Galois Theory and Solvable Equations of Prime Degree

In this article we review classical and modern Galois theory with historical evolution and prove a criterion of Galois for solvability of an irreducible separable polynomial of prime degree over an arbitrary field k and give many illustrative examples.

Comparison of the degree of creativity in the design outcomes using different design methods

This work analyses the influence of several design methods on the degree of creativity of the design outcome. A design experiment has been carried out in which the participants were divided into four teams of three members, and each team was asked to work applying different design methods. The selected methods were Brainstorming, Functional Analysis, and SCAMPER method. The `degree of creativity' of each design outcome is assessed by means of a questionnaire offered to a number of experts and by means of three different metrics: the metric of Moss, the metric of Sarkar and Chakrabarti, and the evaluation of innovative potential. The three metrics share the property of measuring the creativity as a combination of the degree of novelty and the degree of usefulness. The results show that Brainstorming provides more creative outcomes than when no method is applied, while this is not proved for SCAMPER and Functional Analysis.

Influence of initial degree of saturation on swell pressures of compacted Barmer bentonite specimens

Densely compacted bentonite or bentonite-sand mixture has been identified as suitable buffer in deep geological repositories as its exceptionally high swelling capacity enables tight contact between the waste canister and surrounding rock. The degree of saturation of the compacted bentonite buffer can increase upon ingress of groundwater from the surrounding rock mass or decrease from evaporation due to high temperature (50-210 degrees C) derived from the waste canister. Available studies indicate that the influence of initial moisture content or degree of saturation on the swell pressure or swell potential of compacted bentonites is unclear. Some studies suggest that initial degree of saturation has an influence, while others suggest that it does not have bearing on the swell pressure of compacted bentonites. This paper examines the influence of initial degree of saturation in montmorillonite voids (termed,S-r,S-MF) on swell pressure of compacted Barmer bentonite-sand mixtures (dry density range: 1.4-2 Mg/m(3)) from micro-structural considerations. The experimental results bring out that, constant dry density specimens that developed similar number of hydration layers upon wetting developed comparable swell pressures and were unaffected by variations in initial S-r,S-MF values. Comparatively, constant dry density specimens that developed dis-similar number of hydration layers upon wetting established different swell pressures and were responsive to variations in initial S-r,S-MF. (C) 2015 Elsevier Ltd. All rights reserved.

SEPARATION DIMENSION OF BOUNDED DEGREE GRAPHS

The separation dimension of a graph G is the smallest natural number k for which the vertices of G can be embedded in R-k such that any pair of disjoint edges in G can be separated by a hyperplane normal to one of the axes. Equivalently, it is the smallest possible cardinality of a family F of total orders of the vertices of G such that for any two disjoint edges of G, there exists at least one total order in F in which all the vertices in one edge precede those in the other. In general, the maximum separation dimension of a graph on n vertices is Theta(log n). In this article, we focus on bounded degree graphs and show that the separation dimension of a graph with maximum degree d is at most 2(9) (log*d)d. We also demonstrate that the above bound is nearly tight by showing that, for every d, almost all d-regular graphs have separation dimension at least d/2]

Lower Bounds for Sums of Powers of Low Degree Univariates

We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degree polynomials. We prove a lower bound of Omega(root d/t) for writing an explicit univariate degree-d polynomial f(x) as a sum of powers of degree-t polynomials.

Recolonisation of temporary streams and evolution of a degree of stability of the zoocenose [Translation from: Ecologia Mediterranea No.1 149-164, 1976]

When flow returns to a temporary stream a certain number of plant and animal species establish themselves more or less rapidly on the stream-bed constituting the initial phase of evolution of the re-population. This phase is essentially characterised by the ”awakening” of animal species that passed the dry season in a dormant state and by the development of the first unicellular algae that constitute the periphyton. Then they are succeeded by more or less stable animal groups and the structural complexity increases. The authors of the present study aim to analyse the dynamics of community succession from the return of water to the biotope until its drying up. It is attempted to determine the influence of the duration of flow on this evolution. This work is based on the analysis of population diversity with reference to its two complementary aspects, species richness and equitability. The River Destel which was studied for this project is situated in the Gorge of Ollioules near the town of Toulon.

Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation

It is shown that stochastic electromagnetic beams may have different degrees of polarization on propagation, even though they have the same coherence properties in the source plane. This fact is due to a possible difference in the anisotropy of the field in the source plane. The result is illustrated by some examples.

A study of the degree of relaxation of AlGaN epilayers on GaN template

The strain state of 570nm AlXGa1-xN layers grown on 600nm GaN template by metal organic chemical vapor deposition was studied using Rutherford backscattering (RBS)/channeling and triple-axis X-ray diffraction measurements. The results showed that the degree of relaxation (R) of AlxGa1-xN layers increased almost linearly when x less than or equal to 0.42 and reached to 70% when x = 0.42. Above 0.42, the value of R varied slowly and AI(x)Ga(1-x)N layers almost full relaxed when x = 1 (AIN). In this work the underlying GaN layer was in compressive strain, which resulted in the reduction of lattice misfit between GaN and AlxGa1-xN, and a 570nm AlxGa1-xN layer with the composition of about 0.16 might be grown on GaN coherently from the extrapolation. The different shape of (0004) diffraction peak was discussed to be related to the relaxation. (C) 2004 Elsevier B.V. All rights reserved.

Geometry property of multi-degree of freedom neurons

In this paper, we study a problem of geometric inequalities for a Multi-degree of Freedom Neurons. Some new geometric inequalities for a Multi-degree of Freedom Neurons are established. As special cases, some known inequalities are deduced.

SYNTHESIS AND CHARACTERIZATION OF A CROSSLINKING POLYETHYLENIMINE AS SMART GENE CARRIER AND EFFECTS OF PEGYLATION DEGREE

A smart biodegradable cationic polymer (CBA-PEI) based on the disulfide bond-containing cross-linker cystamine bisacrylamide (CBA) and low molecular weight branched polyethylenimine (1800-Da, PEI1800) was successfully synthesized by Michael addition reaction in our recent study. Furthermore, a series of copolymers (CBA-PEI-PEG) with different PEGylation degree were obtained by the mPEG-SPA (5000-Da) reacting with CBA-PEI at various weight ratios directly. The molecular structures of the resulting polymers CBA-PEI and CBA-PEI-PEG were evaluated by nuclear magnetic resonance spectroscopy (H-1-NMR) and capillary viscosity measurements, all of which had successfully verified formation of the copolymers. The polymer/DNA complexes based on CBA-PEI and CBA-PEI-PEG were measured by dynamic light scattering and gel retardation assay. The results showed that the particle size and zeta potential of complexes were reduced with increasing amount of PEG grafting, even no particle formation. The particle size of CBA-PEI/DNA complexes was in range of 103.1 to 129.1 nm, and the zeta potential was in range of 14.2 to 24.3 mV above the 2:1 weight ratio. In the same measure condition, the particle size of CBA-PEI-PEG complexes was reduced to a range of 32.2 to 55 nm, and the zeta potential was in range of 9.3 to 13.8 mV at the 2:1 weight ratio.