIF4E in myeloid leukemia has been ascertained and drugs targeting its functions have found their place in clinical trials. Little is known, however, about the pertinence of eIF4E to the biology of lymphocytic leukemia and a paucity of literature is available in this regard that prospectively evaluates the topic to guide practice in hematological cancer. A comprehensive analysis on the significance of eIF4E translation factor in the clinical picture of leukemia arises, therefore, as a compelling need. This review presents aspects of eIF4E involvement in the realm of the lymphoblastic leukemia status; translational control of immunological function via eIF4E and the state-of-the-art in drugs will also be outlined., V. Venturi, T. Masek, M. Pospisek., and Obsahuje bibliografii
Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let $C_0(T) = \lbrace f\: T \rightarrow I$, $f$ is continuous and vanishes at infinity$\rbrace $ be endowed with the supremum norm. Starting with the Borel extension theorem for $X$-valued $\sigma $-additive Baire measures on $T$, an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map $u\: C_0(T) \rightarrow X$ to be weakly compact.
We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length are rank-one, as it was shown in [6] (Shue, Anderson, Dey 1998). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.
Let $G$ be a graph with vertex set $V(G)$, and let $k\ge 1$ be an integer. A subset $D \subseteq V(G)$ is called a {\it $k$-dominating set} if every vertex $v\in V(G)-D$ has at least $k$ neighbors in $D$. The $k$-domination number $\gamma _k(G)$ of $G$ is the minimum cardinality of a $k$-dominating set in $G$. If $G$ is a graph with minimum degree $\delta (G)\ge k+1$, then we prove that $$\gamma _{k+1}(G)\le \frac {|V(G)|+\gamma _k(G)}2.$$ In addition, we present a characterization of a special class of graphs attaining equality in this inequality.
Fuzzy transform is a new type of function transforms that has been successfully used in different applications. In this paper, we provide a broad prospective on fuzzy transform. Specifically, we show that fuzzy transform naturally appears when, in addition to measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location x, but also from the nearby locations.
A thioredoxin-like protein (txl) gene was cloned from the bumblebee, Bombus ignitus. The B. ignitus txl (Bitxl) gene spans 1777 bp and consists of three introns and four exons coding for 285 amino acid residues with a conserved active site (CGPC). The deduced amino acid sequence of the Bitxl cDNA was 65% similar to the Drosophila melanogaster txl. Northern blot analysis revealed the presence of Bitxl transcripts in all tissues examined. When H2O2 was injected into the body cavity of B. ignitus workers, Bitxl mRNA expression was up-regulated in the fat body tissue. In addition, the expression levels of Bitxl mRNA in the fat body greatly increased when B. ignitus workers were exposed to low (4°C) or high (37°C) temperatures, or injected with lipopolysaccharide (LPS), which suggests that the Bitxl possibly protects against oxidative stress caused by extreme temperatures and bacterial infection.