On Double Basic Algebras and Pseudo-effect Algebras

Double basic algebras are a counterpart of bounded lattices with order-antiautomorphisms on principal filters. In the paper, an independent axiomatization of double basic algebras is given and lattice pseudo-effect algebras are characterized in the setting of double basic algebras.     

Optimization of Streptomyces bacteriophage ��C31 integrase system to prevent post integrative gene silencing in pulmonary type II cells

φC31 integrase has emerged as a potent tool for achieving long-term gene expression in different tissues. The present study aimed at optimizing elements of φC31 integrase system for alveolar type II cells. Luciferase and β-galactosidase activities were measured at different time points post transfection. 5-Aza-2''deoxycytidine (AZA) and trichostatin A (TSA) were used to inhibit DNA methyltransferase and histone deacetylase complex (HDAC) respectively. In A549 cells, expression of the integrase using a CMV promoter resulted in highest integrase activity, whereas in MLE12 cells, both CAG and CMV promoter were equally effective. Effect of polyA site was observed only in A549 cells, where replacement of SV40 polyA by bovine growth hormone (BGH) polyA site resulted in an enhancement of integrase activity. Addition of a C-terminal SV40 nuclear localization signal (NLS) did not result in any significant increase in integrase activity. Long-term expression studies with AZA and TSA, provided evidence for post-integrative gene silencing. In MLE12 cells, both DNA methylases and HDACs played a significant role in silencing, whereas in A549 cells, it could be attributed majorly to HDAC activity. Donor plasmids comprising cellular promoters ubiquitin B (UBB), ubiquitin C (UCC) and elongation factor 1α (EF1α) in an improved backbone prevented post-integrative gene silencing. In contrast to A549 and MLE12 cells, no silencing could be observed in human bronchial epithelial cells, BEAS-2B. Donor plasmid coding for murine erythropoietin under the EF1α promoter when combined with φC31 integrase resulted in higher long-term erythropoietin expression and subsequently higher hematocrit levels in mice after intravenous delivery to the lungs. These results provide evidence for cell specific post integrative gene silencing with φC31 integrase and demonstrate the pivotal role of donor plasmid in long-term expression attained with this system.     

Analogues to Fermat primes related to Pell��s equation

The coefficients of some weight 3 modular forms give reason to study primes of the form p = 2x ² ? 1 = 2dy ² + 1. If x _a , y _a are the positive solutions of Pell??s equation x ² ? dy ² = 1, given by ${x_a + y_a \sqrt{d} = (x_1 + y_1 \sqrt{d})^a}The coefficients of some weight 3 modular forms give reason to study primes of the form p = 2x ² − 1 = 2dy ² + 1. If x _a , y _a are the positive solutions of Pell’s equation x ² − dy ² = 1, given by x_a + y_a ?d = (x₁ + y₁ ?d)^a{x_a + y_a \sqrt{d} = (x_1 + y_1 \sqrt{d})^a}, and if p_a = 2 x_a² - 1{p_a = 2 x_a^2 - 1} is prime, then a = 2 ^m is a power of 2. So there are analogues to the Fermat numbers 2 ^a + 1.     

Permeability of Pore Networks Under Compaction

The characteristic pore length fixes the scale of permeability of a porous medium. For pore networks undergoing strong random compaction, this length becomes singular at transition porosities, revealing a change in the microstructure of the porespace controlling the transport. Nodal balances and lattice Boltzmann simulations of flow in pore networks under compaction show that the scaling between permeability and porosity changes near the transition porosities. Simulation results are compared with experimental permeability data from transparent two-dimensional micromodels of networks decorated with the same pore size distribution. Permeability?Cporosity data of media undergoing smooth compaction is well described by a single power law. Under strong compaction, however, the scaling between permeability and porosity is possible by traits only, the scaling exponent changes notably at given transition porosities. These behaviors are common to a wealth of permeability?Cporosity data thus far unexplained.     

Codimension and pseudometric in co-Heyting algebras

In this paper, we introduce a notion of dimension and codimension for every element of a bounded distributive lattice L. These notions prove to have a good behavior when L is a co-Heyting algebra. In this case the codimension gives rise to a pseudometric on L which satisfies the ultrametric triangle inequality. We prove that the Hausdorff completion of L with respect to this pseudometric is precisely the projective limit of all its finite dimensional quotients. This completion has some familiar metric properties, such as the convergence of every monotonic sequence in a compact subset. It coincides with the profinite completion of L if and only if it is compact or equivalently if every finite dimensional quotient of L is finite. In this case we say that L is precompact. If L is precompact and Hausdorff, it inherits many of the remarkable properties of its completion, specially those regarding the join/meet irreducible elements. Since every finitely presented co-Heyting algebra is precompact Hausdorff, all the results we prove on the algebraic structure of the latter apply in particular to the former. As an application, we obtain the existence for every positive integers n, d of a term t _{n, d} such that in every co-Heyting algebra generated by an n-tuple a, t _{n, d} (a) is precisely the maximal element of codimension d.     

A p-nilpotency criterion

Let G be a finite group, p a fixed prime and P a Sylow p-subgroup of G. In this short note we prove that if p is odd, then G is p-nilpotent if and only if P controls fusion of cyclic groups of order p. For the case p = 2, we show that G is p-nilpotent if and only if P controls fusion of cyclic groups of order 2 and 4.     

Biomimetic surface preparation of inert polymer films via grafting long monoalkyl chain phosphatidylcholine

To explore construction of novel mimicking biomembrane on biomaterials surfaces,a new polymerizable phosphatidylcholine containing a long monoalkyl chain ended with acryl group(AASOPC) was designed and synthesized, which was easily derived from the terminal amino group of 9-(2-amino-ethylcarbamoyl)-nonyl-1-phosphatidyl-choline (ASOPC) reacting with acryloyl chloride.The obtained AASOPC was grafted on poly(ethylene terephthalate)(PET) via surface-initiated atom-transfer radical polymerization(SI-ATRP) to form mimicking biomembrane.These modified surface structures of PET were investigated using water contact angle(WAC),X-ray photoelectron spectroscopy(XPS) and atomic force microscopy(AFM).The results indicated that the new mimicking phosphatidylcholine biomembrane could be prepared on inert polymer surfaces by using the acryloyl phosphatidylcholine(AASOPC) via surface-initiated atom transfer radical polymerization(SI-ATRP).