In this paper, we consider some properties of the family of indefinite binary quadratic forms and elliptic curves. In the first section, we give some preliminaries from binary quadratic forms and elliptic curves. In the second section, we define a special family of indefinite forms Fi and then we obtain some properties of these forms. In the third section, we consider the number of rational poi...

In this article, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond matroid rank functions . This is a versatile valuation class with several desirable properties (such as monotonicity submodularity), which naturally lends itself number real-world domains. We use these our advantage; first, show that when agent valuations are ...

AbstractOur goal is to allocate items maximize efficiency while ensuring fairness. Since Envy-freeness may not always exist, we consider the relaxed notion, up one item (EF1) that guaranteed exist. We add further constraint of maximizing efficiency, utilitarian social welfare (USW) among fair allocations. In general, finding USW allocations EF1, i.e., EEF1, an NP-Hard problem even for additive ...

We consider the fair division problem of indivisible items. It is well-known that an envy-free allocation may not exist, and a relaxed version envy-freeness, envy-freeness up to one item (EF1), has been widely considered. In EF1 allocation, agent envy others' allocated shares, but only item. many applications, we wish specify subset prioritized agents where strict needs be guaranteed from these...

Despite the agricultural importance of species in the Grapholitini (Lepidoptera: Tortricidae), and the value of gene expression analysis for improved population management, few gene expression studies based on quantitative real-time PCR (qPCR) have been conducted for this tribe. Part of the reason for this lack of information is that suitable reference genes, which are fundamental for accurate ...

Reverse transcription quantitative polymerase chain reaction (qRT-PCR) has rapidly become the most sensitive and accurate method for the quantification of gene expression. To facilitate gene expression studies and obtain more accurate qRT-PCR data, normalization relative to stable housekeeping genes is required. These housekeeping genes need to show stable expression under the given experimenta...

Whereas most traditional classifications identify Ischnocera as a major suborder of lice in the order Phthiraptera, a recent molecular study based on one gene did not recover monophyly of Ischnocera. In this study we test the monophyly of Ischnocera using sequences of portions of three different genes: two nuclear (EF1 alpha and 18S) and one mitochondrial (COI). Analysis of EF1 alpha and COI se...

Human hematopoietic stem cells (hHSCs) have enormous potential for clinical use in cell-based therapies, especially as a gene delivery system. Moreover, lentiviral transduction in stem cells is very often associated with low transduction efficiency and low levels of foreign gene expression. Therefore, it is important to analyze vector and promoter systems that can generate robust foreign gene e...

To accurately assess gene expression levels, it is essential to normalize real-time quantitative PCR (RT-qPCR) data with suitable internal reference genes. For the red imported fire ant, Solenopsis invicta, reliable reference genes to assess the transcript expression levels of the target genes have not been previously investigated. In this study, we examined the expression levels of five candid...

Molecular phylogenetic analyses have recently shown that the unicellular amoeboid protist Capsaspora owczarzaki is unlikely to be a nucleariid or an ichthyosporean as previously described, but is more closely related to Metazoa, Choanoflagellata, and Ichthyosporea. However, the specific phylogenetic relationship of Capsaspora to other protist opisthokont lineages was poorly resolved. To test th...