Given a 3-uniform hypergraph H consisting of set V vertices, and T?V3 triples, null labelling is an assignment ±1 to the triples such that each vertex contained in equal number labelled +1 ?1. Thus, signed degree zero. A necessary condition for every even. The Null Labelling Problem determine whether has labelling. It proved this problem NP-complete. Computer enumerations suggest most hypergrap...

We analyze a popular probabilistic model for generating instances of Satissability. According to this model, each literal of a set L = fv 1 ; v r g of literals appears independently in each of n clauses with probability p. This model allows null clauses and the frequency of occurrence of such clauses depends on the relationship between the parameters n, r, and p. If an instance contains a null ...

A subset X of a Polish group G is called Haar null if there exists a Borel set B ⊃ X and Borel probability measure μ on G such that μ(gBh) = 0 for every g, h ∈ G. We prove that there exist a set X ⊂ R that is not Lebesgue null and a Borel probability measure μ such that μ(X + t) = 0 for every t ∈ R. This answers a question from David Fremlin’s problem list by showing that one cannot simplify th...

A subset X of a Polish group G is called Haar null if there exists a Borel set B ⊃ X and Borel probability measure μ on G such that μ(gBh) = 0 for every g, h ∈ G. We prove that there exist a set X ⊂ R that is not Lebesgue null and a Borel probability measure μ such that μ(X + t) = 0 for every t ∈ R. This answers a question from David Fremlin’s problem list by showing that one cannot simplify th...

Glutathione S-transferases (GSTs; EC: 2.5.1.18) are a ubiquitous family of eukaryotic and prokaryotic phase II metabolic isozymes. Genes encoding GSTM1 (OMIM: 138350), and GSTT1 (OMIM: 600436) are members of class mu and theta, respectively. The most common polymorphism in the GSTM1 is a deletion of the whole GSTM1 gene with a lack of enzyme activity. A homozygous deletion in the GSTT1 has also...

Context: Null-checking conditionals are a straightforward solution against null dereferences. However, their frequent repetition is considered a sign of poor program design, since they introduce source code duplication and complexity that impacts code comprehension and maintenance. The Null Object design pattern enables the replacement of null-checking conditionals with polymorphic method invoc...

in this paper, a new method was proposed for the navigation of a mobile robot in an unknown dynamic environment. the robot could detect only a limited radius of its surrounding with its sensors and it went on the shortest null space (sns) toward the goal. in the case of no obstacle, sns was a direct path from the robot to goal; however, in the presence of obstacles, sns was a space around the r...

For any h ∈ N, a graph G = (V, E) is said to be h-magic if there exists a labeling l : E(G) → Zh − {0} such that the induced vertex labeling l : V (G) → Zh defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h ∈ N for which G admits a zero-sum h-magic labeling. A graph G is said to b...

Studies of genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. However, with the presence of null alleles, an observed genotype can represent one of several possible true genotypes. This results in biased estimates of relatedness. As the numbers of marker loci are often limited, loci with null alleles cannot be abandoned without substantial los...