Chiral mirror and optical resonator designs for circularly polarized light: suppression of cross-polarized reflectances and transmittances

A left-handed chiral sculptured thin film (STF) that reflects strongly at the wavelength of the circular Bragg resonance tends to partially convert the handedness of incident LCP (left-circularly-polarized) light to RCP (right-circularly-polarized). We show that the cross-polarized component of the reflected RCP beam can be eliminated by interference with an additional RCP beam that is reflected at the interface of an isotropic cover and an AR (antireflecting) layer. For best results the refractive index and thickness of the AR layer need to accommodate a phase change on reflection that occurs at the chiral film. Effective suppression of the reflectances R_RR, R_RL, R_LR and the transmittances T_RL, T_LR can be achieved by sandwiching the chiral reflector between such amplitude and phase-matched AR coatings. Co-polarized chiral reflectors of this type may form efficient handed optical resonators. For LCP light the optical properties of such a handed resonator are formally the same as the properties of the isotropic passive or active Fabry–Perot resonators, but the handed resonator is transparent to RCP light.     

Statistical limit theorems for suspension flows

In dynamical systems theory, a standard method for passing from discrete time to continuous time is to construct the suspension flow under a roof function. In this paper, we give conditions under which statistical laws, such as the central limit theorem and almost sure invariance principle, for the underlying discrete time system are inherited by the suspension flow. As a consequence, we give a simpler proof of the results of Ratner (1973) and recover the results of Denker and Philipp (1984) for Axiom A flows. Morcover, we obtain several new results for nonuniformly and partially hyperbolic flows, including frame flows on negatively curved manifolds satisfying a pinching condition.     

Formation of Sim and SimCn clusters by C60 sputtering of Si

The secondary ion mass spectrum of silicon sputtered by high energy C₆₀⁺ ions in sputter equilibrium is found to be dominated by Si clusters and we report the relative yields of Si_m⁺ (1 ≤ m ≤ 15) and various Si_mC_n⁺ clusters (1 ≤ m ≤ 11 for n = 1; 1 ≤ m ≤ 6 for n = 2; 1 ≤ m ≤ 4 for n = 3). The yields of Si_m⁺ clusters up to Si₇⁺ are significant (between 0.1 and 0.6 of the Si⁺ yield) with even numbered clusters Si₄⁺ and Si₆⁺ having the highest probability of formation. The abundances of cluster ions between Si₈⁺ and Si₁₁⁺ are still significant (>1% relative to Si⁺) but drop by a factor of ∼100 between Si₁₁⁺ and Si₁₃⁺. The probability of formation of clusters Si₁₃⁺-Si₁₅⁺ is approximately constant at ∼5 × 10⁻⁴ relative to Si⁺ and rising a little for Si₁₅⁺, but clusters beyond Si₁₅ are not detected (Si_m≥16⁺/Si⁺ < 1 × 10⁻⁴). The probability of formation of Si_m⁺ and Si_mC_n⁺ clusters depends only very weakly on the C₆₀⁺ primary ion energy between 13.5 keV and 37.5 keV. The behaviour of Si_m⁺ and Si_mC_n⁺ cluster ions was also investigated for impacts onto a fresh Si surface to study the effects that saturation of the surface with C₆₀⁺ in reaching sputter equilibrium may have had on the measured abundances. By comparison, there are very minor amounts of pure Si_m⁺ clusters produced during C₆₀⁺ sputtering of silica (SiO₂) and various silicate minerals. The abundances for clusters heavier than Si₂⁺ are very small compared to the case where Si is the target.The data reported here suggest that Si_m⁺ and Si_mC_n⁺ cluster abundances may be consistent in a qualitative way with theoretical modelling by others which predicts each carbon atom to bind with 3-4 Si atoms in the sample. This experimental data may now be used to improve theoretical modelling.     

