Definition 19. A generalized complex structure (GCS) on E is an integrable orthogonal complex structure J : E E, i.e. a map s.t. → • �JA, JB� = �A,B� • L = Ker (J − i1) Note. 1. �JA,B� = �JA, JB� = −�A, JB�, and thus �J·, ·� is a symplectic struction on E compatible with �, �. 2. L is maximal isotropic and so is L, and thus E = L ⊕ L = L ⊕ L∗ and we get a Lie bialgebroid. 3. V must be even dime...

Thermodynamic Constraints Finite set of thermodynamic conditions We show that, if the Wegscheider conditions are satisfied forM2 = M0 −M1 basis vectors {b(i), i = 1, 2, . . . ,M2} of the null space of S0, whereM0 is the total number of (reversible) reactions in a closed biochemical reaction system with stoichiometry matrix S0 and M1 = rank(S0), then they will also be satisfied for all b ∈ null(...

background: hla-g gene contains 15 alleles including a null allele, hla-g*0105n. previous studies have shown that hla-g*0105n does not encode the complete hla-g1 or hla-g5 isoforms but encodes a functional hla-g protein with the ability to in-hibit nk cell cytolysis. thus, although the biological functions of hla-g1 and hla-g5 proteins are abrogated, other isoforms such as hla-g2 can replace th...

We have seen so far two types of statistical estimation frameworks: confidence intervals and point estimation. Hypothesis testing is a third inference framework that is concerned with choosing a hypothesis supported by available data out of a number of competing alternatives. We start with the basic definitions and then proceed to describe a few important cases. We assume that we have data X1, ...

Background: The glutathione S-transferase (GST) family of metabolising enzymes plays an important role in the detoxification of mutagens and carcinogens. The expression of many of these cancer susceptibility enzymes is genetically polymorphic. An increased frequency of GST-null genotypes has been associated with several malignancies. Objective: To investigate the rate of GSTT1 and GSTM1 null ge...

The false discovery rate (FDR) has been discussed extensively and it has been pointed out that the distribution of the null p-values must be “correct” or conservative for FDR estimation or any other standard statistical significance measure to behave properly. What is meant for distribution of the null p-values to be correct is that they are Uniformly distributed in the interval (0,1). The null...

I show that the definition of angular momentum at null infinity given by A. Rizzi, Phys. Rev. Lett. 81, 1150 ~1998!, reduces to the Arnowitt-Deser-Misner definition at spatial infinity in the appropriate limit. This identification reinforces the gauge condition of the null definition as well as the null definition itself. Insight into the place of the null and spatial definitions is also gained...

Let F*(K) be the set of all fuzzy complex numbers. In this paper some classical and measure-theoretical notions are extended to the case of complex fuzzy sets. They are fuzzy complex number-valued distance on F*(K), fuzzy complex number-valued measure on F*(K), and some related notions, such as null-additivity, pseudo-null-additivity, null-subtraction, pseudo-null-subtraction, autocontionuous f...