Synthetic methods for polyamine linkers and their application to combinatorial chemistry

Summary Polyamines and polyamine conjugates display a diverse range of important biological functions, ranging from antibiotics to immunosuppressants and glutamate receptor antagonists. For these reasons, polyamines provide an excellent template/scaffold for combinatorial chemistry. In this paper we present methods for the solid-phase immobilisation of polyamines for use in synthetic and combinatorial chemistry and describe how they have been employed in the preparation of a number of important polyamine conjugates and polyamine libraries. Thus, we have designed, synthesised and utilised a number of polyamine linkers for both solution and resin screening combinatorial application.     

On Subordination Chains with Normalization Given by a Time-dependent Linear Operator

In this paper we are concerned with solutions, in particular with univalent solutions, of the Loewner differential equation associated with non-normalized subordination chains on the Euclidean unit ball B ⁿ in \mathbbCⁿ{\mathbb{C}^n}. The main result is a generalization to higher dimensions of a well known result due to Becker. Various particular cases of this result have been recently obtained for subordination chains with normalization Df(0,t)=e^tI_n{Df(0,t)=e^tI_n} or Df(0, t) = e ^tA , t ≥ 0, where A ? L(\mathbbCⁿ,\mathbbCⁿ){A\in L(\mathbb{C}^n,\mathbb{C}^n)}. We also determine the form of the standard solutions to the Loewner differential equation associated with generalized spirallike mappings. In the last section we obtain the form of the solution in the presence of coefficient bounds.     

Periodic solution of a higher dimensional ecological system

The main purpose of this article is to study the periodicity of a Lotka-Volterra''s competition system with feedback controls. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions. Our method is base on combining matrix''s spectral theory and inequality $|x(t)|\leq x(t_{0})+\int_{0}^{\omega }|\dot{x}(t)|{\rm d}t$. Some examples and their simulations show the feasibility of our main result.     

Student Perceptions of a Summer Ventures in Science and Mathematics Camp Experience

“As the world becomes increasingly technological, the value of (the ideas and skills of its population) will be determined in no small measure by the effectiveness of science, technology, engineering, and mathematics (STEM) education in the United States” and “STEM education will determine whether the United States will remain a leader among nations and whether we will be able to solve immense challenges in such areas as energy, health, environmental protection, and national security” (President's Council of Advisors on Science and Technology, 2010, p. vii). Research on the effectiveness of STEM‐focused school and other learning experiences (e.g., short‐term camps) on student attitudes and performance outcomes is sparse. In this study, we documented the influence of an intensive STEM summer program on high school students’ attitudes toward STEM concepts and interests in STEM careers. Attending the summer program was associated with gains on students’ attitudes toward some aspects of STEM as well as specific career interests. Notably, students reported statistically significant views of important aspects of STEM and their attitudes toward science and mathematics were more positive than their attitudes about engineering and technology.     

On K‐Theory of Simplicial Rings and Degreewise Constructions

We give a measure of the difference between Waldhausen's definition of the Ktheory of a simplicial ring and the definition we obtain by extending Quillen's definition degreewise. This has computational advantages as the degreewise Ktheory sometimes is simpler to work with.     

Raman Spectroscopic Study of the Molybdate Mineral Szenicsite and Comparison with Other Paragenetically Related Molybdate Minerals

Abstract

The molybdate‐bearing mineral szenicsite, Cu₃(MoO₄)(OH)₄, has been studied by Raman and infrared spectroscopy. A comparison of the Raman spectra is made with those of the closely related molybdate‐bearing minerals, wulfenite, powellite, lindgrenite, and iriginite, which show common paragenesis. The Raman spectrum of szenicsite displays an intense, sharp band at 898 cm^?1, attributed to the ν₁ symmetric stretching vibration of the MoO₄ units. The position of this particular band may be compared with the values of 871 cm^?1 for wulfenite and scheelite and 879 cm^?1 for powellite. Two Raman bands are observed at 827 and 801 cm^?1 for szenicsite, which are assigned to the ν₃(E _g ) vibrational mode of the molybdate anion. The two MO₄ ν₂ modes are observed at 349 (B _g ) and 308 cm^?1 (A _g ). The Raman band at 408 cm^?1 for szenicsite is assigned to the ν₄(E _g ) band. The Raman spectra are assigned according to a factor group analysis and are related to the structure of the minerals. The various minerals mentioned have characteristically different Raman spectra.